From df5cff82946e84e8ddb6807f1b689d7b5f2ff0d4 Mon Sep 17 00:00:00 2001 From: Samir Chowdhury Date: Fri, 17 Dec 2021 08:18:51 -0700 Subject: [PATCH] uploaded new files and refreshed directory --- code/dimReducMethods/L2_distance.m | 73 - code/dimReducMethods/backprop.m | 86 - code/dimReducMethods/backprop_gradient.m | 79 - code/dimReducMethods/cca.m | 413 --- code/dimReducMethods/cfa.m | 189 -- code/dimReducMethods/cg_update.m | 102 - code/dimReducMethods/charting.m | 85 - code/dimReducMethods/checkgrad.m | 52 - code/dimReducMethods/combn.m | 104 - code/dimReducMethods/components.m | 46 - code/dimReducMethods/compute_mapping.m | 422 --- code/dimReducMethods/compute_recon_err.m | 54 - code/dimReducMethods/computegr.c | 124 - code/dimReducMethods/computegr.dll | Bin 7168 -> 0 bytes code/dimReducMethods/computegr.mexa64 | Bin 9340 -> 0 bytes code/dimReducMethods/computegr.mexglx | Bin 6588 -> 0 bytes code/dimReducMethods/computegr.mexmaci | Bin 12784 -> 0 bytes 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code/tools/turbo.m/license.txt delete mode 100755 code/tools/turbo.m/turbo.m delete mode 100755 code/tools/writeNPY.m delete mode 100755 code/tools/writemyfile.m delete mode 100755 code/tools/writemyfilevar.m diff --git a/code/dimReducMethods/L2_distance.m b/code/dimReducMethods/L2_distance.m deleted file mode 100644 index d14eb76..0000000 --- a/code/dimReducMethods/L2_distance.m +++ /dev/null @@ -1,73 +0,0 @@ -function d = L2_distance(a, b) -% L2_DISTANCE - computes Euclidean distance matrix -% -% E = L2_distance(A,B) -% -% A - (DxM) matrix -% B - (DxN) matrix -% -% Returns: -% E - (MxN) Euclidean distances between vectors in A and B -% -% -% Description : -% This fully vectorized (VERY FAST!) m-file computes the -% Euclidean distance between two vectors by: -% -% ||A-B|| = sqrt ( ||A||^2 + ||B||^2 - 2*A.B ) -% -% Example : -% A = rand(400,100); B = rand(400,200); -% d = distance(A,B); - -% Author : Roland Bunschoten -% University of Amsterdam -% Intelligent Autonomous Systems (IAS) group -% Kruislaan 403 1098 SJ Amsterdam -% tel.(+31)20-5257524 -% bunschot@wins.uva.nl -% Last Rev : Wed Oct 20 08:58:08 MET DST 1999 -% Tested : PC Matlab v5.2 and Solaris Matlab v5.3 - -% Copyright notice: You are free to modify, extend and distribute -% this code granted that the author of the original code is -% mentioned as the original author of the code. - -% Fixed by JBT (3/18/00) to work for 1-dimensional vectors -% and to warn for imaginary numbers. Also ensures that -% output is all real, and allows the option of forcing diagonals to -% be zero. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if nargin < 2 - error('Not enough input arguments'); - end - if size(a, 1) ~= size(b, 1) - error('A and B should be of same dimensionality'); - end - if ~isreal(a) || ~isreal(b) - warning('Computing distance table using imaginary inputs. Results may be off.'); - end - - % Padd zeros if necessray - if size(a, 1) == 1 - a = [a; zeros(1, size(a, 2))]; - b = [b; zeros(1, size(b, 2))]; - end - - % Compute distance table - d = sqrt(bsxfun(@plus, sum(a .* a)', bsxfun(@minus, sum(b .* b), 2 * a' * b))); - - % Make sure result is real - d = real(d); - diff --git a/code/dimReducMethods/backprop.m b/code/dimReducMethods/backprop.m deleted file mode 100644 index 4c486b2..0000000 --- a/code/dimReducMethods/backprop.m +++ /dev/null @@ -1,86 +0,0 @@ -function network = backprop(network, X, T, max_iter, noise, lambda) -%BACKPROP Trains a network on a dataset using backpropagation -% -% network = backprop(network, X, T, max_iter, noise, lambda) -% -% The function trains the specified network using backpropagation on -% dataset X with targets T for max_iter iterations. The dataset X is an NxD -% matrix, whereas the targets matrix T has size NxM. The function returns -% the trained network in network. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - - if ~exist('max_iter', 'var') || isempty(max_iter) - max_iter = 10; - end - if ~exist('noise', 'var') || isempty(noise) - noise = 0; - end - if ~exist('lambda', 'var') || isempty(lambda) - lambda = 0; - end - - % Initialize some variables - n = size(X, 1); - no_layers = length(network); - batch_size = max(round(n / 100), 100); - - % Perform the backpropagation - for iter=1:max_iter - disp([' - iteration ' num2str(iter) ' of ' num2str(max_iter) '...']); - - % Loop over all batches - index = randperm(n); - for batch=1:batch_size:n - - % Select current batch - tmpX = X(index(batch:min([batch + batch_size - 1 n])),:); - tmpT = T(index(batch:min([batch + batch_size - 1 n])),:); - - % Randomly black out some of the input data - if noise > 0 - tmpX(rand(size(tmpX)) < noise) = 0; - end - - % Convert the weights and store them in the network - v = []; - for i=1:length(network) - v = [v; network{i}.W(:); network{i}.bias_upW(:)]; - end - - % Conjugate gradient minimization using 3 linesearches -% checkgrad('backprop_gradient', v, 1e-5, network, tmpX, tmpT) - [v, fX] = minimize(v, 'backprop_gradient', 3, network, tmpX, tmpT, lambda); - - % Deconvert the weights and store them in the network - ind = 1; - for i=1:no_layers - network{i}.W = reshape(v(ind:ind - 1 + numel(network{i}.W)), size(network{i}.W)); ind = ind + numel(network{i}.W); - network{i}.bias_upW = reshape(v(ind:ind - 1 + numel(network{i}.bias_upW)), size(network{i}.bias_upW)); ind = ind + numel(network{i}.bias_upW); - end - - % Stop upon convergence - if isempty(fX) - reconX = run_data_through_autoenc(network, X); - C = sum((T(:) - reconX(:)) .^ 2) ./ n; - disp([' - final noisy MSE: ' num2str(C)]); - return - end - end - - % Estimate the current error - reconX = run_data_through_autoenc(network, X); - C = sum((T(:) - reconX(:)) .^ 2) ./ n; - disp([' - current noisy MSE: ' num2str(C)]); - end - \ No newline at end of file diff --git a/code/dimReducMethods/backprop_gradient.m b/code/dimReducMethods/backprop_gradient.m deleted file mode 100644 index 965c72e..0000000 --- a/code/dimReducMethods/backprop_gradient.m +++ /dev/null @@ -1,79 +0,0 @@ -function [C, dC] = backprop_gradient(v, network, X, targets, lambda) -%BACKPROP Compute the cost gradient for CG optimization of a neural network -% -% [C, dC] = backprop_gradient(v, network, X, targets, lambda) -% -% Compute the value of the cost function, as well as the corresponding -% gradient for conjugate-gradient optimization of a neural network. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Initialize some variables - n = size(X, 1); - no_layers = length(network); - middle_layer = ceil(no_layers / 2); - - % Deconvert the weights and store them in the network - ind = 1; - for i=1:no_layers - network{i}.W = reshape(v(ind:ind - 1 + numel(network{i}.W)), size(network{i}.W)); ind = ind + numel(network{i}.W); - network{i}.bias_upW = reshape(v(ind:ind - 1 + numel(network{i}.bias_upW)), size(network{i}.bias_upW)); ind = ind + numel(network{i}.bias_upW); - end - - % Run the data through the network - activations = cell(1, no_layers + 1); - activations{1} = [X ones(n, 1)]; - for i=1:no_layers - if i ~= middle_layer && i ~= no_layers - activations{i + 1} = [1 ./ (1 + exp(-(activations{i} * [network{i}.W; network{i}.bias_upW]))) ones(n, 1)]; - else - activations{i + 1} = [activations{i} * [network{i}.W; network{i}.bias_upW] ones(n, 1)]; - end - end - - % Compute value of cost function (= MSE) - C = (1 / (2 * n)) .* sum(sum((activations{end}(:,1:end - 1) - targets) .^ 2)) + lambda .* sum(v .^ 2); - - % Only compute gradient if requested - if nargout > 1 - - % Compute gradients - dW = cell(1, no_layers); - db = cell(1, no_layers); - Ix = (activations{end}(:,1:end - 1) - targets) ./ n; - for i=no_layers:-1:1 - - % Compute update - delta = activations{i}' * Ix; - dW{i} = delta(1:end - 1,:); - db{i} = delta(end,:); - - % Backpropagate error - if i > 1 - if i ~= middle_layer + 1 - Ix = (Ix * [network{i}.W; network{i}.bias_upW]') .* activations{i} .* (1 - activations{i}); - else - Ix = Ix * [network{i}.W; network{i}.bias_upW]'; - end - Ix = Ix(:,1:end - 1); - end - end - - % Convert gradient information - dC = zeros(numel(v), 1); - ind = 1; - for i=1:no_layers - dC(ind:ind - 1 + numel(dW{i})) = dW{i}(:); ind = ind + numel(dW{i}); - dC(ind:ind - 1 + numel(db{i})) = db{i}(:); ind = ind + numel(db{i}); - end - dC = dC + 2 .* lambda .* v; - end diff --git a/code/dimReducMethods/cca.m b/code/dimReducMethods/cca.m deleted file mode 100755 index b95179c..0000000 --- a/code/dimReducMethods/cca.m +++ /dev/null @@ -1,413 +0,0 @@ -function [Z, ccaEigen, ccaDetails] = cca(X, Y, EDGES, OPTS) -% -% Function [Z, CCAEIGEN, CCADETAILS] = CCA(X, Y, EDGES, OPTS) computes a low -% dimensional embedding Z in R^d that maximally preserves angles among input -% data X that lives in R^D, with the algorithm Conformal Component Analysis. -% -% The embedding Z is constrained to be Z = L*Y where Y is a partial basis that -% spans the space of R^d. Such Y can be computed from graph Laplacian (such as -% the outputs of Laplacian eigenmap and Locally Linear Embedding, ie, LLE). -% The parameterization matrix L is found by this function as to maximally -% prserve angles between edges coded in the sparse matrix EDGES. -% -% A basic usage of this function is given below: -% -% Inputs: -% X: input data stored in matrix (D x N) where D is the dimensionality -% -% Y: partial basis stored in matrix (d x N) -% -% EDGES: a sparse matrix of (N x N). In each column i, the row indices j to -% nonzero entrices define data points that are in the nearest neighbors of -% data point i. -% -% OPTS: -% OPTS.method: 'CCA' -% -% Outputs: -% Z: low dimensional embedding (d X N) -% CCAEIGN: eigenspectra of the matrix P = L'*L. If P is low-rank (say d' < d), -% then Z can be cutoff at d' dimension as dimensionality reduced further. -% -% The CCA() function is fairly versatile. For more details, consult the file -% README. -% -% by feisha@cs.berkeley.edu Aug 18, 2006 -% Feel free to use it for educational and research purpose. - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % sanity check - if nargin ~= 4 - error('Incorrect number of inputs supplied to cca().'); - end - N = size(X,2); - if (N~=size(Y,2)) || (N ~= size(EDGES,1)) || (N~=size(EDGES,2)) - disp('Unmatched matrix dimensions in cca().'); - fprintf('# of data points: %d\n', N); - fprintf('# of data points in Y: %d\n', size(Y,2)); - fprintf('Size of the sparse matrix for edges: %d x %d\n', size(EDGES,1), size(EDGES,2)); - error('All above 4 numbers should be the same.'); - end - % check necessary programs - if exist('mexCCACollectData') ~= 3 - error('Missing mexCCACollectData mex file on the path'); - end - if exist('csdp') ~= 2 - error('You will need CSDP solver to run cca(). Please make sure csdp.m is in your path'); - end - % check options - OPTS = check_opt(OPTS); - - D = size(X, 1); - d = size(Y, 1); - - %disp('Step I. collect data needed for SDP formulation'); - [tnn, vidx] = triangNN(EDGES, OPTS.CCA); - [erow, ecol, evalue] = sparse_nn(tnn); - - irow = int32(erow); icol = int32(ecol); - ividx = int32(vidx); ivalue = int32(evalue); - [A,B, g] = mexCCACollectData(X,Y, irow, icol, int32(OPTS.relative), ivalue, ividx ); - clear erow ecol irow icol tnn ividx ivalue evalue vidx; - lst = find(g~=0); - g = g(lst); B = B(:, lst); - if OPTS.CCA == 1 - BG = B*spdiags(1./sqrt(g),0, length(g),length(g)); - Q = A - BG*BG'; - BIAS = OPTS.regularizer*reshape(eye(d), d^2,1); - else - Q = A; BIAS = 2*sum(B,2)+OPTS.regularizer*reshape(eye(d), d^2,1); - end - [V, E] = eig(Q+eye(size(Q))); % adding an identity matrix to Q for numerical - E = E-eye(size(Q)); % stability - E(E<0) = 0; - if ~isreal(diag(E)) - warning('\tThe quadratic matrix is not positive definite..forced to be positive definite...\n'); - E=real(E); - V = real(V); - S = sqrt(E)*V'; - else - S = sqrt(E)*V'; - end - - % Formulate the SDP problem - [AA, bb, cc] = formulateSDP(S, d, BIAS, (OPTS.CCA==1)); - sizeSDP = d^2+1 + d + 2*(OPTS.CCA==1); - csdppars.s = sizeSDP; - csdpopts.printlevel = 0; - - % Solve it using CSDP - [xx, yy, zz, info] = csdp(AA, bb, cc, csdppars,csdpopts); - ccaDetails.sdpflag = info; - - % The negate of yy is our solution - yy = -yy; - idx = 0; - P = zeros(d); - for col=1:d - for row = col:d - idx=idx+1; - P(row, col) = yy(idx); - end - end - - % Convert P to a positive definite matrix - P = P + P' - diag(diag(P)); - - % Transform the original projection to the new projection - [V, E] = eig(P); - E(E < 0) = 0; - L = diag(sqrt(diag(E))) * V'; - newY = L * Y; - - % Eigenvalue of the new projection, doing PCA using covariance matrix - [newV, newE] = eig(newY * newY'); - newE = diag(newE); - [dummy, idx] = sort(newE); - newE = newE(idx(end:-1:1)); - newY = newV' * newY; - Z = newY(idx(end:-1:1),:); - - ccaEigen = newE; - ccaDetails.cost = P(:)'*Q*P(:) - BIAS'*P(:) + sum(g(:))*(OPTS.MVU==1); - if OPTS.CCA == 1 - ccaDetails.c = spdiags(1./sqrt(g),0, length(g),length(g))*B'*P(:); - else - ccaDetails.c = []; - end - ccaDetails.P = P; - ccaDetails.opts = OPTS; - - -%%%%%%%%%%%%%%%%%%%% FOLLOWING IS SUPPORTING MATLAB FUNCTIONS -function [A, b, c] = formulateSDP(S, D, bb, TRACE) - [F0, FI, c] = localformulateSDP(S, D, bb, TRACE); - [A, b, c] = sdpToSeDuMi(F0, FI, c); - - -function [F0, FI, c] = localformulateSDP(S, D, b, TRACE) -% formulate SDP problem -% each FI that corresponds to the LMI for the quadratic cost function has -% precisely 2*D^2 nonzero elements. But we need only D^2 storage for -% indexing these elements since the FI are symmetric - tempFidx = zeros(D^2, 3); - dimF = (D^2+1) + D + 2*TRACE; - idx= 0; - tracearray = ones(TRACE,1); - for col=1:D - for row=col:D - idx = idx+1; - lindx1 = sub2ind([D D], row, col); - lindx2 = sub2ind([D D], col, row); - tempFidx(:,1) = [1:D^2]'; - tempFidx(:,2) = D^2+1; - if col==row - tempFidx(:,3) = S(:, lindx1) ; - FI{idx} = sparse([tempFidx(:,1); ... % for cost function - tempFidx(:,2); ... % symmetric - row+D^2+1; ... % for P being p.s.d - tracearray*(D^2+1+D+1); % for trace - tracearray*(D^2+1+D+2); % for negate trace - ], ... - [tempFidx(:,2); ... % for cost function - tempFidx(:,1); ... % symmetric - row+D^2+1; ... % for P being p.s.d - tracearray*(D^2+1+D+1); % for trace - tracearray*(D^2+1+D+2); % for negate trace - ],... - [tempFidx(:,3); ... % for cost function - tempFidx(:,3); ... % symmetric - 1; % for P being p.s.d - tracearray*1; % for trace - tracearray*(-1); % for negate trace - ], dimF, dimF); - else - - tempFidx(:,3) = S(:, lindx1) + S(:, lindx2); - FI{idx} = sparse([tempFidx(:,1); ... % for cost function - tempFidx(:,2); ... % symmetric - row+D^2+1; ... % for P being p.s.d - col+D^2+1; ... % symmetric - ], ... - [tempFidx(:,2); ... % for cost function - tempFidx(:,1); ... % symmetric - col+D^2+1; ... % for P being p.s.d - row+D^2+1; ... % being symmetric - ],... - [tempFidx(:,3); ... % for cost function - tempFidx(:,3); ... % symmetric - 1; % for P being p.s.d - 1; % symmetric - ], dimF, dimF); - - end - end - end - idx=idx+1; - % for the F matrix corresponding to t - FI{idx} = sparse(D^2+1, D^2+1, 1, dimF, dimF); - - % now for F0 - if TRACE==1 - F0 = sparse( [[1:D^2] dimF-1 dimF], [[1:D^2] dimF-1 dimF], [ones(1, D^2) -1 1], dimF, dimF); - else - F0 = sparse( [[1:D^2]], [[1:D^2]], [ones(1, D^2)], dimF, dimF); - end - - % now for c - b = reshape(-b, D, D); - b = b*2 - diag(diag(b)); - c = zeros(idx-1,1); - kdx=0; - %keyboard; - for col=1:D - for row=col:D - kdx = kdx+1; - c(kdx) = b(row, col); - end - end - %keyboard; - c = [c; 1]; % remember: we use only half of P - return; - - -function [A, b, c] = sdpToSeDuMi(F0, FI, cc) -% convert the canonical SDP dual formulation: -% (see Vandenberche and Boyd 1996, SIAM Review) -% max -Tr(F0 Z) -% s.t. Tr(Fi Z) = cci and Z is positive definite -% -% in which cc = (cc1, cc2, cc3,..) and FI = {F1, F2, F3,...} -% -% to SeDuMi format (formulated as vector decision variables ): -% min c'x -% s.t. Ax = b and x is positive definite (x is a vector, so SeDuMi -% really means that vec2mat(x) is positive definite) -% -% by feisha@cis.upenn.edu, June, 10, 2004 - - if nargin < 3 - error('Cannot convert SDP formulation to SeDuMi formulation in sdpToSeDumi!'); - end - - [m, n] = size(F0); - if m ~= n - error('F0 matrix must be squared matrix in sdpToSeDumi(F0, FI, b)'); - end - - p = length(cc); - if p ~= length(FI) - error('FI matrix cellarray must have the same length as b in sdpToSeDumi(F0,FI,b)'); - end - - % should check every element in the cell array FI...later.. - - % x = reshape(Z, n*n, 1); % optimization variables from matrix to vector - - % converting objective function of the canonical SDP - c = reshape(F0', n*n,1); - - % converting equality constraints of the canonical SDP - zz= 0; - for idx=1:length(FI) - zz= zz + nnz(FI{idx}); - end - A = spalloc( n*n, p, zz); - for idx = 1:p - temp = reshape(FI{idx}, n*n,1); - lst = find(temp~=0); - A(lst, idx) = temp(lst); - end - % The SeDuMi solver actually expects the transpose of A as in following - % dual problem - % max b'y - % s.t. c - A'y is positive definite - % Therefore, we transpose A - % A = A'; - - % b doesn't need to be changed - b = cc; - return; - - - % Check OPTS that is passed into - function OPTS = check_opt(OPTS) - if isfield(OPTS,'method') == 0 - OPTS.method = 'cca'; - disp('Options does''t have method field, so running CCA'); - end - - if strncmpi(OPTS.method, 'MVU',3)==1 - OPTS.CCA = 0; OPTS.MVU = 1; - else - OPTS.CCA = 1; OPTS.MVU = 0; - end - - if isfield(OPTS, 'relative')==0 - OPTS.relative = 0; - end - - if OPTS.CCA==1 && OPTS.relative ==1 - disp('Running CCA, so the .relative flag set to 0'); - OPTS.relative = 0; - end - - if isfield(OPTS, 'regularizer')==0 - OPTS.regularizer = 0; - end - return - - - - function [tnn vidx]= triangNN(snn, TRI) - % function [TNN VIDX]= triangNN(SNN) triangulates a sparse graph coded by spare matrix - % SNN. TNN records the original edges in SNN as well as those that are - % triangulated. Each edge is associated with a scaling factor that is specific - % to a vertex. And VIDX records the id of the vertex. - % - % by feisha@cs.berkeley.edu Aug. 15, 2006. - - N = size(snn,1); - %fprintf('The graph has %d vertices\n', N); - % figure out maximum degree a vertex has - connectivs = sum(snn,1); - maxDegree = max(connectivs); - tnn = spalloc(N, N, round(maxDegree*N)); % prealloc estimated storage for speedup - - % triangulation - for idx=1:N - lst = find(snn(:, idx)>0); - for jdx=1:length(lst) - col = min (idx, lst(jdx)); - row = max(idx, lst(jdx)); - tnn(row, col) = tnn(row, col)+1; - if TRI == 1 - for kdx = jdx+1:length(lst) - col = min(lst(jdx), lst(kdx)); - row = max(lst(jdx), lst(kdx)); - tnn(row, col) = tnn(row, col)+1; - end - end - end - end - - numVertexIdx = full(sum(tnn(:))); - %fprintf('%d vertex entries are needed\n', numVertexIdx); - - rowIdx = zeros(numVertexIdx,1); - colIdx = zeros(numVertexIdx,1); - vidx = zeros(numVertexIdx,1); - - whichEdge = 0; - for idx=1:N - lst = find(snn(:, idx)>0); - for jdx=1:length(lst) - col = min(lst(jdx), idx); - row = max(lst(jdx), idx); - whichEdge = whichEdge+1; - rowIdx(whichEdge) = row; - colIdx(whichEdge) = col; - vidx(whichEdge) = idx; - if TRI==1 - for kdx = jdx+1:length(lst) - col = min(lst(jdx), lst(kdx)); - row = max(lst(jdx), lst(kdx)); - whichEdge = whichEdge+1; - rowIdx(whichEdge) = row; - colIdx(whichEdge) = col; - vidx(whichEdge) = idx; - end - end - end - end - linearIdx = sub2ind([N N],rowIdx, colIdx); - [sa, sIdx] = sort(linearIdx); - vidx = vidx(sIdx); - return - - - % turn sparse graph snn into row and col indices - function [edgesrow, edgescol, value] = sparse_nn(snn) - N = size(snn,1); - edgescol = zeros(N+1,1); - nnzer = nnz(snn); - edgesrow = zeros(nnzer,1); - value = zeros(nnzer,1); - - edgescol(1) = 0; - for jdx=1:N - lst = find(snn(:, jdx)>0); - %lst = lst(find(lst>jdx)); - edgescol(jdx+1) = edgescol(jdx)+length(lst); - edgesrow(edgescol(jdx)+1:edgescol(jdx+1)) = lst-1; - value(edgescol(jdx)+1:edgescol(jdx+1)) = snn(lst, jdx); - end - return \ No newline at end of file diff --git a/code/dimReducMethods/cfa.m b/code/dimReducMethods/cfa.m deleted file mode 100644 index 3eb33d6..0000000 --- a/code/dimReducMethods/cfa.m +++ /dev/null @@ -1,189 +0,0 @@ -function mappedX = cfa(X, no_dims, no_analyzers, no_iterations) -%CFA Performs coordinated factor analysis on dataset X -% -% mappedX = cfa(X, no_dims, no_analyzers, no_iterations) -% -% Performs coordinated factor analysis on dataset X to reduce its dimensionality to -% no_dims dimensions. The variable no_analyzers determines the number of -% local factor analyzers that is used in the mixture of factor analyzers -% (default = 40). The variable no_iterations sets the number of -% iterations that is employed in the EM algorithm (default = 200). -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('no_analyzers', 'var') - no_analyzers = 40; - end - if ~exist('no_iterations', 'var') - no_iterations = 200; - end - - % Make sure data is zero-mean, unit-variance - X = X - repmat(mean(X, 1), [size(X, 1) 1]); - X = X ./ repmat(var(X, 1), [size(X, 1) 1]); - - % Initialize some parameters - min_var = 1e-5; % minimum STD of Gaussians - X = X'; - [D n] = size(X); - c = no_analyzers; - d = no_dims; - - % Randomly initialize the parameters of the CFA model - SigmaN = repmat(eye(d), [1 1 n]); - Z = rand(d, n) * .1; - Pi = repmat(1 / c, [1 c]); - Kappa = rand(d, c) * .1; - Mu = randn(D, c) * .1; - SigmaC = repmat(eye(d), [1 1 c]); - Lambda = rand(D, d, c) * .1; - Psi = zeros(D, D, c); - for j=1:c - tmp = zeros(D, D); - tmp(1:size(tmp, 2) + 1:end) = rand(D, 1) * .05; - Psi(:,:,j) = tmp + tmp'; - end - - % Perform the EM algorithm for the optimization - iter = 0; - while iter < no_iterations - - % E-step - % ==================================================== - - % Do some precomputations for speed - invPsi = zeros(size(Psi)); - detSigmaC = zeros(1, c); - detPsi = zeros(1, c); - logPi = zeros(1, c); - for j=1:c - invPsi(:,:,j) = inv(Psi(:,:,j) + eye(D)); - detSigmaC(j) = det(SigmaC(:,:,j)); - detPsi(j) = det(Psi(:,:,j)); - logPi(j) = log(Pi(j)); - end - - % Compute matrices Epsilon, Vc, and m - Eps = zeros(n, c); - Vc = zeros(d, d, c); - m = zeros(d, c); - const = ((D + d) / 2) * log(2 * pi); - for j=1:c - - % Precomputations - Xnc = X - repmat(Mu(:,j), [1 n]); - Znc = Z - repmat(Kappa(:,j), [1 n]); - tmpProd = Lambda(:,:,j)' * invPsi(:,:,j) * Lambda(:,:,j); - - % Compute Epsilon - for i=1:n - normX = (Xnc(:,i) - Lambda(:,:,j) * Znc(:,i)); - Eps(i, j) = -logPi(j) + const ... - + (.5 * log(detSigmaC(j))) + (.5 * detPsi(j)) ... - + (.5 * trace(SigmaC(:,:,j) * (SigmaN(:,:,i) + Znc(:,i) * Znc(:,i)'))) ... - + (.5 * trace(SigmaN(:,:,i) * tmpProd)) ... - + (.5 * normX' * invPsi(:,:,j) * normX); - end - - % Compute Vc and m - Vc(:,:,j) = inv(SigmaC(:,:,j) + eps * eye(d)) + tmpProd; - m(:,j) = Kappa(:,j) + (Vc(:,:,j) \ Lambda(:,:,j)') * invPsi(:,:,j) * mean(Xnc, 2); - end - - % Update estimate of Q - Q = (repmat(sum(exp(-Eps), 2), [1 c]) .^ -1) .* exp(-Eps); - - % Update estimate of SigmaN - for i=1:n - tmp = zeros(d, d); - for j=1:c - tmp = tmp + Q(i, j) * Vc(:,:,j); - end - - % Compute covariance matrix - SigmaN(:,:,i) = inv(tmp + eps * eye(d)); % code above gave us inv(SigmaN) - end - - % Update estimate of Z (= mappedX) - for i=1:n - tmp = zeros(d, 1); - for j=1:c - tmp = tmp + (Q(i, j) * Vc(:,:,j) * m(:,j)); - end - Z(:,i) = SigmaN(:,:,i) * tmp; - end - - % M-step - % ==================================================== - - % Update estimate of Pi - Pi = sum(Q, 1) ./ n; - - % Update estimate of Mu and Kappa - for j=1:c - tmpQ = Q(:,c) ./ sum(Q(:,c)); - Mu(:,c) = sum(repmat(tmpQ', [D 1]) .* X, 2); - Kappa(:,c) = sum(repmat(tmpQ', [d 1]) .* Z, 2); - end - - % Update estimate of SigmaC - for j=1:c - tmp = 0; - tmpQ = Q(:,c) ./ sum(Q(:,c)); - for i=1:n - Znc = Z(:,i) - Kappa(:,j); - tmp = tmp + (tmpQ(i) * (SigmaN(:,:,i) + Znc * Znc')); - end - - % Enforce some variance - tmp(1:size(tmp, 1) + 1:end) = max(min_var, tmp(1:size(tmp, 1) + 1:end)); - SigmaC(:,:,j) = tmp; - end - - % Update estimate of Lambda - for j=1:c - Sc = zeros(D, d); - tmpQ = Q(:,j) ./ sum(Q(:,j)); - Xnc = X - repmat(Mu(:,j), [1 n]); - Znc = Z - repmat(Kappa(:,j), [1 n]); - for i=1:n - Sc = Sc + tmpQ(i) * (Xnc(:,i) * Znc(:,i)'); - end - Lambda(:,:,j) = Sc / (SigmaC(:,:,j) + eps * eye(d)); - end - - % Update estimate of Psi - for j=1:c - tmpPsi = zeros(D, D); - tmpQ = Q(:,j) ./ sum(Q(:,j)); - Xnc = X - repmat(Mu(:,j), [1 n]); - Znc = Z - repmat(Kappa(:,j), [1 n]); - tmpProd = Lambda(:,:,j) * SigmaN(:,:,i) * Lambda(:,:,j)'; - for i=1:n - tmpPsi(1:size(tmpPsi, 2) + 1:end) = tmpPsi(1:size(tmpPsi, 2) + 1:end) + ... - tmpQ(i) * (((Xnc(:,i) - Lambda(:,:,j) * Znc(:,i)) .^ 2)' + tmpProd(1:size(tmpProd, 2) + 1:end)); - end - Psi(:,:,c) = tmpPsi; - end - - % Update number of iterations - iter = iter + 1; - if rem(iter, 5) == 0 - fprintf('.'); - end - end - - % Transpose to get lowdimensional data representation - mappedX = Z'; - \ No newline at end of file diff --git a/code/dimReducMethods/cg_update.m b/code/dimReducMethods/cg_update.m deleted file mode 100755 index 63b715a..0000000 --- a/code/dimReducMethods/cg_update.m +++ /dev/null @@ -1,102 +0,0 @@ -% Version 1.000 -% -% Code provided by Ruslan Salakhutdinov and Geoff Hinton -% -% Permission is granted for anyone to copy, use, modify, or distribute this -% program and accompanying programs and documents for any purpose, provided -% this copyright notice is retained and prominently displayed, along with -% a note saying that the original programs are available from our -% web page. -% The programs and documents are distributed without any warranty, express or -% implied. As the programs were written for research purposes only, they have -% not been tested to the degree that would be advisable in any important -% application. All use of these programs is entirely at the user's own risk. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - -function [f, df] = cg_update(VV, Dim, XX) - - l1 = Dim(1); - l2 = Dim(2); - l3 = Dim(3); - l4 = Dim(4); - l5 = Dim(5); - l6 = Dim(6); - l7 = Dim(7); - l8 = Dim(8); - l9 = Dim(9); - N = size(XX, 1); - - % Extract weights back from VV - w1 = reshape(VV(1:(l1 + 1) * l2), l1 + 1, l2); - xxx = (l1 + 1) * l2; - w2 = reshape(VV(xxx + 1:xxx + (l2 + 1) * l3), l2 + 1, l3); - xxx = xxx + (l2 + 1) * l3; - w3 = reshape(VV(xxx + 1:xxx + (l3 + 1) * l4), l3 + 1, l4); - xxx = xxx + (l3 + 1) * l4; - w4 = reshape(VV(xxx + 1:xxx + (l4 + 1) * l5), l4 + 1, l5); - xxx = xxx + (l4 + 1) * l5; - w5 = reshape(VV(xxx + 1:xxx + (l5 + 1) * l6), l5 + 1, l6); - xxx = xxx + (l5 + 1) * l6; - w6 = reshape(VV(xxx + 1:xxx + (l6 + 1) * l7), l6 + 1, l7); - xxx = xxx + (l6 + 1) * l7; - w7 = reshape(VV(xxx + 1:xxx + (l7 + 1) * l8), l7 + 1, l8); - xxx = xxx + (l7 + 1) * l8; - w8 = reshape(VV(xxx + 1:xxx + (l8 + 1) * l9), l8 + 1, l9); - - % Evaluate points - XX = [XX ones(N, 1)]; - w1probs = 1 ./ (1 + exp(-XX * w1)); w1probs = [w1probs ones(N,1)]; - w2probs = 1 ./ (1 + exp(-w1probs * w2)); w2probs = [w2probs ones(N,1)]; - w3probs = 1 ./ (1 + exp(-w2probs * w3)); w3probs = [w3probs ones(N,1)]; - w4probs = w3probs * w4; w4probs = [w4probs ones(N,1)]; - w5probs = 1 ./ (1 + exp(-w4probs * w5)); w5probs = [w5probs ones(N,1)]; - w6probs = 1 ./ (1 + exp(-w5probs * w6)); w6probs = [w6probs ones(N,1)]; - w7probs = 1 ./ (1 + exp(-w6probs * w7)); w7probs = [w7probs ones(N,1)]; - XXout = 1 ./ (1 + exp(-w7probs * w8)); - - % Compute gradients - f = (-1 / N) * sum(sum(XX(:,1:end - 1) .* log(XXout) + (1 - XX(:,1:end - 1)) .* log(1 - XXout))); - IO = (1 / N) * (XXout - XX(:,1:end - 1)); - Ix8 = IO; - dw8 = w7probs'*Ix8; - - Ix7 = (Ix8 * w8') .* w7probs .* (1 - w7probs); - Ix7 = Ix7(:,1:end - 1); - dw7 = w6probs' * Ix7; - - Ix6 = (Ix7*w7') .* w6probs .* (1 - w6probs); - Ix6 = Ix6(:,1:end - 1); - dw6 = w5probs' * Ix6; - - Ix5 = (Ix6 * w6') .* w5probs .* (1 - w5probs); - Ix5 = Ix5(:,1:end - 1); - dw5 = w4probs' * Ix5; - - Ix4 = (Ix5 * w5'); - Ix4 = Ix4(:,1:end - 1); - dw4 = w3probs' * Ix4; - - Ix3 = (Ix4 * w4') .* w3probs .* (1 - w3probs); - Ix3 = Ix3(:,1:end - 1); - dw3 = w2probs' * Ix3; - - Ix2 = (Ix3 * w3') .* w2probs .* (1 - w2probs); - Ix2 = Ix2(:,1:end - 1); - dw2 = w1probs' * Ix2; - - Ix1 = (Ix2 * w2') .* w1probs .* (1 - w1probs); - Ix1 = Ix1(:,1:end - 1); - dw1 = XX' * Ix1; - - % Return gradients - df = [dw1(:)' dw2(:)' dw3(:)' dw4(:)' dw5(:)' dw6(:)' dw7(:)' dw8(:)']'; diff --git a/code/dimReducMethods/charting.m b/code/dimReducMethods/charting.m deleted file mode 100644 index 660749f..0000000 --- a/code/dimReducMethods/charting.m +++ /dev/null @@ -1,85 +0,0 @@ -function [mappedX, mapping] = charting(X, no_dims, no_analyzers, max_iterations, eig_impl) -%CHARTING Performs manifold charting on dataset X -% -% [mappedX, mapping] = charting(X, no_dims, no_analyzers, max_iterations, eig_impl) -% -% Performs manifold charting on dataset X to reduce its dimensionality to -% no_dims dimensions. The variable no_analyzers determines the number of -% local factor analyzers that is used in the mixture of factor analyzers -% (default = 40). The variable max_iterations sets the maximum number of -% iterations that is employed in the EM algorithm (default = 200). -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('no_analyzers', 'var') - no_analyzers = 40; - end - if ~exist('max_iterations', 'var') - max_iterations = 200; - end - - % Initialize some parameters - tol = 1e-10; % regularization parameter - min_std = 1e-3; % minimum STD of Gaussians - kf = no_analyzers * (no_dims + 1); - - % Construct MFA model on the data - disp('Running EM algorithm and compute local factor analyzers...'); - [LX, MX, PX] = mppca(X', no_dims, no_analyzers, tol, max_iterations, min_std); - [R, Z] = infermfa(X', LX, MX, PX); - - % Adds last entry = 1 in posterior mean to handle means of factor analyzers - Z(no_dims + 1,:,:) = 1; - Z = permute(Z, [1 3 2]); - - % Construct blockdiagonal matrix D - disp('Performing manifold charting...'); - D = zeros((no_dims + 1) * no_analyzers, (no_dims + 1) * no_analyzers); - for i=1:no_analyzers - Ds = zeros(no_dims + 1, no_dims + 1); - for j=1:size(X, 1) - Ds = Ds + R(i, j) .* (Z(:,i,j) * Z(:,i,j)'); - end - D((i - 1) * (no_dims + 1) + 1:i * (no_dims + 1), (i - 1) * (no_dims + 1) + 1:i * (no_dims + 1)) = Ds; - end - - % Construct responsibility weighted local representation matrix U - R = reshape(R, [1 no_analyzers size(X, 1)]); - U = reshape(bsxfun(@times, R, Z), [kf size(X, 1)])'; - - % Solve generalized eigenproblem - if strcmp(eig_impl, 'Matlab') - options.disp = 0; - options.isreal = 1; - options.issym = 1; - [V, lambda] = eigs(D - U' * U, U' * U, no_dims + 1, 'SM', options); - else - options.Disp = 0; - options.LSolver = 'bicgstab'; - [V, lambda] = jdqz(D - U' * U, U' * U, no_dims + 1, 'SM', options); - end - [lambda, ind] = sort(diag(lambda)); - V = V(:,ind(2:end)); - - % Compute final lowdimensional data representation - mappedX = U * V; - - % Store mapping data for out-of-sample extension - if nargout > 1 - mapping.LX = LX; - mapping.MX = MX; - mapping.PX = PX; - mapping.V = V; - end - \ No newline at end of file diff --git a/code/dimReducMethods/checkgrad.m b/code/dimReducMethods/checkgrad.m deleted file mode 100644 index 21a7c71..0000000 --- a/code/dimReducMethods/checkgrad.m +++ /dev/null @@ -1,52 +0,0 @@ -function d = checkgrad(f, X, e, P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12, P13, P14, P15, P16) - -% checkgrad checks the derivatives in a function, by comparing them to finite -% differences approximations. The partial derivatives and the approximation -% are printed and the norm of the diffrence divided by the norm of the sum is -% returned as an indication of accuracy. -% -% usage: checkgrad('f', X, e, P1, P2, ...) -% -% where X is the argument and e is the small perturbation used for the finite -% differences. and the P1, P2, ... are optional additional parameters which -% get passed to f. The function f should be of the type -% -% [fX, dfX] = f(X, P1, P2, ...) -% -% where fX is the function value and dfX is a vector of partial derivatives. -% -% Carl Edward Rasmussen, 2001-08-01. - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - -argstr = [f, '(X']; % assemble function call strings -argstrd = [f, '(X+dx']; -for i = 1:(nargin - 3) - argstr = [argstr, ',P', int2str(i)]; - argstrd = [argstrd, ',P', int2str(i)]; -end -argstr = [argstr, ')']; -argstrd = [argstrd, ')']; - -[y dy] = eval(argstr); % get the partial derivatives dy - -dh = zeros(length(X),1) ; -for j = 1:length(X) - disp([' - ' num2str(j) ' of ' num2str(length(X))]); - dx = zeros(length(X),1); - dx(j) = dx(j) + e; % perturb a single dimension - y2 = eval(argstrd); - dx = -dx ; - y1 = eval(argstrd); - dh(j) = (y2 - y1)/(2*e); -end - -disp([dy dh]) % print the two vectors -d = norm(dh-dy)/norm(dh+dy); % return norm of diff divided by norm of sum diff --git a/code/dimReducMethods/combn.m b/code/dimReducMethods/combn.m deleted file mode 100644 index 0ab9101..0000000 --- a/code/dimReducMethods/combn.m +++ /dev/null @@ -1,104 +0,0 @@ -function [M,IND] = combn(V,N) -% COMBN - all combinations of elements -% M = COMBN(V,N) returns all combinations of N elements of the elements in -% vector V. M has the size (length(V).^N)-by-N. -% -% [M,I] = COMBN(V,N) also returns the index matrix I so that M = V(I). -% -% V can be an array of numbers, cells or strings. -% -% Example: -% M = COMBN([0 1],3) returns the 8-by-3 matrix: -% 0 0 0 -% 0 0 1 -% 0 1 0 -% 0 1 1 -% ... -% 1 1 1 -% -% All elements in V are regarded as unique, so M = COMBN([2 2],3) returns -% a 8-by-3 matrix with all elements equal to 2. -% -% NB Matrix sizes increases exponentially at rate (n^N)*N. -% -% COMBN is very fast using a single matrix multiplication, without any -% explicit for-loops. -% -% See also PERMS, NCHOOSEK -% and ALLCOMB, PERMPOS on the File Exchange - -% for Matlab R13 -% version 3.2 (may 2006) -% (c) Jos van der Geest -% email: jos@jasen.nl - -% History -% 1.1 updated help text -% 2.0 new faster algorithm -% 3.0 (aug 2006) implemented very fast algorithm -% 3.1 (may 2007) Improved algorithm Roger Stafford pointed out that for some values, the floor -% operation on floating points, according to the IEEE 754 standard, could return -% erroneous values. His excellent solution was to add (1/2) to the values -% of A. -% 3.2 (may 2007) changed help and error messages slightly - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - -if nargin ~=2, - error('Two arguments required.') ; -end - -if isempty(V) || N == 0, - M = [] ; - IND = [] ; -elseif fix(N) ~= N || N < 1 || numel(N) ~= 1 ; - error('Second argument should be a positive integer.') ; -else - nV = numel(V) ; - % use a math trick - A = [0:nV^N-1]+(1/2) ; - B = [nV.^(1-N:0)] ; - IND = rem(floor((A(:) * B(:)')),nV) + 1 ; - M = V(IND) ; -end - -% Previous algorithms - -% Version 2.0 -% for i = N:-1:1 -% X = repmat(1:nV,nV^(N-i),nV^(i-1)); -% IND(:,i) = X(:); -% end -% M = V(IND) ; - -% Version 1.0 -% nV = numel(V) ; -% % don waste space, if only one output is requested -% [IND{1:N}] = ndgrid(1:nV) ; -% IND = fliplr(reshape(cat(ndims(IND{1}),IND{:}),[],N)) ; -% M = V(IND) ; - -% Combinations using for-loops -% can be implemented in C or VB -% nv = length(V) ; -% C = zeros(nv^N,N) ; % declaration -% for ii=1:N, -% cc = 1 ; -% for jj=1:(nv^(ii-1)), -% for kk=1:nv, -% for mm=1:(nv^(N-ii)), -% C(cc,ii) = V(kk) ; -% cc = cc + 1 ; -% end -% end -% end -% end - - diff --git a/code/dimReducMethods/components.m b/code/dimReducMethods/components.m deleted file mode 100644 index 6e6ccdf..0000000 --- a/code/dimReducMethods/components.m +++ /dev/null @@ -1,46 +0,0 @@ -function blocks = components(A) -%COMPONENTS Finds connected components in a graph defined by a adjacency matrix -% -% blocks = components(A) -% -% Finds connected components in a graph defined by the adjacency matrix A. -% The function outputs an n-vector of integers 1:k in blocks, meaning that -% A has k components. The vector blocks labels the vertices of A according -% to component. -% If the adjacency matrix A is undirected (i.e. symmetric), the blocks are -% its connected components. If the adjacency matrix A is directed (i.e. -% unsymmetric), the blocks are its strongly connected components. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Check size of adjacency matrix - [n, m] = size(A); - if n ~= m, error ('Adjacency matrix must be square'), end; - - % Compute Dulmage-Mendelsohn permutation on A - if ~all(diag(A)) - [foo, p, bar, r] = dmperm(A | speye(size(A))); - else - [foo, p, bar, r] = dmperm(A); - end - - % Compute sizes and number of clusters - sizes = diff(r); - k = length(sizes); - - % Now compute the array blocks - blocks = zeros(1, n); - blocks(r(1:k)) = ones(1, k); - blocks = cumsum(blocks); - - % Permute blocks so it maps vertices of A to components - blocks(p) = blocks; diff --git a/code/dimReducMethods/compute_mapping.m b/code/dimReducMethods/compute_mapping.m deleted file mode 100644 index bd6b1c7..0000000 --- a/code/dimReducMethods/compute_mapping.m +++ /dev/null @@ -1,422 +0,0 @@ -function [mappedA, mapping] = compute_mapping(A, type, no_dims, varargin) -%COMPUTE_MAPPING Performs dimensionality reduction on a dataset A -% -% mappedA = compute_mapping(A, type) -% mappedA = compute_mapping(A, type, no_dims) -% mappedA = compute_mapping(A, type, no_dims, ...) -% -% Performs a technique for dimensionality reduction on the data specified -% in A, reducing data with a lower dimensionality in mappedA. -% The data on which dimensionality reduction is performed is given in A -% (rows correspond to observations, columns to dimensions). A may also be a -% (labeled or unlabeled) PRTools dataset. -% The type of dimensionality reduction used is specified by type. Possible -% values are 'PCA', 'LDA', 'MDS', 'ProbPCA', 'FactorAnalysis', 'GPLVM', -% 'Sammon', 'Isomap', 'LandmarkIsomap', 'LLE', 'Laplacian', 'HessianLLE', -% 'LTSA', 'MVU', 'CCA', 'LandmarkMVU', 'FastMVU', 'DiffusionMaps', -% 'KernelPCA', 'GDA', 'SNE', 'SymSNE', 'tSNE', 'LPP', 'NPE', 'LLTSA', -% 'SPE', 'Autoencoder', 'LLC', 'ManifoldChart', 'CFA', 'NCA', 'MCML', and 'LMNN'. -% The function returns the low-dimensional representation of the data in the -% matrix mappedA. If A was a PRTools dataset, then mappedA is a PRTools -% dataset as well. For some techniques, information on the mapping is -% returned in the struct mapping. -% The variable no_dims specifies the number of dimensions in the embedded -% space (default = 2). For the supervised techniques ('LDA', 'GDA', 'NCA', -% 'MCML', and 'LMNN'), the labels of the instances should be specified in -% the first column of A (using numeric labels). -% -% mappedA = compute_mapping(A, type, no_dims, parameters) -% mappedA = compute_mapping(A, type, no_dims, parameters, eig_impl) -% -% Free parameters of the techniques can be defined as well (on the place of -% the dots). These parameters differ per technique, and are listed below. -% For techniques that perform spectral analysis of a sparse matrix, one can -% also specify in eig_impl the eigenanalysis implementation that is used. -% Possible values are 'Matlab' and 'JDQR' (default = 'Matlab'). We advice -% to use the 'Matlab' for datasets of with 10,000 or less datapoints; -% for larger problems the 'JDQR' might prove to be more fruitful. -% The free parameters for the techniques are listed below (the parameters -% should be provided in this order): -% -% PCA: - none -% LDA: - none -% MDS: - none -% ProbPCA: - max_iterations -> default = 200 -% FactorAnalysis: - none -% GPLVM: - sigma -> default = 1.0 -% Sammon: - none -% Isomap: - k -> default = 12 -% LandmarkIsomap: - k -> default = 12 -% - percentage -> default = 0.2 -% LLE: - k -> default = 12 -% - eig_impl -> {['Matlab'], 'JDQR'} -% Laplacian: - k -> default = 12 -% - sigma -> default = 1.0 -% - eig_impl -> {['Matlab'], 'JDQR'} -% HessianLLE: - k -> default = 12 -% - eig_impl -> {['Matlab'], 'JDQR'} -% LTSA: - k -> default = 12 -% - eig_impl -> {['Matlab'], 'JDQR'} -% MVU: - k -> default = 12 -% - eig_impl -> {['Matlab'], 'JDQR'} -% CCA: - k -> default = 12 -% - eig_impl -> {['Matlab'], 'JDQR'} -% LandmarkMVU: - k -> default = 5 -% FastMVU: - k -> default = 5 -% - finetune -> default = true -% - eig_impl -> {['Matlab'], 'JDQR'} -% DiffusionMaps: - t -> default = 1.0 -% - sigma -> default = 1.0 -% KernelPCA: - kernel -> {'linear', 'poly', ['gauss']} -% - kernel parameters: type HELP GRAM for info -% GDA: - kernel -> {'linear', 'poly', ['gauss']} -% - kernel parameters: type HELP GRAM for info -% SNE: - perplexity -> default = 30 -% SymSNE: - perplexity -> default = 30 -% tSNE: - initial_dims -> default = 30 -% - perplexity -> default = 30 -% LPP: - k -> default = 12 -% - sigma -> default = 1.0 -% - eig_impl -> {['Matlab'], 'JDQR'} -% NPE: - k -> default = 12 -% - eig_impl -> {['Matlab'], 'JDQR'} -% LLTSA: - k -> default = 12 -% - eig_impl -> {['Matlab'], 'JDQR'} -% SPE: - type -> {['Global'], 'Local'} -% - if 'Local': k -> default = 12 -% Autoencoder: - lambda -> default = 0 -% LLC: - k -> default = 12 -% - no_analyzers -> default = 20 -% - max_iterations -> default = 200 -% - eig_impl -> {['Matlab'], 'JDQR'} -% ManifoldChart: - no_analyzers -> default = 40 -% - max_iterations -> default = 200 -% - eig_impl -> {['Matlab'], 'JDQR'} -% CFA: - no_analyzers -> default = 2 -% - max_iterations -> default = 200 -% NCA: - lambda -> default = 0.0 -% MCML: - none -% LMNN: - k -> default = 3 -% -% -% In the parameter list above, {.., ..} indicates a list of options, and [] -% indicates the default setting. The variable k indicates the number of -% nearest neighbors in a neighborhood graph. Alternatively, k may also have -% the value 'adaptive', indicating the use of adaptive neighborhood selection -% in the construction of the neighborhood graph. Note that in LTSA and -% HessianLLE, the setting 'adaptive' might cause singularities. Using the -% JDQR-solver or a fixed setting of k might resolve this problem. SPE does -% not yet support adaptive neighborhood selection. -% -% The variable sigma indicates the variance of a Gaussian kernel. The -% parameters no_analyzers and max_iterations indicate repectively the number -% of factor analyzers that is used in an MFA model and the number of -% iterations that is used in an EM algorithm. -% -% The variable lambda represents an L2-regularization parameter. - - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - welcome; - - % Check inputs - if nargin < 2 - error('Function requires at least two inputs.'); - end - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~isempty(varargin) && strcmp(varargin{length(varargin)}, 'JDQR') - eig_impl = 'JDQR'; - varargin(length(varargin)) = []; - elseif ~isempty(varargin) && strcmp(varargin{length(varargin)}, 'Matlab') - eig_impl = 'Matlab'; - varargin(length(varargin)) = []; - else - eig_impl = 'Matlab'; - end - mapping = struct; - - % Handle PRTools dataset - if strcmp(class(A), 'dataset') - prtools = 1; - AA = A; - if ~strcmp(type, {'LDA', 'FDA', 'GDA', 'KernelLDA', 'KernelFDA', 'MCML', 'NCA', 'LMNN'}) - A = A.data; - else - A = [double(A.labels) A.data]; - end - else - prtools = 0; - end - - % Make sure there are no duplicates in the dataset - A = double(A); -% if size(A, 1) ~= size(unique(A, 'rows'), 1) -% error('Please remove duplicates from the dataset first.'); -% end - - % Check whether value of no_dims is correct - if ~isnumeric(no_dims) || no_dims > size(A, 2) || ((no_dims < 1 || round(no_dims) ~= no_dims) && ~any(strcmpi(type, {'PCA', 'KLM'}))) - error('Value of no_dims should be a positive integer smaller than the original data dimensionality.'); - end - - % Switch case - switch type - case 'Isomap' - % Compute Isomap mapping - if isempty(varargin), [mappedA, mapping] = isomap(A, no_dims, 12); - else [mappedA, mapping] = isomap(A, no_dims, varargin{1}); end - mapping.name = 'Isomap'; - - case 'LandmarkIsomap' - % Compute Landmark Isomap mapping - if isempty(varargin), [mappedA, mapping] = landmark_isomap(A, no_dims, 12, 0.2); - elseif length(varargin) == 1, [mappedA, mapping] = landmark_isomap(A, no_dims, varargin{1}, 0.2); - elseif length(varargin) > 1, [mappedA, mapping] = landmark_isomap(A, no_dims, varargin{1}, varargin{2}); end - mapping.name = 'LandmarkIsomap'; - - case {'Laplacian', 'LaplacianEig', 'LaplacianEigen' 'LaplacianEigenmaps'} - % Compute Laplacian Eigenmaps-based mapping - if isempty(varargin), [mappedA, mapping] = laplacian_eigen(A, no_dims, 12, 1, eig_impl); - elseif length(varargin) == 1, [mappedA, mapping] = laplacian_eigen(A, no_dims, varargin{1}, 1, eig_impl); - elseif length(varargin) > 1, [mappedA, mapping] = laplacian_eigen(A, no_dims, varargin{1}, varargin{2}, eig_impl); end - mapping.name = 'Laplacian'; - - case {'HLLE', 'HessianLLE'} - % Compute Hessian LLE mapping - if isempty(varargin), mappedA = hlle(A, no_dims, 12, eig_impl); - else mappedA = hlle(A, no_dims, varargin{1}, eig_impl); end - mapping.name = 'HLLE'; - - case 'LLE' - % Compute LLE mapping - if isempty(varargin), [mappedA, mapping] = lle(A, no_dims, 12, eig_impl); - else [mappedA, mapping] = lle(A, no_dims, varargin{1}, eig_impl); end - mapping.name = 'LLE'; - - case 'GPLVM' - % Compute GPLVM mapping - if isempty(varargin), mappedA = gplvm(A, no_dims, 1); - else mappedA = gplvm(A, no_dims, varargin{1}); end - mapping.name = 'GPLVM'; - - case 'LLC' - % Compute LLC mapping - if isempty(varargin), mappedA = run_llc(A', no_dims, 12, 20, 200, eig_impl); - elseif length(varargin) == 1, mappedA = run_llc(A', no_dims, varargin{1}, 20, 200, eig_impl); - elseif length(varargin) == 2, mappedA = run_llc(A', no_dims, varargin{1}, varargin{2}, 200, eig_impl); - else mappedA = run_llc(A', no_dims, varargin{1}, varargin{2}, varargin{3}, eig_impl); end - mappedA = mappedA'; - mapping.name = 'LLC'; - - case {'ManifoldChart', 'ManifoldCharting', 'Charting', 'Chart'} - % Compute mapping using manifold charting - if isempty(varargin), [mappedA, mapping] = charting(A, no_dims, 40, 200, eig_impl); - elseif length(varargin) == 1, [mappedA, mapping] = charting(A, no_dims, varargin{1}, 200, eig_impl); - else [mappedA, mapping] = charting(A, no_dims, varargin{1}, varargin{2}, eig_impl); end - mapping.name = 'ManifoldChart'; - - case 'CFA' - % Compute mapping using Coordinated Factor Analysis - if isempty(varargin), mappedA = cfa(A, no_dims, 2, 200); - elseif length(varargin) == 1, mappedA = cfa(A, no_dims, varargin{1}, 200); - else mappedA = cfa(A, no_dims, varargin{1}, varargin{2}); end - mapping.name = 'CFA'; - - case 'LTSA' - % Compute LTSA mapping - if isempty(varargin), mappedA = ltsa(A, no_dims, 12, eig_impl); - else mappedA = ltsa(A, no_dims, varargin{1}, eig_impl); end - mapping.name = 'LTSA'; - - case 'LLTSA' - % Compute LLTSA mapping - if isempty(varargin), [mappedA, mapping] = lltsa(A, no_dims, 12, eig_impl); - else [mappedA, mapping] = lltsa(A, no_dims, varargin{1}, eig_impl); end - mapping.name = 'LLTSA'; - - case {'LMVU', 'LandmarkMVU'} - % Compute Landmark MVU mapping - if isempty(varargin), [mappedA, mapping] = lmvu(A', no_dims, 5); - else [mappedA, mapping] = lmvu(A', no_dims, varargin{1}); end - mappedA = mappedA'; - mapping.name = 'LandmarkMVU'; - - case 'FastMVU' - % Compute MVU mapping - if isempty(varargin), [mappedA, mapping] = fastmvu(A, no_dims, 12, eig_impl); - elseif length(varargin) == 1, [mappedA, mapping] = fastmvu(A, no_dims, varargin{1}, true, eig_impl); - elseif length(varargin) == 2, [mappedA, mapping] = fastmvu(A, no_dims, varargin{1}, varargin{2}, eig_impl);end - mapping.name = 'FastMVU'; - - case {'Conformal', 'ConformalEig', 'ConformalEigen', 'ConformalEigenmaps', 'CCA', 'MVU'} - % Perform initial LLE (to higher dimensionality) - disp('Running normal LLE...') - tmp_dims = min([size(A, 2) 4 * no_dims + 1]); - if isempty(varargin), [mappedA, mapping] = lle(A, tmp_dims, 12, eig_impl); - else [mappedA, mapping] = lle(A, tmp_dims, varargin{1}, eig_impl); end - - % Now perform the MVU / CCA optimalization - if strcmp(type, 'MVU'), - disp('Running Maximum Variance Unfolding...'); - opts.method = 'MVU'; - else - disp('Running Conformal Eigenmaps...'); - opts.method = 'CCA'; - end - disp('CSDP OUTPUT ============================================================================='); - mappedA = cca(A(mapping.conn_comp,:)', mappedA', mapping.nbhd(mapping.conn_comp, mapping.conn_comp)', opts); - disp('========================================================================================='); - mappedA = mappedA(1:no_dims,:)'; - - case {'DM', 'DiffusionMaps'} - % Compute diffusion maps mapping - if isempty(varargin), mappedA = diffusion_maps(A, no_dims, 1, 1); - elseif length(varargin) == 1, mappedA = diffusion_maps(A, no_dims, varargin{1}, 1); - else mappedA = diffusion_maps(A, no_dims, varargin{1}, varargin{2}); end - mapping.name = 'DM'; - - case 'SPE' - % Compute SPE mapping - if isempty(varargin), mappedA = spe(A, no_dims, 'Global'); - elseif length(varargin) == 1, mappedA = spe(A, no_dims, varargin{1}); - elseif length(varargin) == 2, mappedA = spe(A, no_dims, varargin{1}, varargin{2}); end - mapping.name = 'SPE'; - - case 'LPP' - % Compute LPP mapping - if isempty(varargin), [mappedA, mapping] = lpp(A, no_dims, 12, 1, eig_impl); - elseif length(varargin) == 1, [mappedA, mapping] = lpp(A, no_dims, varargin{1}, 1, eig_impl); - else [mappedA, mapping] = lpp(A, no_dims, varargin{1}, varargin{2}, eig_impl); end - mapping.name = 'LPP'; - - case 'NPE' - % Compute NPE mapping - if isempty(varargin), [mappedA, mapping] = npe(A, no_dims, 12, eig_impl); - else [mappedA, mapping] = npe(A, no_dims, varargin{1}, eig_impl); end - mapping.name = 'NPE'; - - case 'SNE' - % Compute SNE mapping - if isempty(varargin), mappedA = sne(A, no_dims); - else mappedA = sne(A, no_dims, varargin{1}); end - mapping.name = 'SNE'; - - case {'SymSNE', 'SymmetricSNE'} - % Compute Symmetric SNE mapping - if isempty(varargin), mappedA = sym_sne(A, no_dims); - elseif length(varargin) == 1, mappedA = sym_sne(A, no_dims, varargin{1}); - else mappedA = sym_sne(A, no_dims, varargin{1}, varargin{2}); end - mapping.name = 'SymSNE'; - - case {'tSNE', 't-SNE'} - % Compute t-SNE mapping - if isempty(varargin), mappedA = tsne(A, [], no_dims); - else mappedA = tsne(A, [], no_dims, varargin{1}); end - mapping.name = 't-SNE'; - - case {'AutoEncoder', 'Autoencoder'} - - % Train deep autoencoder to map data - layers = [ceil(size(A, 2) * 1.2) + 5 max([ceil(size(A, 2) / 4) no_dims + 2]) + 3 max([ceil(size(A, 2) / 10) no_dims + 1]) no_dims]; - disp(['Network size: ' num2str(layers)]); -% [mappedA, network, binary_data, mean_X, var_X] = train_autoencoder(A, net_structure); - if isempty(varargin), [network, mappedA] = train_deep_autoenc(A, layers, 0); - else [network, mappedA] = train_deep_autoenc(A, layers, varargin{1}); end - mapping.network = network; - mapping.name = 'Autoencoder'; - - case {'KPCA', 'KernelPCA'} - % Apply kernel PCA with polynomial kernel - if isempty(varargin), [mappedA, mapping] = kernel_pca(A, no_dims); - else [mappedA, mapping] = kernel_pca(A, no_dims, varargin{:}); end - mapping.name = 'KernelPCA'; - - case {'KLDA', 'KFDA', 'KernelLDA', 'KernelFDA', 'GDA'} - % Apply GDA with Gaussian kernel - if isempty(varargin), mappedA = gda(A(:,2:end), uint8(A(:,1)), no_dims); - else mappedA = gda(A(:,2:end), uint8(A(:,1)), no_dims, varargin{:}); end - mapping.name = 'KernelLDA'; - - case {'LDA', 'FDA'} - % Run LDA on labeled dataset - [mappedA, mapping] = lda(A(:,2:end), A(:,1), no_dims); - mapping.name = 'LDA'; - - case 'MCML' - % Run MCML on labeled dataset - mapping = mcml(A(:,2:end), A(:,1), no_dims); - mappedA = bsxfun(@minus, A(:,2:end), mapping.mean) * mapping.M; - mapping.name = 'MCML'; - - case 'NCA' - % Run NCA on labeled dataset - if isempty(varargin), lambda = 0; else lambda = varargin{1}; end - [mappedA, mapping] = nca(A(:,2:end), A(:,1), no_dims, lambda); - mapping.name = 'NCA'; - - case 'MDS' - % Perform MDS - mappedA = mds(A, no_dims); - mapping.name = 'MDS'; - - case 'Sammon' - mappedA = sammon(A, no_dims); - mapping.name = 'Sammon'; - - case {'PCA', 'KLM'} - % Compute PCA mapping - [mappedA, mapping] = pca(A, no_dims); - mapping.name = 'PCA'; - - case {'SPCA', 'SimplePCA'} - % Compute PCA mapping using Hebbian learning approach - [mappedA, mapping] = spca(A, no_dims); - mapping.name = 'SPCA'; - - case {'PPCA', 'ProbPCA', 'EMPCA'} - % Compute probabilistic PCA mapping using an EM algorithm - if isempty(varargin), [mappedA, mapping] = em_pca(A, no_dims, 200); - else [mappedA, mapping] = em_pca(A, no_dims, varargin{1}); end - mapping.name = 'PPCA'; - - case {'FactorAnalysis', 'FA'} - % Compute factor analysis mapping (using an EM algorithm) - [mappedA, mapping] = fa(A, no_dims); - mapping.name = 'FA'; - - case 'LMNN' - % Perform large-margin nearest neighbor metric learning - Y = A(:,1); A = A(:,2:end); - mapping.mean = mean(A, 1); - A = bsxfun(@minus, A, mapping.mean); - [foo, mapping.M, mappedA] = lmnn(A, Y); - mapping.name = 'LMNN'; - - otherwise - error('Unknown dimensionality reduction technique.'); - end - - % JDQR makes empty figure; close it - if strcmp(eig_impl, 'JDQR') - close(gcf); - end - - % Handle PRTools dataset - if prtools == 1 - if sum(strcmp(type, {'Isomap', 'LandmarkIsomap', 'FastMVU'})) - AA = AA(mapping.conn_comp,:); - end - AA.data = mappedA; - mappedA = AA; - end - \ No newline at end of file diff --git a/code/dimReducMethods/compute_recon_err.m b/code/dimReducMethods/compute_recon_err.m deleted file mode 100644 index e54a68f..0000000 --- a/code/dimReducMethods/compute_recon_err.m +++ /dev/null @@ -1,54 +0,0 @@ -function err = compute_recon_err(machine, X) -%COMPUTE_RECON_ERROR Computes reconstruction error of RBM on dataset X -% -% err = compute_recon_error(machine, X) -% err = compute_recon_error(network, X) -% -% Computes reconstruction error of the RBM specified in machine or the RBMs -% specified in the netwerk, on the dataset specified in X. The -% reconstruction error is normalized for the number of datapoints, and is -% returned in err. -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if iscell(machine) - - % Run for every layer in the network - err = zeros(1, length(machine)); - vis = double(X); - for i=1:length(machine) - - % Compute probabilities for hidden nodes - if i < length(machine) - hid = 1 ./ (1 + exp(-(bsxfun(@plus, vis * machine{i}.W, machine{i}.bias_upW)))); - else - hid = bsxfun(@plus, vis * machine{i}.W, machine{i}.bias_upW); - end - - % Compute probabilities for visible nodes - rec = 1 ./ (1 + exp(-(bsxfun(@plus, hid * machine{i}.W', machine{i}.bias_downW)))); - - % Compute reconstruction error - err(i) = sum(sum((vis - rec) .^ 2)) ./ size(X, 1); - vis = hid; - end - else - - % Compute probabilities for hidden nodes - hid = 1 ./ (1 + exp(-(bsxfun(@plus, double(X) * machine.W, machine.bias_upW)))); - - % Compute probabilities for visible nodes - rec = 1 ./ (1 + exp(-(bsxfun(@plus, hid * machine.W', machine.bias_downW)))); - - % Compute reconstruction error - err = sum(sum((X - rec) .^ 2)) ./ size(X, 1); - end - \ No newline at end of file diff --git a/code/dimReducMethods/computegr.c b/code/dimReducMethods/computegr.c deleted file mode 100644 index cc40c1b..0000000 --- a/code/dimReducMethods/computegr.c +++ /dev/null @@ -1,124 +0,0 @@ -/* - * ============================================================= - * computegr.c - * - * input: x,i,j,d - * x : matrix DxN - * i,j : indices of neighbors 1xC - * d : distances 1xC - * - * output: - * dx : matrix DxN - * ============================================================= - */ - -/* $Revision: 1.1 $ */ - -#include "mex.h" - -/* If you are using a compiler that equates NaN to zero, you must - * compile this example using the flag -DNAN_EQUALS_ZERO. For - * example:ç - * - * mex -DNAN_EQUALS_ZERO findnz.c - * - * This will correctly define the IsNonZero macro for your - compiler. */ - -#if NAN_EQUALS_ZERO -#define IsNonZero(d) ((d) != 0.0 || mxIsNaN(d)) -#else -#define IsNonZero(d) ((d) != 0.0) -#endif - -#define Xp prhs[0] -#define ip prhs[1] -#define jp prhs[2] -#define distp prhs[3] - -double square(double x) { return(x*x);} - -void mexFunction(int nlhs, mxArray *plhs[], - int nrhs, const mxArray *prhs[]) -{ - /* Declare variables. */ - - double *obj,objective,*dX, *X, *dist,weight,curdist, *ind1,*ind2,*v1,*v2,*vo, *dummy; - double pev=1.0,mev=1.0,*ev,*av,*bv; - int m,p,n,inds; - int oldi1=-1,i1,i2,j,i,r,c; - int ione=1; - char *chu="U"; - char *chl="L"; - char *chn2="T"; - char *chn="N"; - double minusone=-1.0,one=1.0, zero=0.0; - - - - /* Check for proper number of input and output arguments. */ - if (nrhs!=4) mexErrMsgTxt("Exactly one or two input arguments required."); - - - if (nlhs > 2) { - mexErrMsgTxt("Too many output arguments."); - } - - /* Check data type of input argument. */ - if (!(mxIsDouble(prhs[0]))) { - mexErrMsgTxt("Input array must be of type double."); - } - - n = mxGetN(Xp); - m = mxGetM(Xp); - c = mxGetNumberOfElements(distp); - - /* Get the data. */ - X = mxGetPr(Xp); - ind1 = mxGetPr(ip); - ind2 = mxGetPr(jp); - dist = mxGetPr(distp); - - /* Create output matrix */ - plhs[0]=mxCreateDoubleMatrix(m,n,mxREAL); - dX=mxGetPr(plhs[0]); - plhs[1]=mxCreateDoubleMatrix(1,1,mxREAL); - obj=mxGetPr(plhs[1]); - - /* create space for dummy vectors */ - dummy=malloc(m*sizeof(double)); - - weight=0; - oldi1=-1; - v1=&X[0];v2=&X[0];vo=&dX[0]; - objective=0; - for(i=0;i4Ho}RrTasyInqP$pkMD$s{g5^O5$j&%U+qocnP1 zc8yWJm75Dyx5LG#ege?!U;1Hs@#mgj zjLs~4b>*O|;nkJ?a3slf%ZW}o7~|T5@pwYv+9Xa^<6I=p)!*O5#S$UOTUvTYMbUMm zh){!T0jg);0%WyGw0Pwrmy1Dnz?ikTt#?B20jZ>855*-2xvXg#KZV_JCCNY|c~K)` zM+|6R>{=1>6S@weJove7YeeYKZ72Wr39lmcDqzmI;R12dz8JUdl|!i2D~Ezguox>4 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W{U3%BPC7d42(S8TU5Sdz20U$GtWB0=~$uCF8b6TglqLHHFeqKgn~ zq2Eimh(2c0|6$U}A}SRG`Vf)IhyR3=LfoYD|J0z{O?ud6&^;zyzsR5|ZX=<6`u`nL z7>VcxGrmG08ITsEwjkV*MN>B@H^V;&4I4DFj9)N|UYA8bo<%=x&=cd~?I!=9a(J~Z zT#f4*Tr@`;E;}y#ia)PTzCiMtkQEW1A+8CnO6${9P5NvdLP=VCjHDN1Qr5k~WjY)P zR#jG(2Sa6~Yk|khgJo4A{;UbF=Fh4y=(VeURE{$I+d&}^UXQxvayoIB5U4H>Rzb&P HzWDzII4Uv^ diff --git a/code/dimReducMethods/mgs.m b/code/dimReducMethods/mgs.m deleted file mode 100644 index cef15d8..0000000 --- a/code/dimReducMethods/mgs.m +++ /dev/null @@ -1,34 +0,0 @@ -function [Q, R] = mgs(A) -%MGS Performs a modified Gram-Schmidt orthogonalization -% -% [Q, R] = mgs(A) -% -% Performs a modified Gram-Schmidt orthogonalization. This is a more stable -% way to compute the Gram-Schmidt orthogonalization than Matlab's one. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Perform Gram-Schmidt orthogonalization - [m, n] = size(A); - V = A; - R = zeros(n, n); - for i=1:n - R(i,i) = norm(V(:,i)); - V(:,i) = V(:,i) / R(i, i); - if (i < n) - for j=i+1:n - R(i,j) = V(:,i)' * V(:,j); - V(:,j) = V(:,j) - R(i, j) * V(:,i); - end - end - end - Q = V; diff --git a/code/dimReducMethods/minimize.m b/code/dimReducMethods/minimize.m deleted file mode 100644 index da94b82..0000000 --- a/code/dimReducMethods/minimize.m +++ /dev/null @@ -1,156 +0,0 @@ -function [X, fX, i] = minimize(X, f, length, P1, P2, P3, P4, P5, P6); - -% Minimize a continuous differentialble multivariate function. Starting point -% is given by "X" (D by 1), and the function named in the string "f", must -% return a function value and a vector of partial derivatives. The Polack- -% Ribiere flavour of conjugate gradients is used to compute search directions, -% and a line search using quadratic and cubic polynomial approximations and the -% Wolfe-Powell stopping criteria is used together with the slope ratio method -% for guessing initial step sizes. Additionally a bunch of checks are made to -% make sure that exploration is taking place and that extrapolation will not -% be unboundedly large. The "length" gives the length of the run: if it is -% positive, it gives the maximum number of line searches, if negative its -% absolute gives the maximum allowed number of function evaluations. You can -% (optionally) give "length" a second component, which will indicate the -% reduction in function value to be expected in the first line-search (defaults -% to 1.0). The function returns when either its length is up, or if no further -% progress can be made (ie, we are at a minimum, or so close that due to -% numerical problems, we cannot get any closer). If the function terminates -% within a few iterations, it could be an indication that the function value -% and derivatives are not consistent (ie, there may be a bug in the -% implementation of your "f" function). The function returns the found -% solution "X", a vector of function values "fX" indicating the progress made -% and "i" the number of iterations (line searches or function evaluations, -% depending on the sign of "length") used. -% -% Usage: [X, fX, i] = minimize(X, f, length, P1, P2, P3, P4, P5, P6) -% -% See also: checkgrad -% -% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13 -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - -RHO = 0.01; % a bunch of constants for line searches -SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions -INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket -EXT = 3.0; % extrapolate maximum 3 times the current bracket -MAX = 20; % max 20 function evaluations per line search -RATIO = 100; % maximum allowed slope ratio - -argstr = [f, '(X']; % compose string used to call function -for i = 1:(nargin - 3) - argstr = [argstr, ',P', int2str(i)]; -end -argstr = [argstr, ')']; - -if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end -if length>0, S=['Linesearch']; else S=['Function evaluation']; end - -i = 0; % zero the run length counter -ls_failed = 0; % no previous line search has failed -fX = []; -[f1 df1] = eval(argstr); % get function value and gradient -i = i + (length<0); % count epochs?! -s = -df1; % search direction is steepest -d1 = -s'*s; % this is the slope -z1 = red/(1-d1); % initial step is red/(|s|+1) - -while i < abs(length) % while not finished - i = i + (length>0); % count iterations?! - - X0 = X; f0 = f1; df0 = df1; % make a copy of current values - X = X + z1*s; % begin line search - [f2 df2] = eval(argstr); - i = i + (length<0); % count epochs?! - d2 = df2'*s; - f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1 - if length>0, M = MAX; else M = min(MAX, -length-i); end - success = 0; limit = -1; % initialize quanteties - while 1 - while ((f2 > f1+z1*RHO*d1) | (d2 > -SIG*d1)) & (M > 0) - limit = z1; % tighten the bracket - if f2 > f1 - z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit - else - A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit - B = 3*(f3-f2)-z3*(d3+2*d2); - z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok! - end - if isnan(z2) | isinf(z2) - z2 = z3/2; % if we had a numerical problem then bisect - end - z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits - z1 = z1 + z2; % update the step - X = X + z2*s; - [f2 df2] = eval(argstr); - M = M - 1; i = i + (length<0); % count epochs?! - d2 = df2'*s; - z3 = z3-z2; % z3 is now relative to the location of z2 - end - if f2 > f1+z1*RHO*d1 | d2 > -SIG*d1 - break; % this is a failure - elseif d2 > SIG*d1 - success = 1; break; % success - elseif M == 0 - break; % failure - end - A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation - B = 3*(f3-f2)-z3*(d3+2*d2); - z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok! - if ~isreal(z2) | isnan(z2) | isinf(z2) | z2 < 0 % num prob or wrong sign? - if limit < -0.5 % if we have no upper limit - z2 = z1 * (EXT-1); % the extrapolate the maximum amount - else - z2 = (limit-z1)/2; % otherwise bisect - end - elseif (limit > -0.5) & (z2+z1 > limit) % extraplation beyond max? - z2 = (limit-z1)/2; % bisect - elseif (limit < -0.5) & (z2+z1 > z1*EXT) % extrapolation beyond limit - z2 = z1*(EXT-1.0); % set to extrapolation limit - elseif z2 < -z3*INT - z2 = -z3*INT; - elseif (limit > -0.5) & (z2 < (limit-z1)*(1.0-INT)) % too close to limit? - z2 = (limit-z1)*(1.0-INT); - end - f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2 - z1 = z1 + z2; X = X + z2*s; % update current estimates - [f2 df2] = eval(argstr); - M = M - 1; i = i + (length<0); % count epochs?! - d2 = df2'*s; - end % end of line search - - if success % if line search succeeded - f1 = f2; fX = [fX' f1]'; -% fprintf('%s %6i; Value %4.6e\r', S, i, f1); - s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction - tmp = df1; df1 = df2; df2 = tmp; % swap derivatives - d2 = df1'*s; - if d2 > 0 % new slope must be negative - s = -df1; % otherwise use steepest direction - d2 = -s'*s; - end - z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO - d1 = d2; - ls_failed = 0; % this line search did not fail - else - X = X0; f1 = f0; df1 = df0; % restore point from before failed line search - if ls_failed | i > abs(length) % line search failed twice in a row - break; % or we ran out of time, so we give up - end - tmp = df1; df1 = df2; df2 = tmp; % swap derivatives - s = -df1; % try steepest - d1 = -s'*s; - z1 = 1/(1-d1); - ls_failed = 1; % this line search failed - end -end diff --git a/code/dimReducMethods/mppca.m b/code/dimReducMethods/mppca.m deleted file mode 100644 index 8961dca..0000000 --- a/code/dimReducMethods/mppca.m +++ /dev/null @@ -1,124 +0,0 @@ -function [LX, MX, PX] = mppca(X, no_dims, no_analyzers, tol, maxiter, minstd) -%MPPCA Runs EM algorithm and computes local factor analyzers -% -% [LX, MX, PX] = mppca(X, no_dims, no_analyzers, tol, maxiter, minstd) -% -% Runs EM algorithm to determine coordinates of factor analyzers. The data -% is given in the DxN matrix X. no_dims indicates the number of dimensions that -% the local factor analyzers compute their embedding in. The number of -% factor analyzers that is used is given by no_analyzers. The variable tol indicates -% the tolreance in considering the EM as converged, whereas maxiter -% indicates the maximum number of iterations for the EM algorithm. The -% variable minstd sets the minimum standard deviation of the Gaussians that -% the EM algorithm fits. -% The function returns in LX the lowdimensional representations of X of all -% factor analyzers, in MX the means of the factors analyzers, and in PX the -% noise covariances. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Initialize some variables - [D N] = size(X); % size of data - epsilon = 1e-9; % regularization parameter - - % Estimate minimum variance allowed - minvar = minstd ^ 2; - - % Randomly initialize factor analyzers - mm = mean(X, 2); - ss = cov(X'); - try % for small problems - cc = chol(ss); - MX = bsxfun(@plus, cc' * randn(D, no_analyzers), mm); - LX = minstd * randn(D, no_dims, no_analyzers); - PX = 2 * mean(diag(cc)) * ones(D, 1); - catch % for large problems (or nearly singular covariance matrices) - cc = std(X, [], 2); - MX = bsxfun(@plus, bsxfun(@times, cc, randn(D, no_analyzers)), mm); - LX = minstd * randn(D, no_dims, no_analyzers); - PX = 2 * mean(cc) * ones(D, 1); - end - clear mm ss cc - - % Compute squared data - X2 = X .^ 2; - - % Initialize some variables - const = -D / 2 * log(2 * pi); - lik = -Inf; - R = zeros(no_analyzers, N); - czz = zeros(no_dims, no_dims, no_analyzers); - zz = zeros(no_dims, N, no_analyzers); - - % Run for maxiter iterations at max - for i=1:maxiter - - % Progress bar - if rem(i, 10) == 0 - fprintf('.'); - end - - % E step - pii = 1 ./ PX; - for k=1:no_analyzers - l = LX(:,:,k); % select k-th local representation - ltpi = bsxfun(@times, pii, l)'; - ltpil = ltpi * l; - iltpil = eye(no_dims) + ltpil; - cc = chol(iltpil); - cci = inv(cc); - covz = cci * cci'; % compute covariance - delta = X - MX(:,k * ones(1, N)); - meanz = ((eye(no_dims) - ltpil * covz) * ltpi) * delta; - czz(:,:,k) = covz; - zz(:,:,k) = meanz; % update local representation - R(k,:) = -.5 * (pii' * (delta .* delta) - sum(meanz .* (iltpil * meanz), 1)) - ... % update reponsibilie - sum(log(diag(cc))); - end - - % Compute responsibilities of datapoints to the clusters - R = R + const + .5 * sum(log(pi)); - R = exp(bsxfun(@minus, R, max(R, [], 1))); - R = bsxfun(@rdivide, R, sum(R, 1)); - - % Update likelihood of estimation - oldlik = lik; - lik = sum(max(R, [], 1) + log(sum(R, 1))); - - % Stop EM after convergence - if abs(oldlik - lik) < tol - break; - end - - % M step - PX = 0; - for k=1:no_analyzers % Update all factor analyzers - r = R(k,:); - z = zz(:,:,k); - rz = bsxfun(@times, z, r); - sr = sum(r); - srz = sum(rz, 2); - srxz = X * rz'; - srx = X * r'; - m1 = [srxz srx]; - m2 = [sr * czz(:,:,k) + z * rz' srz; srz' sr]; - m1 = m1 / (m2 + (rand(size(m2)) * epsilon)); % random regularization to make sure that INV(m2) does not contain Infs - LX(:,:,k) = m1(:,1:no_dims); - MX(:,k) = m1(:,no_dims + 1); - PX = PX + X2 * r' - sum(LX(:,:,k) .* srxz, 2) - MX(:,k) .* srx; - end - PX = max(minvar, PX / N); - PX(:) = mean(PX); - end - - % Done - disp(' '); diff --git a/code/dimReducMethods/mvu_x.m b/code/dimReducMethods/mvu_x.m deleted file mode 100644 index 7fed5f9..0000000 --- a/code/dimReducMethods/mvu_x.m +++ /dev/null @@ -1,47 +0,0 @@ -function Y = mvu_x(X, no_dims, K, lambda) -%MVU_X This file is not currently used by the toolbox - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('lambda', 'var') || isempty(lambda) - lambda = .5; - end - - % Build nearest neighborhood graph and compute distances - disp('Computing nearest-neighbor graph...'); - N = size(X, 1); - [D, ni] = find_nn(X, K); - DX = zeros(N, K); - for n=1:N - DX(n,:) = full(D(n, ni(n,:))); - end - DX = DX .^ 2; - - % Initialize solution - init_Y = compute_mapping(X, 'PCA', no_dims); - Y = cell(length(lambda), 1); - - % Loop over all values of lambda -% checkgrad('mvu_x_grad', init_Y(:), 1e-7, N, no_dims, ni, K, DX, lambda) - for i=1:length(lambda) - - % Perform learning - Y{i} = init_Y; - options.Method = 'lbfgs'; - options.MaxIter = 5000; - options.MaxFunEvals = 10000; - options.Display = 'on'; - Y{i} = reshape(minFunc(@mvu_x_grad, Y{i}(:), options, N, no_dims, ni, K, DX, lambda(i)), [N no_dims]); - - % Make sure solution is zero-mean - Y{i} = bsxfun(@minus, Y{i}, mean(Y{i}, 1)); - end -end - diff --git a/code/dimReducMethods/mvu_x_grad.m b/code/dimReducMethods/mvu_x_grad.m deleted file mode 100644 index 41b74be..0000000 --- a/code/dimReducMethods/mvu_x_grad.m +++ /dev/null @@ -1,45 +0,0 @@ -function [C, dC] = mvu_x_grad(Y, N, no_dims, ni, K, DX, lambda) -%MVU_X_GRAD This file is not currently used by the toolbox - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - - % Decode solution - Y = reshape(Y, [N no_dims]); - - % Compute slack - DY = zeros(N, K); - sum_Y = sum(Y .^ 2, 2); - for k=1:K - DY(:,k) = sum_Y + sum_Y(ni(:,k)) - 2 * sum(Y .* Y(ni(:,k),:), 2); - end - slack = DX - DY; - - % Compute cost function - Yn = bsxfun(@minus, Y, mean(Y, 1)); - C = -lambda .* sum(Yn(:) .^ 2) + (1 - lambda) .* sum(abs(slack(:))); - - % Compute gradient - if nargout > 1 - - % Compute gradient w.r.t. objective - dC = 2 .* lambda .* Yn; - - % Add gradient w.r.t. slack - for k=1:K - grad = bsxfun(@times, 2 .* (1 - lambda) .* sign(slack(:,k)), Y - Y(ni(:,k),:)); - dC = dC - grad; - for d=1:no_dims - dC(:,d) = dC(:,d) + accumarray(ni(:,k), grad(:,d), [N 1]); - end - end - dC = dC(:); - end - \ No newline at end of file diff --git a/code/dimReducMethods/nca.m b/code/dimReducMethods/nca.m deleted file mode 100644 index cf70e11..0000000 --- a/code/dimReducMethods/nca.m +++ /dev/null @@ -1,70 +0,0 @@ -function [mappedX, mapping] = nca(X, labels, no_dims, lambda) -%NCA Performs NCA on the specified dataset -% -% [mappedX, mapping] = nca(X, labels, no_dims, lambda) -% -% Performs linear Neighborhood Components Analysis (NCA) on the -% dataset specified through X and labels to reduce the data dimensionality -% to no_dims dimensions. If valid_X and valid_labels are specified, the -% function uses early stopping based on NN errors. -% The function returns a embedded data in mappedX, as well as th mapping. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - - if ~exist('no_dims', 'var') || isempty(no_dims) - no_dims = size(X, 2); - end - if ~exist('lambda', 'var') || isempty(lambda) - lambda = 0; - end - - % Make sure data is zero mean - mapping.mean = mean(X, 1); - X = bsxfun(@minus, X, mapping.mean); - - % Initialize some variables - max_iter = 200; - [n, d] = size(X); - batch_size = min(5000, n); - no_batches = ceil(n / batch_size); - max_iter = ceil(max_iter / no_batches); - [lablist, foo, labels] = unique(labels); - A = randn(d, no_dims) * .01; - converged = false; - iter = 0; - - % Main iteration loop - while iter < max_iter && ~converged - - % Loop over batches - iter = iter + 1; - disp(['Iteration ' num2str(iter) ' of ' num2str(max_iter) '...']); - ind = randperm(n); - for batch=1:batch_size:n - - % Run NCA minimization using three linesearches - cur_X = double(X(ind(batch:min([batch + batch_size - 1 n])),:)); - cur_labels = labels(ind(batch:min([batch + batch_size - 1 n]))); - [A, f] = minimize(A(:), 'nca_lin_grad', 5, cur_X, cur_labels, no_dims, lambda); - A = reshape(A, [d no_dims]); - if isempty(f) || f(end) - f(1) > -1e-4 - disp('Converged!'); - converged = true; - end - end - end - - % Compute embedding - mapping.M = A; - mappedX = X * mapping.M; - \ No newline at end of file diff --git a/code/dimReducMethods/nca_lin_grad.m b/code/dimReducMethods/nca_lin_grad.m deleted file mode 100644 index cf1340e..0000000 --- a/code/dimReducMethods/nca_lin_grad.m +++ /dev/null @@ -1,66 +0,0 @@ -function [F, dF] = nca_lin_grad(x, X, labels, no_dims, lambda) -%NCA_LIN_GRAD Computes NCA gradient on the specified dataset -% -% [C, dC] = nca_lin_grad(x, X, labels, no_dims, lambda) -% -% Computes the linear Neighborhood Components Analysis (NCA) gradient -% on the dataset specified through X and labels to reduce the data -% dimensionality to no_dims dimensions. The current solutions is specified -% in x. The function returns the current value of the cost function in C -% and the gradient in dC. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('lambda', 'var') || isempty(lambda) - lambda = 0; - end - - % Initialize some variables - n = size(X, 1); - A = reshape(x, [numel(x) / no_dims no_dims]); - F = 0; - dF = zeros(size(A)); - - % Transform the data - Y = X * A; - - % Compute conditional probabilities for current solution - sumY = sum(Y .^ 2, 2); - P = exp(bsxfun(@minus, bsxfun(@minus, 2 * (Y * Y'), sumY'), sumY)); - P(1:n+1:end) = 0; - P = bsxfun(@rdivide, P, sum(P, 2)); - P = max(P, eps); - - % Compute value of cost function and gradient - for i=1:n - - % Sum cost function - inds = (labels == labels(i)); - Pi = sum(P(i, inds)); - F = F + Pi; - - % Sum gradient - if nargout > 1 - xikA = bsxfun(@minus, Y(i,:), Y); - xik = bsxfun(@minus, X(i,:), X); - dF = dF + Pi * (bsxfun(@times, xik, P(i,:)')' * xikA) - ... - bsxfun(@times, xik(inds,:), P(i, inds)')' * xikA(inds,:); - end - end - - % Include regularization term - F = F - lambda .* sum(A(:) .^ 2) ./ numel(A); - dF = 2 * dF - 2 * lambda .* A ./ numel(A); - - % Prepare to pass to minimize - F = -F; - dF = -dF(:); diff --git a/code/dimReducMethods/npe.m b/code/dimReducMethods/npe.m deleted file mode 100644 index d4356f6..0000000 --- a/code/dimReducMethods/npe.m +++ /dev/null @@ -1,122 +0,0 @@ -function [mappedX, mapping] = npe(X, no_dims, k, eig_impl) -%NPE Perform the Neighborhood Preserving Embedding algorithm -% -% [mappedX, mapping] = npe(X, no_dims, k) -% [mappedX, mapping] = npe(X, no_dims, k, eig_impl) -% -% Runs the Neighborhood Preserving Embedding algorithm on dataset X to -% reduce it to dimensionality no_dims. The number of neighbors that is used -% by LPP is specified by k (default = 12). -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if size(X, 2) > size(X, 1) - error('Number of samples should be higher than number of dimensions.'); - end - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('eig_impl', 'var') - eig_impl = 'Matlab'; - end - - % Get dimensionality and number of dimensions - [n, d] = size(X); - mapping.mean = mean(X, 1); - - % Compute pairwise distances and find nearest neighbours (vectorized implementation) - disp('Finding nearest neighbors...'); - [distance, neighborhood] = find_nn(X, k); - max_k = size(neighborhood, 2); - if nargout > 1 - mapping.nbhd = distance; - end - X = X'; - neighborhood = neighborhood'; - - % Find reconstruction weights for all points by solving the MSE problem - % of reconstructing a point from each neighbours. A used constraint is - % that the sum of the reconstruction weights for a point should be 1. - disp('Compute reconstruction weights...'); - if k > d - tol = 1e-5; - else - tol = 0; - end - - % Construct reconstruction weight matrix - W = zeros(max_k, n); - for i=1:n - nbhd = neighborhood(:,i); - if ischar(k) - nbhd = nbhd(nbhd ~= 0); - end - kt = numel(nbhd); - z = X(:,nbhd) - repmat(X(:,i), 1, kt); % Shift point to origin - C = z' * z; % Compute local covariance - C = C + eye(kt, kt) * tol * trace(C); % Regularization of covariance (if K > D) - wi = C \ ones(kt, 1); % Solve linear system - wi = wi / sum(wi); % Make sure that sum is 1 - W(:,i) = [wi; nan(max_k - kt, 1)]; - end - - % Now that we have the reconstruction weights matrix, we define the - % sparse cost matrix M = (I-W)'*(I-W). - M = sparse(1:n, 1:n, ones(1, n), n, n, 4 * max_k * n); - for i=1:n - w = W(:,i); - w(isnan(w)) = 0; - j = neighborhood(:,i); - w = w(j ~= 0); - j = j(j ~= 0); - M(i, j) = M(i, j) - w'; - M(j, i) = M(j, i) - w; - M(j, j) = M(j, j) + w * w'; - end - - % For sparse datasets, we might end up with NaNs or Infs in M. We just set them to zero for now... - M(isnan(M)) = 0; - M(isinf(M)) = 0; - - % Compute XWX and XX and make sure these are symmetric - X = X'; - WP = X' * M * X; - DP = X' * X; - DP = (DP + DP') / 2; - WP = (WP + WP') / 2; - - % Solve generalized eigenproblem - if size(X, 1) > 1500 && no_dims < (size(X, 1) / 10) - if strcmp(eig_impl, 'JDQR') - options.Disp = 0; - options.LSolver = 'bicgstab'; - [eigvector, eigvalue] = jdqz(WP, DP, no_dims, 'SA', options); - else - options.disp = 0; - options.issym = 1; - options.isreal = 0; - [eigvector, eigvalue] = eigs(WP, DP, no_dims, 'SA', options); - end - else - [eigvector, eigvalue] = eig(WP, DP); - end - - % Sort eigenvalues in descending order and get smallest eigenvectors - [eigvalue, ind] = sort(diag(eigvalue), 'ascend'); - eigvector = eigvector(:,ind(1:no_dims)); - - % Compute final linear basis and map data - mappedX = X * eigvector; - mapping.M = eigvector; diff --git a/code/dimReducMethods/param.csdp b/code/dimReducMethods/param.csdp deleted file mode 100644 index c98303b..0000000 --- a/code/dimReducMethods/param.csdp +++ /dev/null @@ -1,16 +0,0 @@ -axtol=1.000000e-08 -atytol=1.000000e-08 -objtol=1.000000e-08 -pinftol=1.000000e+08 -dinftol=1.000000e+08 -maxiter=100 -minstepfrac=9.000000e-01 -maxstepfrac=9.700000e-01 -minstepp=1.000000e-08 -minstepd=1.000000e-08 -usexzgap=1 -tweakgap=0 -affine=0 -printlevel= 0 -printlevel=1 -printlevel=0 diff --git a/code/dimReducMethods/pca.m b/code/dimReducMethods/pca.m deleted file mode 100644 index 230f62a..0000000 --- a/code/dimReducMethods/pca.m +++ /dev/null @@ -1,67 +0,0 @@ -function [mappedX, mapping] = pca(X, no_dims) -%PCA Perform the PCA algorithm -% -% [mappedX, mapping] = pca(X, no_dims) -% -% The function runs PCA on a set of datapoints X. The variable -% no_dims sets the number of dimensions of the feature points in the -% embedded feature space (no_dims >= 1, default = 2). -% For no_dims, you can also specify a number between 0 and 1, determining -% the amount of variance you want to retain in the PCA step. -% The function returns the locations of the embedded trainingdata in -% mappedX. Furthermore, it returns information on the mapping in mapping. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - - % Make sure data is zero mean - mapping.mean = mean(X, 1); - X = bsxfun(@minus, X, mapping.mean); - - % Compute covariance matrix - if size(X, 2) < size(X, 1) - C = cov(X); - else - C = (1 / size(X, 1)) * (X * X'); % if N>D, we better use this matrix for the eigendecomposition - end - - % Perform eigendecomposition of C - C(isnan(C)) = 0; - C(isinf(C)) = 0; - [M, lambda] = eig(C); - - % Sort eigenvectors in descending order - [lambda, ind] = sort(diag(lambda), 'descend'); - if no_dims < 1 - no_dims = find(cumsum(lambda ./ sum(lambda)) >= no_dims, 1, 'first'); - disp(['Embedding into ' num2str(no_dims) ' dimensions.']); - end - if no_dims > size(M, 2) - no_dims = size(M, 2); - warning(['Target dimensionality reduced to ' num2str(no_dims) '.']); - end - M = M(:,ind(1:no_dims)); - lambda = lambda(1:no_dims); - - % Apply mapping on the data - if ~(size(X, 2) < size(X, 1)) - M = bsxfun(@times, X' * M, (1 ./ sqrt(size(X, 1) .* lambda))'); % normalize in order to get eigenvectors of covariance matrix - end - mappedX = X * M; - - % Store information for out-of-sample extension - mapping.M = M; - mapping.lambda = lambda; - \ No newline at end of file diff --git a/code/dimReducMethods/readsol.m b/code/dimReducMethods/readsol.m deleted file mode 100644 index 1b1dccc..0000000 --- a/code/dimReducMethods/readsol.m +++ /dev/null @@ -1,210 +0,0 @@ -function [x,y,z]=readsol(fname,K,m) -%READSOL Read solution from CSDP -% -% [x,y,z]=readsol(fname,K,m) -% -% fname File name to read solution from. -% K structure of the matrices. -% m size of y vector. -% -% Modified 7/15/04, for greater MATLAB acceleration. -% -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - -% -% First, eliminate special cases that we don't handle. -% -% -% Check for any quadratic cone constraints. -% -if isfield(K,'q') - if ((~isempty(K.q)) & (K.q ~= 0)) - fprintf('quadratic cone constraints are not supported.\n'); - return - end -end -% -% Check for any rotated cone constraints. -% -if isfield(K,'r') - if ((~isempty(K.r)) & (K.r ~= 0)) - fprintf('rotated cone constraints are not supported.\n'); - return - end -end -% -% Check for any free variables. -% -if isfield(K,'f') - if ((~isempty(K.f)) & (K.f ~= 0)) - fprintf('Free variables are not supported.\n'); - return - end -end -% -% Figure out the structure of the LP and SDP blocks. -% -if (isfield(K,'l')) - if (K.l > 0) - nlin=K.l; - else - K.l=0; - nlin=0; - end -else - K.l=0; - nlin=0; -end -% -% Patched on 10/23/03 to handle all kinds of stupid ways of indicating -% no SDP block. -% -if (isfield(K,'s')) - if (length(K.s) > 1) - nsdpblocks=length(K.s); - else - if (length(K.s)==1) - if (K.s==0) - nsdpblocks=0; - K.s=[]; - else - nsdpblocks=1; - end - else - nsdpblocks=0; - K.s=[]; - end - end -else - K.s=[]; - nsdpblocks=0; -end - -% -% First, where everything is in the vector. -% -% vecsdpbase(i)=point in vector at which SDP block i starts. -% v(1..nlin) LP variables. -% -base=nlin+1; -for i=1:length(K.s) - vecsdpbase(i)=base; - base=base+(K.s(i))^2; -end - -% -% Second, where everything is in the matrix. -% -% matsdpbase(i)= index of upper left corner of SDP block i. -% matlpbase index of start of LP block. -% -base=1; -for i=1:length(K.s) - matsdpbase(i)=base; - base=base+K.s(i); -end -matlpbase=base; -% -% Setup an array containing blocksizes. blocksize(i) is used as a faster -% synonym for K.s(i) in what follows. This is because MATLAB doesn't -% accelerate statements involving fields. -% -if (nsdpblocks >= 1) - blocksizes=zeros(nsdpblocks,1); - for i=1:nsdpblocks - blocksizes(i)=K.s(i); - end -end -% -% Open up the file. -% -fid=fopen(fname,'r'); -if (fid == -1) - fprintf('file does not exist!\n'); - return -end -% -% Read y. -% -y=fscanf(fid,'%le',m); -% -% Read the remaining entries. -% -[A,count]=fscanf(fid,'%d %d %d %d %le',[5,inf]); -count=count/5; -% -% Allocate storage for x and z. -% -if ((length(K.s) > 1) | (length(K.s==1) & (K.s>0))) - veclength=vecsdpbase(length(K.s))+K.s(nsdpblocks)^2-1; -else - veclength=nlin; -end -% -% Allocate space for x and z. We could use sparse vectors here, but -% the dense vector is vastly faster. -% -x=zeros(veclength,1); -z=zeros(veclength,1); -% -% now, loop through the entries and put them into x and z. -% -for i=1:count - if (A(1,i)==1) -% -% A z entry. -% - blk=A(2,i); - indexi=A(3,i); - indexj=A(4,i); - ent=A(5,i); - - if (blk==nsdpblocks+1) - z(indexi)=ent; - else -% -% In one of the SDP blocks. -% -% [blk, indexi, indexj, K.s(blk)] - - z(vecsdpbase(blk)+indexi+(indexj-1)*blocksizes(blk)-1)=ent; - z(vecsdpbase(blk)+indexj+(indexi-1)*blocksizes(blk)-1)=ent; - end - else -% -% An x entry. -% - blk=A(2,i); - indexi=A(3,i); - indexj=A(4,i); - ent=A(5,i); - - if (blk==nsdpblocks+1) - x(indexi)=ent; - else -% -% In one of the SDP blocks. -% - x(vecsdpbase(blk)+indexi+(indexj-1)*blocksizes(blk)-1)=ent; - x(vecsdpbase(blk)+indexj+(indexi-1)*blocksizes(blk)-1)=ent; - end - end -end -% -% Correction for the difference between CSDP and SeDuMi primal/dual pair. -% -y=-y; -% -% close the file. -% -fclose(fid); diff --git a/code/dimReducMethods/recon_data_from_autoenc.m b/code/dimReducMethods/recon_data_from_autoenc.m deleted file mode 100644 index 4f37a6d..0000000 --- a/code/dimReducMethods/recon_data_from_autoenc.m +++ /dev/null @@ -1,28 +0,0 @@ -function reconX = recon_data_from_autoenc(network, mappedX) -%RUN_DATA_THROUGH_AUTOENC Summary of this function goes here -% Detailed explanation goes here - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Initialize some variables - n = size(mappedX, 1); - no_layers = length(network); - - % Run data through autoencoder - activations = [mappedX ones(n, 1)]; - middle_layer = ceil(no_layers / 2); - for i=middle_layer + 1:no_layers - if i ~= no_layers - activations = [1 ./ (1 + exp(-(activations * [network{i}.W; network{i}.bias_upW]))) ones(n, 1)]; - else - activations = [activations * [network{i}.W; network{i}.bias_upW] ones(n, 1)]; - end - end - reconX = activations(:,1:end-1); diff --git a/code/dimReducMethods/roll_out.m b/code/dimReducMethods/roll_out.m deleted file mode 100644 index cc38f0a..0000000 --- a/code/dimReducMethods/roll_out.m +++ /dev/null @@ -1,29 +0,0 @@ -function autoenc = roll_out(network) -%ROLL_OUT Rolls out an autoencoder -% -% network = roll_out(network) -% -% Rolls out a stack of RBMs as an autoencoder that can be finetuned using, -% e.g., backpropagation. -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Initialize some variables - no_layers = length(network); - autoenc = cell(1, 2 * no_layers); - - % Roll out network - for i=1:no_layers - autoenc{i} = network{i}; - autoenc{2 * no_layers - i + 1}.W = network{i}.W'; - autoenc{2 * no_layers - i + 1}.bias_upW = network{i}.bias_downW; - autoenc{2 * no_layers - i + 1}.bias_downW = network{i}.bias_upW; - end diff --git a/code/dimReducMethods/run_data_through_autoenc.m b/code/dimReducMethods/run_data_through_autoenc.m deleted file mode 100644 index 5afcea7..0000000 --- a/code/dimReducMethods/run_data_through_autoenc.m +++ /dev/null @@ -1,39 +0,0 @@ -function [reconX, mappedX] = run_data_through_autoenc(network, X) -%RUN_DATA_THROUGH_AUTOENC Intermediate representation and reconstruction -% -% [reconX, mappedX] = run_data_through_autoenc(network, X) -% -% Computes intermediate representation and reconstruction of the specified -% data from the specified autoencoder. -% -% -% (C) Laurens van der Maaten -% Delft University of Technology, 2011 - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Initialize some variables - n = size(X, 1); - no_layers = length(network); - middle_layer = ceil(no_layers / 2); - - % Run data through autoencoder - activations = [X ones(n, 1)]; - for i=1:no_layers - if i ~= middle_layer && i ~= no_layers - activations = [1 ./ (1 + exp(-(activations * [network{i}.W; network{i}.bias_upW]))) ones(n, 1)]; - else - activations = [activations * [network{i}.W; network{i}.bias_upW] ones(n, 1)]; - if i == middle_layer - mappedX = activations(:,1:end-1); - end - end - end - reconX = activations(:,1:end-1); diff --git a/code/dimReducMethods/run_data_through_network.m b/code/dimReducMethods/run_data_through_network.m deleted file mode 100644 index ba7f2a8..0000000 --- a/code/dimReducMethods/run_data_through_network.m +++ /dev/null @@ -1,26 +0,0 @@ -function mappedX = run_data_through_network(network, X) -%RUN_DATA_THROUGH_NETWORK Run data through the network -% -% mappedX = run_data_through_network(network, X) -% -% Runs the dataset X through the parametric t-SNE embedding defined in -% network. The result is returned in mappedX. -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Run the data through the network - n = size(X, 1); - mappedX = [X ones(n, 1)]; - for i=1:length(network) - 1 - mappedX = [1 ./ (1 + exp(-(mappedX * [network{i}.W; network{i}.bias_upW]))) ones(n, 1)]; - end - mappedX = mappedX * [network{end}.W; network{end}.bias_upW]; - \ No newline at end of file diff --git a/code/dimReducMethods/run_llc.m b/code/dimReducMethods/run_llc.m deleted file mode 100644 index 4ea4cf4..0000000 --- a/code/dimReducMethods/run_llc.m +++ /dev/null @@ -1,58 +0,0 @@ -function mappedX = run_llc(X, no_dims, k, no_analyzers, max_iterations, eig_impl) -%RUN_LLC Performs the LLC algorithm for dimensionality reduction -% -% mappedX = run_llc(X, no_dims, k, no_analyzers, max_iterations) -% -% Performs the Locally Linear Coordination (LLC) algorithm to reduce the -% dimensionality of dataset X to no_dims dimensions. The variable k -% indicates the number of neighbors that is used in the nieghborhood graph. -% The variable no_analyzers indicates the number of factor analyzers that -% is used, and max_iterations indicates the maximum number of iterations of -% the EM-algorithm that estimates the factor analyzers. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('no_analyzers', 'var') - no_analyzers = 40; - end - if ~exist('max_iterations', 'var') - max_iterations = 200; - end - - % Initialize some parameters - tol = 1e-10; % regularization parameter - min_std = 1e-3; % minimum STD of Gaussians - - % Computes mixture of factor analyzers (using EM and PCA) - disp('Running EM algorithm and compute local factor analyzers...'); - [LX, MX, PX] = mppca(X, no_dims, no_analyzers, tol, max_iterations, min_std); - % Variables contain respectively: - % - LX Lowdimensional representations of X of all factor analyzers - % - MX Means of factor analyzers of X - % - PX Noise covariance of X - - % Construct Mixture of Factor Analyzers based on results - disp('Constructing mixture of factor analyzers...'); - [R, Z] = infermfa(X, LX, MX, PX); - % Variables contain respectively: - % - R Responsibilities of components of MFA - % - Z Mean of posteriors over latent variables of MFA - - % Run the Local Linear Coordination algorithm on the MoFA - mappedX = llc(X, k, no_dims, R, Z, eig_impl); - \ No newline at end of file diff --git a/code/dimReducMethods/sammon.m b/code/dimReducMethods/sammon.m deleted file mode 100644 index d05f105..0000000 --- a/code/dimReducMethods/sammon.m +++ /dev/null @@ -1,205 +0,0 @@ -function [y, E] = sammon(x, n, opts) -%SAMMON Performs Sammon's MDS mapping on dataset X -% -% Y = SAMMON(X) applies Sammon's nonlinear mapping procedure on -% multivariate data X, where each row represents a pattern and each column -% represents a feature. On completion, Y contains the corresponding -% co-ordinates of each point on the map. By default, a two-dimensional -% map is created. Note if X contains any duplicated rows, SAMMON will -% fail (ungracefully). -% -% [Y,E] = SAMMON(X) also returns the value of the cost function in E (i.e. -% the stress of the mapping). -% -% An N-dimensional output map is generated by Y = SAMMON(X,N) . -% -% A set of optimisation options can also be specified using a third -% argument, Y = SAMMON(X,N,OPTS) , where OPTS is a structure with fields: -% -% MaxIter - maximum number of iterations -% TolFun - relative tolerance on objective function -% MaxHalves - maximum number of step halvings -% Input - {'raw','distance'} if set to 'distance', X is -% interpreted as a matrix of pairwise distances. -% Display - {'off', 'on', 'iter'} -% Initialisation - {'pca', 'random'} -% -% The default options structure can be retrieved by calling SAMMON with -% no parameters. -% -% References : -% -% [1] Sammon, John W. Jr., "A Nonlinear Mapping for Data Structure -% Analysis", IEEE Transactions on Computers, vol. C-18, no. 5, -% pp 401-409, May 1969. -% -% See also : SAMMON_TEST - -% -% File : sammon.m -% -% Date : Monday 12th November 2007. -% -% Author : Gavin C. Cawley and Nicola L. C. Talbot -% -% Description : Simple vectorised MATLAB implementation of Sammon's non-linear -% mapping algorithm [1]. -% -% References : [1] Sammon, John W. Jr., "A Nonlinear Mapping for Data -% Structure Analysis", IEEE Transactions on Computers, -% vol. C-18, no. 5, pp 401-409, May 1969. -% -% History : 10/08/2004 - v1.00 -% 11/08/2004 - v1.10 Hessian made positive semidefinite -% 13/08/2004 - v1.11 minor optimisation -% 12/11/2007 - v1.20 initialisation using the first n principal -% components. -% -% Thanks : Dr Nick Hamilton (nick@maths.uq.edu.au) for supplying the -% code for implementing initialisation using the first n -% principal components (introduced in v1.20). -% -% To do : The current version does not take advantage of the symmetry -% of the distance matrix in order to allow for easy -% vectorisation. This may not be a good choice for very large -% datasets, so perhaps one day I'll get around to doing a MEX -% version using the BLAS library etc. for very large datasets. -% -% Copyright : (c) Dr Gavin C. Cawley, November 2007. -% -% This program is free software; you can redistribute it and/or modify -% it under the terms of the GNU General Public License as published by -% the Free Software Foundation; either version 2 of the License, or -% (at your option) any later version. -% -% This program is distributed in the hope that it will be useful, -% but WITHOUT ANY WARRANTY; without even the implied warranty of -% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -% GNU General Public License for more details. -% -% You should have received a copy of the GNU General Public License -% along with this program; if not, write to the Free Software -% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % use the default options structure - if nargin < 3 - opts.Display = 'iter'; - opts.Input = 'raw'; - opts.MaxHalves = 20; - opts.MaxIter = 500; - opts.TolFun = 1e-9; - opts.Initialisation = 'random'; - - end - - % the user has requested the default options structure - if nargin == 0 - y = opts; - return; - end - - % Create a two-dimensional map unless dimension is specified - if nargin < 2 - n = 2; - end - - % Set level of verbosity - if strcmp(opts.Display, 'iter') - display = 2; - elseif strcmp(opts.Display, 'on') - display = 1; - else - display = 0; - end - - % Create distance matrix unless given by parameters - if strcmp(opts.Input, 'distance') - D = x; - else - D = euclid(x, x); - end - - % Remaining initialisation - N = size(x, 1); - scale = 0.5 / sum(D(:)); - D = D + eye(N); - Dinv = 1 ./ D; - if strcmp(opts.Initialisation, 'pca') - [UU,DD] = svd(x); - y = UU(:,1:n)*DD(1:n,1:n); - else - y = randn(N, n); - end - one = ones(N,n); - d = euclid(y,y) + eye(N); - dinv = 1./d; - delta = D - d; - E = sum(sum((delta.^2).*Dinv)); - - % Get on with it - for i=1:opts.MaxIter - - % Compute gradient, Hessian and search direction (note it is actually - % 1/4 of the gradient and Hessian, but the step size is just the ratio - % of the gradient and the diagonal of the Hessian so it doesn't - % matter). - delta = dinv - Dinv; - deltaone = delta * one; - g = delta * y - y .* deltaone; - dinv3 = dinv .^ 3; - y2 = y .^ 2; - H = dinv3 * y2 - deltaone - 2 * y .* (dinv3 * y) + y2 .* (dinv3 * one); - s = -g(:) ./ abs(H(:)); - y_old = y; - - % Use step-halving procedure to ensure progress is made - for j=1:opts.MaxHalves - y(:) = y_old(:) + s; - d = euclid(y, y) + eye(N); - dinv = 1 ./ d; - delta = D - d; - E_new = sum(sum((delta .^ 2) .* Dinv)); - if E_new < E - break; - else - s = 0.5*s; - end - end - - % Bomb out if too many halving steps are required - if j == opts.MaxHalves - warning('MaxHalves exceeded. Sammon mapping may not converge...'); - end - - % Evaluate termination criterion - if abs((E - E_new) / E) < opts.TolFun - if display - fprintf(1, 'Optimisation terminated - TolFun exceeded.\n'); - end - break; - end - - % Report progress - E = E_new; - if display > 1 - fprintf(1, 'epoch = %d : E = %12.10f\n', i, E * scale); - end - end - - % Fiddle stress to match the original Sammon paper - E = E * scale; -end - -function d = euclid(x, y) - d = sqrt(sum(x.^2,2)*ones(1,size(y,1))+ones(size(x,1),1)*sum(y.^2,2)'-2*(x*y')); -end - diff --git a/code/dimReducMethods/sdecca2.m b/code/dimReducMethods/sdecca2.m deleted file mode 100644 index 49ac5ea..0000000 --- a/code/dimReducMethods/sdecca2.m +++ /dev/null @@ -1,218 +0,0 @@ -function [P, newY, L, newV, idx]= sdecca2(Y, snn, regularizer, relative) -% doing semidefinitve embedding/MVU with output being parameterized by graph -% laplacian's eigenfunctions.. -% -% the algorithm is same as conformal component analysis except that the scaling -% factor there is set as 1 -% -% -% function [P, newY, Y] = CDR2(X, Y, NEIGHBORS) implements the -% CONFORMAL DIMENSIONALITY REDUCTION of data X. It finds a linear map -% of Y -> L*Y such that X and L*Y is related by a conformal mapping. -% -% No tehtat The algorithm use the formulation of only distances. -% -% Input: -% Y: matrix of d'xN, with each column is a point in R^d' -% NEIGHBORS: matrix of KxN, each column is a list of indices (between 1 -% and N) to the nearest-neighbor of the corresponding column in X -% Output: -% P: square of the linear map L, i.e., P = L'*L -% newY: transformed data points, i.e., newY = L*Y; -% Y: the linear map L itself, i.e., L = L -% -% The algorithm finds L by solving a semidefinite programming problem. It -% calls csdp() SDP solver by default and assumes that it is on the path. -% -% written by feisha@cis.upenn.edu -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Collect the data - [erow, ecol, edist] = sparse_nn(snn); - irow = int32(erow); - icol = int32(ecol); - [A, B, g] = mexCCACollectData2(Y, irow, icol, edist, int32(relative)); - BG = 2 * sum(B, 2); - Q = A ; - [V, E] = eig(Q + eye(size(Q))); - E = E - eye(size(Q)); - E(E < 0) = 0; - if ~isreal(diag(E)) - E = real(E); - V = real(V); - S = sqrt(E) * V'; - else - S = sqrt(E) * V'; - end - - % Put the regularizer in there - BG = BG + regularizer * reshape(eye(size(Y, 1)), size(Y, 1) ^ 2, 1); - - % Formulate the SDP problem - [AA, bb, cc] = formulateSDP(S, size(Y, 1), BG); - sizeSDP = size(Y, 1) ^ 2 + 1 + size(Y, 1); - pars.s = sizeSDP; - opts.printlevel = 1; - - % Solve it using CSDP - [xx, yy] = csdp(AA, bb, cc, pars, opts); - - % The negate of yy is our solution - yy = -yy; - idx = 0; - P = zeros(size(Y, 1)); - for col=1:size(Y, 1) - for row = col:size(Y, 1) - idx = idx + 1; - P(row, col) = yy(idx); - end - end - - % Convert P to a positive definite matrix - P = P + P' - diag(diag(P)); - - % Transform the original projection to the new projection - [V, E] = eig(P); - E(E < 0) = 0; - L = diag(sqrt(diag(E))) * V'; - newY = L * Y; % multiply with Laplacian - - % Eigendecomposition of the new projection: doing PCA because the - % dimensionality of newY or Y is definitely less than the number of - % points - [newV, newE] = eig(newY * newY'); - newE = diag(newE); - [dummy, idx] = sort(newE); - newY = newV' * newY; - newY = newY(idx(end:-1:1),:); -return - - -% Function that formulates the SDP problem -function [A, b, c]=formulateSDP(S, D, bb) - [F0, FI, c] = localformulateSDP(S, D, bb); - [A, b, c] = sdpToSeDuMi(F0, FI, c); -return - - -% Function that formulates the SDP problem -function [F0, FI, c] = localformulateSDP(S, D, b) - - % Each FI that corresponds to the LMI for the quadratic cost function has - % precisely 2 * D^2 nonzero elements. But we need only D^2 storage for - tempFidx = zeros(D ^ 2, 3); - dimF = (D ^ 2 + 1) + D; - idx = 0; - for col=1:D - for row=col:D - idx = idx + 1; - lindx1 = sub2ind([D D], row, col); - lindx2 = sub2ind([D D], col, row); - tempFidx(:,1) = [1:D ^ 2]'; - tempFidx(:,2) = D ^ 2 + 1; - if col == row - tempFidx(:,3) = S(:,lindx1) ; - FI{idx} = sparse([tempFidx(:,1); ... % for cost function - tempFidx(:,2); ... % symmetric - row + D^2 + 1 ... % for P being p.s.d - - ], ... - [tempFidx(:,2); ... % for cost function - tempFidx(:,1); ... % symmetric - row + D^2 + 1; ... % for P being p.s.d - - ],... - [tempFidx(:,3); ... % for cost function - tempFidx(:,3); ... % symmetric - 1; % for P being p.s.d - - ], dimF, dimF); - else - - tempFidx(:,3) = S(:, lindx1) + S(:,lindx2); - FI{idx} = sparse([tempFidx(:,1); ... % for cost function - tempFidx(:,2); ... % symmetric - row + D^2 + 1; ... % for P being p.s.d - col + D^2 + 1; ... % symmetric - ], ... - [tempFidx(:,2); ... % for cost function - tempFidx(:,1); ... % symmetric - col + D^2 + 1; ... % for P being p.s.d - row + D^2 + 1; ... % being symmetric - ], ... - [tempFidx(:,3); ... % for cost function - tempFidx(:,3); ... % symmetric - 1; % for P being p.s.d - 1; % symmetric - ], dimF, dimF); - - end - end - end - idx = idx + 1; - - % For the F matrix corresponding to t - FI{idx} = sparse(D^2 + 1, D^2 + 1, 1, dimF, dimF); - - % Now for F0 - F0 = sparse(1:D^2, 1:D^2, ones(1, D^2), dimF, dimF); - - % Now for c - b = reshape(-b, D, D); - b = b * 2 - diag(diag(b)); - c = zeros(idx - 1,1); - kdx = 0; - for col=1:D - for row=col:D - kdx = kdx + 1; - c(kdx) = b(row, col); - end - end - c = [c; 1]; -return - - -% Function that convertsthe canonical SDP dual formulation to SeDuMi format -function [A, b, c] = sdpToSeDuMi(F0, FI, cc) - - % Check inputs - if nargin < 3 - error('Cannot convert SDP formulation to SeDuMi formulation.'); - end - [m, n] = size(F0); - if m ~= n - error('F0 matrix must be squared matrix.'); - end - p = length(cc); - if p ~= length(FI) - error('FI matrix cellarray must have the same length as b.'); - end - - % Converting objective function of the canonical SDP - c = reshape(F0', n * n, 1); - - % Converting equality constraints of the canonical SDP - zz = 0; - for idx=1:length(FI) - zz= zz + nnz(FI{idx}); - end - A = spalloc(n * n, p, zz); - for idx=1:p - temp = reshape(FI{idx}, n * n, 1); - lst = find(temp ~= 0); - A(lst, idx) = temp(lst); - end - - % We do not need to convert b - b = cc; -return diff --git a/code/dimReducMethods/sne.m b/code/dimReducMethods/sne.m deleted file mode 100644 index 61911f7..0000000 --- a/code/dimReducMethods/sne.m +++ /dev/null @@ -1,84 +0,0 @@ -function Y = sne(X, d, perplexity) -%SNE Implementation of Stochastic Neighbor Embedding -% -% mappedX = sne(X, no_dims, perplexity) -% -% Runs the Stochastic Neighbor Embedding algorithm using a Gaussian kernel -% with fixed perplexity. The high-dimensional datapoints are specified by X. -% The target dimensionality is specified in no_dims, and the variance of -% the Gaussian kernel may be specified through perplexity (default = 30). -% The function returns the embedded points in Y. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('d', 'var') || isempty(d) - d = 2; - end - if ~exist('perplexity', 'var') || isempty(perplexity) - perplexity = 30; - end - - % Initialize some variables - n = size(X, 1); % number of instances - eta = .05; % learning rate - max_iter = 2000; % maximum number of iterations - jitter = 0.3; % initial jitter - jitter_decay = 0.99; % jitter decay - momentum = 0.5; % initial momentum - final_momentum = 0.8; % final momentum - mom_switch_iter = 750; % iteration where momentum changes - - % Initialize embedding coordinates randomly (close to origin) - Y = 0.0001 * rand(n, d); - dC = zeros(n, d); - y_incs = zeros(n, d); - - % Compute Gaussian kernel for high-dimensional data representation - P = x2p(X, perplexity, 1e-5); % use fixed perplexity - P = max(P, eps); - - % Iterating loop - for iter=1:max_iter - - % Compute Gaussian kernel for low-dimensional data representation - sum_Y = sum(Y .^ 2, 2); % precomputation for pairwise distances - Q = exp(-bsxfun(@plus, sum_Y, bsxfun(@plus, sum_Y', -2 * Y * Y')) ./ 2); % Gaussian probabilities - Q(1:n+1:end) = 0; - Q = Q ./ repmat(sum(Q, 2), [1 n]); - Q = max(Q, eps); - - % Compute cost function between P and Q - if ~rem(iter, 20) - costs = sum(P .* log((P + eps) ./ (Q + eps)), 2) ./ n; % division by n corrects for # of datapoints - cost = sum(costs); - disp(['Iteration ' num2str(iter) ': error is ' num2str(cost)]); - end - - % Compute gradient - PQ = P - Q + P' - Q'; - for i=1:n - dC(i,:) = sum(bsxfun(@times, bsxfun(@minus, Y(i,:), Y), PQ(i,:)'), 1); - end - - % Perform the gradient search - y_incs = momentum * y_incs - eta * dC; - Y = Y + y_incs; - Y = Y + jitter * randn(size(Y)); - Y = bsxfun(@minus, Y, mean(Y, 1)); - - % Reduce jitter over time and change momentum - jitter = jitter * jitter_decay; - if iter == mom_switch_iter - momentum = final_momentum; - end - end - \ No newline at end of file diff --git a/code/dimReducMethods/sparse_nn.m b/code/dimReducMethods/sparse_nn.m deleted file mode 100644 index b149787..0000000 --- a/code/dimReducMethods/sparse_nn.m +++ /dev/null @@ -1,27 +0,0 @@ -%SPARSE_NN -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - -function [edgesrow, edgescol,edgesdist] = sparse_nn(snn) - % turn into sparse nearest neighbor graph snn into edgesrow and edgescol index - N = size(snn,1); - edgescol = zeros(N+1,1); - nnzer = nnz(snn); - edgesrow = zeros(nnzer,1); - edgesdist = zeros(nnzer,1); - - edgescol(1) = 0; - for jdx=1:N - lst = find(snn(:, jdx)>0); - %lst = lst(find(lst>jdx)); - edgescol(jdx+1) = edgescol(jdx)+length(lst); - edgesrow(edgescol(jdx)+1:edgescol(jdx+1)) = lst-1; - edgesdist(edgescol(jdx)+1:edgescol(jdx+1))=snn(lst,jdx); - end \ No newline at end of file diff --git a/code/dimReducMethods/spe.m b/code/dimReducMethods/spe.m deleted file mode 100644 index 316479e..0000000 --- a/code/dimReducMethods/spe.m +++ /dev/null @@ -1,97 +0,0 @@ -function Y = spe(X, no_dims, varargin) -%SPE Perform the Stochastic Proximity Embedding algorithm -% -% Y = spe(X, no_dims, 'Global') -% Y = spe(X, no_dims, 'Local', k) -% -% Perform the Stochastic Proximity Embedding algorithm. The SPE algorithm -% can be compared to the MDS algorithm, although it is much more efficient. -% The total number of updates necessary after the random initialization is -% usually less than n^2 (where n is the number of datapoints). X is the set -% of datapoints on which SPE has to be applied, and no_dims the number of -% dimensions in the embedding space. If the method is used with the 'Global' -% switch, a minimization of the traditional MDS raw stress function is -% performed (the default). Execution with the 'Local' switch only retains -% Euclidean distances in the local neighborhood of the datapoints. The size -% of the neighborhood is defined by the variable k (default = 12). -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if nargin <= 2 - variant = 'Global'; - else - variant = varargin{1}; - end - if strcmp(variant, 'Local') - if nargin > 3, k = varargin{2}; - else k = 12; end - end - if ~strcmp(variant, 'Global') && ~strcmp(variant, 'Local') - error('Unknown parameter.'); - end - if exist('k', 'var') && ischar(k) - error('Adaptive neighborhood selection is not yet supported in SPE.'); - end - - % Initialize parameters - lambda = 1; % initial learning parameter - s = 100; % number of updates per iteration - max_iter = 20000 + round(.04 * size(X, 1) ^ 2); % number of iterations - tol = 1e-5; % regularlization parameter - n = size(X, 1); % number of datapoints - if strcmp(variant, 'Local') - max_iter = max_iter * 3; - end - - % Compute proximity matrix in original space - if strcmp(variant, 'Global') - R = L2_distance(X', X'); - R = R / max(max(R)) * sqrt(2); - else - [R, n_ind] = find_nn(X, k); - end - - % Initialize datapoints randomly - Y = rand(n, no_dims); - - % Perform SPE - for i=1:max_iter - if rem(i, 10000) == 0 - disp(['Iteration ' num2str(i) ' of ' num2str(max_iter) '...']); - end - - % Select points that should be updated - J = randperm(n); - ind1 = J(1:s); - if strcmp(variant, 'Global') - ind2 = J(s+1:2*s); - else - ind2 = double(n_ind(ind1,:))'; - J = round(rand(1, size(ind2, 2)) * (k - 1)) + 1; - J = J + ((0:length(J) - 1) * k); - ind2 = ind2(J); - end - - % Compute distances between points in embedded space - D = sqrt(sum((Y(ind1,:) - Y(ind2,:)) .^ 2, 2)); - - % Get corresponding distances in real space - Rt = R((ind1 - 1) * size(R, 1) + ind2)'; - - % Update locations of points - Y(ind1,:) = Y(ind1,:) + lambda * (1/2) * repmat(((Rt - D) ./ (D + tol)), 1, no_dims) .* (Y(ind1,:) - Y(ind2,:)); - Y(ind2,:) = Y(ind2,:) + lambda * (1/2) * repmat(((Rt - D) ./ (D + tol)), 1, no_dims) .* (Y(ind2,:) - Y(ind1,:)); - - % Update learning parameter - lambda = lambda - (lambda / max_iter); - end - \ No newline at end of file diff --git a/code/dimReducMethods/sym_sne.m b/code/dimReducMethods/sym_sne.m deleted file mode 100644 index fcb2c87..0000000 --- a/code/dimReducMethods/sym_sne.m +++ /dev/null @@ -1,85 +0,0 @@ -function Y = sym_sne(X, d, perplexity) -%SNE Implementation of symmetric Stochastic Neighbor Embedding -% -% mappedX = sym_sne(X, no_dims, perplexity) -% -% Runs the symmetric Stochastic Neighbor Embedding algorithm. The -% high-dimensional datapoints are specified by X. The target dimensionality -% is specified in no_dims (default = 2), and the perplexity of the Gaussian -% kernel is specified in perplexity (default = 30). -% The function returns the embedded points in mappedX. -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - - if ~exist('d', 'var') || isempty(d) - d = 2; - end - if ~exist('perplexity', 'var') || isempty(perplexity) - perplexity = 30; - end - - % Initialize some variables - n = size(X, 1); % number of instances - eta = .05; % learning rate - max_iter = 2000; % maximum number of iterations - jitter = 0.3; % initial jitter - jitter_decay = 0.99; % jitter decay - momentum = 0.5; % initial momentum - final_momentum = 0.8; % final momentum - mom_switch_iter = 750; % iteration where momentum changes - - % Initialize embedding coordinates randomly (close to origin) - Y = 0.0001 * rand(n, d); - dC = zeros(n, d); - y_incs = zeros(n, d); - - % Compute Gaussian kernel for high-dimensional data representation - P = x2p(X, perplexity, 1e-5); % use fixed perplexity - P = P + P'; - P = P ./ sum(P(:)); - P = max(P, eps); - - % Iterating loop - for iter=1:max_iter - - % Compute Gaussian kernel for low-dimensional data representation - sum_Y = sum(Y .^ 2, 2); % precomputation for pairwise distances - Q = exp(-bsxfun(@plus, sum_Y, bsxfun(@plus, sum_Y', -2 * Y * Y')) ./ 2); % Gaussian probabilities - Q = Q ./ repmat(sum(Q, 2), [1 n]); - Q = max(Q, eps); - - % Compute cost function between P and Q - if ~rem(iter, 20) - costs = sum(P .* log((P + eps) ./ (Q + eps)), 2) ./ n; % division by n corrects for # of datapoints - cost = sum(costs); - disp(['Iteration ' num2str(iter) ': error is ' num2str(cost)]); - end - - % Compute gradient - PQ = P - Q; - for i=1:n - dC(i,:) = sum(bsxfun(@times, bsxfun(@minus, Y(i,:), Y), PQ(i,:)'), 1); - end - - % Perform the gradient search - y_incs = momentum * y_incs - eta * dC; - Y = Y + y_incs; - Y = Y + jitter * randn(size(Y)); - Y = bsxfun(@minus, Y, mean(Y, 1)); - - % Reduce jitter over time and change momentum - jitter = jitter * jitter_decay; - if iter == mom_switch_iter - momentum = final_momentum; - end - end - \ No newline at end of file diff --git a/code/dimReducMethods/test_toolbox.m b/code/dimReducMethods/test_toolbox.m deleted file mode 100644 index e7ecf93..0000000 --- a/code/dimReducMethods/test_toolbox.m +++ /dev/null @@ -1,149 +0,0 @@ -function test_toolbox -%TEST_TOOLBOX Tests all functionalities of the dimension reduction toolbox -% -% test_toolbox -% -% Tests all functionalities of the dimension reduction toolbox. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Generate data - disp('Testing data generation functions...'); - datasets = {'helix', 'twinpeaks', '3d_clusters', 'intersect', 'swiss'}; - for i=1:length(datasets) - try - X = generate_data(datasets{i}, 500); - catch e - disp(e); - warning(['Generation of data set ' datasets{i} ' failed! Press any key to continue tests...']); - pause - end - end - - % Test prewhitening - disp('Testing prewhitening...'); - try - X = prewhiten(X); - catch e - disp(e); - warning('Prewhitening failed! Press any key to continue tests...'); - pause - end - unscaled_X = X; - X = X - min(X(:)); - X = X / max(X(:)); - - % Test all intrinsic dimensionality estimators - disp('Testing intrinsic dimensionality estimators...'); - techniques = {'CorrDim', 'NearNbDim', 'GMST', 'PackingNumbers', 'EigValue', 'MLE'}; - for i=1:length(techniques) - try - intrinsic_dim(X, techniques{i}); - catch e - disp(e); - warning(['Intrinsic dimensionality estimation using ' techniques{i} ' failed! Press any key to continue tests...']); - pause - end - end - - % Test all unsupervised dimension reduction techniques - disp('Testing dimensionality reduction techniques...'); - techniques = {'PCA', 'MDS', 'ProbPCA', 'FactorAnalysis', 'GPLVM', 'Sammon', 'Isomap', ... - 'LandmarkIsomap', 'LLE', 'Laplacian', 'HessianLLE', 'LTSA', 'MVU', 'CCA', 'LandmarkMVU', ... - 'FastMVU', 'DiffusionMaps', 'KernelPCA', 'GDA', 'SNE', 'SymSNE', 'tSNE', 'LPP', 'NPE', ... - 'LLTSA', 'SPE', 'Autoencoder', 'LLC', 'ManifoldChart', 'CFA'}; - for i=1:length(techniques) - - % Test the dimension reduction technique - try - if any(strcmpi(techniques{i}, {'GPLVM', 'CFA'})) - [mappedX, mapping] = compute_mapping(unscaled_X, techniques{i}, 2); - else - [mappedX, mapping] = compute_mapping(X, techniques{i}, 2); - end - if any(strcmpi(techniques{i}, {'Isomap', 'LandmarkIsomap', 'LLE', 'Laplacian', 'MVU', 'CCA', 'FastMVU', 'LPP', 'NPE', 'LLTSA'})) - [mappedX, mapping] = compute_mapping(X, techniques{i}, 2, 'adaptive'); - end - catch e - disp(e); - warning(['Technique ' techniques{i} ' failed! Press any key to continue tests...']); - pause - end - - % Test the out-of-sample extension code - if any(strcmpi(techniques{i}, {'PCA', 'LPP', 'NPE', 'LLTSA', 'SPCA', 'PPCA', 'FA'})) - try - out_of_sample(X, mapping); - catch e - disp(e); - warning(['Out-of-sample extension for technique ' techniques{i} ' failed! Press any key to continue tests...']); - pause - end - end - - % Test reconstruction code - if any(strcmpi(techniques{i}, {'PCA', 'LPP', 'NPE', 'LLTSA', 'SPCA', 'PPCA', 'FA', 'Autoencoder'})) - try - reconstruct_data(mappedX, mapping); - catch e - disp(e); - warning(['Reconstruction for technique ' techniques{i} ' failed! Press any key to continue tests...']); - pause - end - end - end - - % Test approximate out-of-sample function - try - out_of_sample_est(X, X, mappedX); - catch e - disp(e); - warning(['Approximate out-of-sample extension failed! Press any key to continue tests...']); - pause - end - - % Test all supervised dimension reduction techniques - labels = double(X(:,1) > .5) + 1; - X = [labels X]; - techniques = {'LDA', 'NCA', 'MCML', 'LMNN'}; - for i=1:length(techniques) - - % Test the actual technique - try - [mappedX, mapping] = compute_mapping(X, techniques{i}, 2); - catch e - disp(e); - warning(['Technique ' techniques{i} ' failed! Press any key to continue tests...']); - pause - end - - % Test out-of-sample extension - try - out_of_sample(X(:,2:end), mapping); - catch e - disp(e); - warning(['Out-of-sample extension for technique ' techniques{i} ' failed! Press any key to continue tests...']); - pause - end - - % Test reconstruction code - try - reconstruct_data(mappedX, mapping); - catch e - disp(e); - warning(['Reconstruction for technique ' techniques{i} ' failed! Press any key to continue tests...']); - pause - end - - end - disp('All tests completed!'); - \ No newline at end of file diff --git a/code/dimReducMethods/train_autoencoder.m b/code/dimReducMethods/train_autoencoder.m deleted file mode 100644 index ef0c6e0..0000000 --- a/code/dimReducMethods/train_autoencoder.m +++ /dev/null @@ -1,56 +0,0 @@ -function [network, mappedX, reconX] = train_autoencoder(X, layers, noise, max_iter) -%TRAIN_AUTOENCODER Trains an simple autoencoder -% -% [network, mappedX, reconX] = train_encoder(X, layers, noise, max_iter) -% -% Trains up an autoencoder with the structure that is specified in layers. -% The low-dimensional data is returned in mappedX, and the network in -% network. The variable noise indicates how much of the input data should be -% blacked out (default = 0). -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if nargin < 2 - error('Not enough inputs.'); - end - if isempty(layers) - error('There should be at least one hidden layer.'); - end - if ~exist('noise', 'var') || isempty(noise) - noise = 0; - end - if ~exist('max_iter', 'var') || isempty(max_iter) - max_iter = 50; - end - - % Initialize the network - D = size(X, 2); - no_layers = length(layers) + 1; - network = cell(no_layers, 1); - network{1}.W = randn(D, layers(1)) * .0001; - network{1}.bias_upW = zeros(1, layers(1)); - for i=2:no_layers - 1 - network{i}.W = randn(layers(i - 1), layers(i)) * .0001; - network{i}.bias_upW = zeros(1, layers(i)); - end - network{no_layers}.W = randn(layers(end), D) * .0001; - network{no_layers}.bias_upW = zeros(1, D); - reconX = run_data_through_autoenc(network, X); - disp(['Initial MSE of reconstructions: ' num2str(mean((X(:) - reconX(:)) .^ 2))]); - - % Perform backpropagation to minimize reconstruction error - network = backprop(network, X, X, max_iter, noise); - - % Get representation from hidden layer - [reconX, mappedX] = run_data_through_autoenc(network, X); - disp(['Final MSE of reconstructions: ' num2str(mean((X(:) - reconX(:)) .^ 2))]); - \ No newline at end of file diff --git a/code/dimReducMethods/train_deep_autoenc.m b/code/dimReducMethods/train_deep_autoenc.m deleted file mode 100644 index 0453e8b..0000000 --- a/code/dimReducMethods/train_deep_autoenc.m +++ /dev/null @@ -1,62 +0,0 @@ -function [model, mappedX] = train_deep_autoenc(X, layers, lambda) -%TRAIN_DEEP_AUTOENC Trains a deep feedforward autoencoder on X -% -% [model, mappedX] = train_deep_autoenc(X, layers, lambda) -% -% The function trains a deep feedforward autoencoder on -% the specified X and labels. The variable X should be a Nx1 cell -% array containing DxT matrices (where T can vary). The variable labels -% should be a Nx1 cell array containing KxT matrices. The variable lambda -% specifies the L2 regularization parameter (default = 0). The parameter -% base_eta represents the base learning rate (default = 1). -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - - if ~exist('lambda', 'var') || isempty(lambda) - lambda = 0; - end - - % Pretrain model using stacked denoising auto-encoders - no_layers = length(layers); - model = cell(2 * no_layers, 1); - mappedX = X; - for i=1:no_layers - noise = 0.1; - max_iter = 30; - [network, mappedX] = train_autoencoder(mappedX, layers(i), noise, max_iter); - model{i}.W = network{1}.W; - model{i}.bias_upW = network{1}.bias_upW; - end - for i=1:no_layers - model{no_layers + i}.W = model{no_layers - i + 1}.W'; - if i ~= no_layers - model{no_layers + i}.bias_upW = model{no_layers - i}.bias_upW; - else - model{no_layers + i}.bias_upW = zeros(1, size(X, 2)); - end - end - clear network mappedX - - % Compute mean squared error of initial model predictions - reconX = run_data_through_autoenc(model, X); - disp(['MSE of initial model: ' num2str(mean((reconX(:) - X(:)) .^ 2))]); - - % Finetune model using gradient descent - noise = 0.1; - max_iter = 30; - model = backprop(model, X, X, max_iter, noise, lambda); - - % Compute mean squared error of final model predictions - [reconX, mappedX] = run_data_through_autoenc(model, X); - disp(['MSE of final model: ' num2str(size(X, 2) .* mean((reconX(:) - X(:)) .^ 2))]); -end diff --git a/code/dimReducMethods/train_grbm.m b/code/dimReducMethods/train_grbm.m deleted file mode 100644 index a816513..0000000 --- a/code/dimReducMethods/train_grbm.m +++ /dev/null @@ -1,111 +0,0 @@ -function [machine, err] = train_grbm(X, h, eta, max_iter, weight_cost) -%TRAIN_GRBM Trains a Gaussian Restricted Boltzmann Machine using CD1 -% -% [machine, err] = train_grbm(X, h, eta, max_iter, weight_cost) -% -% Trains a first-order Restricted Boltzmann Machine on dataset X. The RBM -% has h hidden nodes (default = 30). The training is performed by means of -% the contrastive divergence algorithm. The activation functions that -% is applied in the visible and hidden layers are binary stochastic. -% In the training of the RBM, the learning rate is determined by eta -% (default = 0.1). The maximum number of iterations can be specified -% through max_iter (default = 10). The variable weight_cost sets the amount -% of weight decay that is employed (default = 0.0002). -% The trained RBM is returned in the machine struct. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Initialize some variables - eta = 0.001; - cd_iter = 1; - max_iter = 200; - weight_cost = 0.002; - initial_momentum = 0.5; - final_momentum = 0.9; - [n, v] = size(X); - batch_size = 100; - err = zeros(max_iter, 1); - machine.type = 'rbm_continuous'; - machine.W = randn(v, h) * .0001; - machine.bias_upW = zeros(1, h); - machine.bias_downW = zeros(1, v); - delta_E = zeros(v, h); - delta_E_bias = zeros(1, h); - delta_X_bias = zeros(1, v); - - % Main loop - for iter=1:max_iter - - % Set momentum and update batches - ind = randperm(n); - if iter <= 5 - momentum = initial_momentum; - else - momentum = final_momentum; - end - - % Run for all mini-batches - for batch=1:batch_size:n - if batch + batch_size <= n - - % Set values of visible nodes - vis1 = full(X(ind(batch:min([batch + batch_size - 1 n])),:)); - - % Compute probabilities for hidden nodes - hid1 = 1 ./ (1 + exp(-bsxfun(@plus, vis1 * machine.W, machine.bias_upW))); - - % Sample states for hidden nodes - hid_states = hid1 > rand(size(hid1)); - - % Run contrastive divergence iterations - for i=1:cd_iter - - % Compute probabilities for visible nodes - vis2 = bsxfun(@plus, hid_states * machine.W', machine.bias_downW); - - % Compute probabilities for hidden nodes - hid2 = 1 ./ (1 + exp(-bsxfun(@plus, vis2 * machine.W, machine.bias_upW))); - - % Sample states for hidden nodes - hid_states = hid2 > rand(size(hid2)); - end - - % Compute the weight updates - delta_E = momentum * delta_E + (eta ./ batch_size) * ((vis1' * hid1 - vis2' * hid2) - (weight_cost * machine.W)); - delta_E_bias = momentum * delta_E_bias + (eta ./ batch_size) * (sum(hid1, 1) - sum(hid2, 1)); - delta_X_bias = momentum * delta_X_bias + (eta ./ batch_size) * (sum(bsxfun(@minus, vis2, machine.bias_downW), 1) - ... - sum(bsxfun(@minus, vis1, machine.bias_downW), 1)); - - % Update the network weights - machine.W = machine.W + delta_E; - machine.bias_upW = machine.bias_upW + delta_E_bias; - machine.bias_downW = machine.bias_downW + delta_X_bias; - - % Sum reconstruction error - err(iter) = err(iter) + sum((vis1(:) - vis2(:)) .^ 2); - end - end - - % Print reconstruction error estimate - disp(['Iteration ' num2str(iter) ' of ' num2str(max_iter) ' (rec. error = ' num2str(err(iter) ./ n) ')...']); -% subplot(1, 2, 1), imagesc(reshape(vis1(1,:), [28 28])'); colormap gray, colorbar -% subplot(1, 2, 2), imagesc(reshape(vis2(1,:), [28 28])'); colormap gray, colorbar -% drawnow - - % Jump to higher CD-n every now and then - if iter == round(max_iter * .75) - disp('Switching to CD-3...'); - cd_iter = 3; - eta = eta / 3; - end - end - \ No newline at end of file diff --git a/code/dimReducMethods/train_lin_rbm.m b/code/dimReducMethods/train_lin_rbm.m deleted file mode 100644 index ae2e3ed..0000000 --- a/code/dimReducMethods/train_lin_rbm.m +++ /dev/null @@ -1,113 +0,0 @@ -function machine = train_lin_rbm(X, h, eta, max_iter, weight_cost) -%TRAIN_RBM Trains a Restricted Boltzmann Machine with Gaussian hiddens -% -% machine = train_lin_rbm(X, h, eta, max_iter, weight_cost) -% -% Trains a first-order Restricted Boltzmann Machine on dataset X. The RBM -% has h hidden nodes (default = 20). The training is performed by means of -% the contrastive divergence algorithm. The activation functions that -% is applied in the visible and hidden layers are binary stochastic. -% In the training of the RBM, the learning rate is determined by eta -% (default = 0.001). The maximum number of iterations can be specified -% through max_iter (default = 30). The variable weight_cost sets the amount -% of weight decay that is employed (default = 0.0002). -% The trained RBM is returned in the machine struct. -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Process inputs - if ischar(X) - load(X); - end - if ~exist('h', 'var') || isempty(h) - h = 20; - end - if ~exist('eta', 'var') || isempty(eta) - eta = 0.001; - end - if ~exist('max_iter', 'var') || isempty(max_iter) - max_iter = 50; - end - if ~exist('weight_cost', 'var') || isempty(weight_cost) - weight_cost = 0.0002; - end - - % Other parameters - initial_momentum = 0.5; % momentum for first five iterations - final_momentum = 0.9; % momentum for remaining iterations - - % Initialize some variables - [n, v] = size(X); - batch_size = 100; - W = randn(v, h) * 0.1; - bias_upW = zeros(1, h); - bias_downW = zeros(1, v); - deltaW = zeros(v, h); - deltaBias_upW = zeros(1, h); - deltaBias_downW = zeros(1, v); - - % Main loop - for iter=1:max_iter - - % Set momentum - err = 0; - ind = randperm(n); - if iter <= 5 - momentum = initial_momentum; - else - momentum = final_momentum; - end - - % Run for all mini-batches - for batch=1:batch_size:n - if batch + batch_size <= n - - % Set values of visible nodes - vis1 = double(X(ind(batch:min([batch + batch_size - 1 n])),:)); - - % Compute probabilities for hidden nodes - hid1 = bsxfun(@plus, vis1 * W, bias_upW); - - % Sample states for hidden nodes - hid_states = hid1 + randn(size(hid1)); - - % Compute probabilities for visible nodes - vis2 = 1 ./ (1 + exp(-(bsxfun(@plus, hid_states * W', bias_downW)))); - - % Compute probabilities for hidden nodes - hid2 = bsxfun(@plus, vis2 * W, bias_upW); - - % Now compute the weights update - posprods = vis1' * hid1; - negprods = vis2' * hid2; - deltaW = momentum * deltaW + eta * (((posprods - negprods) / batch_size) - (weight_cost * W)); - deltaBias_upW = momentum * deltaBias_upW + (eta / batch_size) * (sum(hid1, 1) - sum(hid2, 1)); - deltaBias_downW = momentum * deltaBias_downW + (eta / batch_size) * (sum(vis1, 1) - sum(vis2, 1)); - - % Update the network weights - W = W + deltaW; - bias_upW = bias_upW + deltaBias_upW; - bias_downW = bias_downW + deltaBias_downW; - - % Estimate the error - err = err + sum(sum((vis1 - vis2) .^ 2)); - end - end - - % Estimation of reconstruction error - disp(['Iteration ' num2str(iter) ': error ~' num2str(err ./ n)]); - end - - % Return RBM - machine.W = W; - machine.bias_upW = bias_upW; - machine.bias_downW = bias_downW; - disp(' '); diff --git a/code/dimReducMethods/train_rbm.m b/code/dimReducMethods/train_rbm.m deleted file mode 100644 index 0630119..0000000 --- a/code/dimReducMethods/train_rbm.m +++ /dev/null @@ -1,106 +0,0 @@ -function machine = train_rbm(X, h, eta, max_iter, weight_cost) -%TRAIN_RBM Trains a Restricted Boltzmann Machine using CD1 -% -% machine = train_rbm(X, h, eta, max_iter, weight_cost) -% -% Trains a first-order Restricted Boltzmann Machine on dataset X. The RBM -% has h hidden nodes (default = 30). The training is performed by means of -% the contrastive divergence algorithm. The activation functions that -% is applied in the visible and hidden layers are binary stochastic. -% In the training of the RBM, the learning rate is determined by eta -% (default = 0.1). The maximum number of iterations can be specified -% through max_iter (default = 10). The variable weight_cost sets the amount -% of weight decay that is employed (default = 0.0002). -% The trained RBM is returned in the machine struct. -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Process inputs - if ischar(X) - load(X); - end - if ~exist('h', 'var') || isempty(h) - h = 30; - end - if ~exist('eta', 'var') || isempty(eta) - eta = 0.1; - end - if ~exist('max_iter', 'var') || isempty(max_iter) - max_iter = 30; - end - if ~exist('weight_cost', 'var') || isempty(weight_cost) - weight_cost = 0.0002; - end - - % Other parameters - initial_momentum = 0.5; % momentum for first five iterations - final_momentum = 0.9; % momentum for remaining iterations - - % Initialize some variables - [n, v] = size(X); - batch_size = 100; - machine.W = randn(v, h) * 0.1; - machine.bias_upW = zeros(1, h); - machine.bias_downW = zeros(1, v); - deltaW = zeros(v, h); - deltaBias_upW = zeros(1, h); - deltaBias_downW = zeros(1, v); - - % Main loop - ind = randperm(n); - for iter=1:max_iter - - % Set momentum and update batches - if iter <= 5 - momentum = initial_momentum; - else - momentum = final_momentum; - end - - % Run for all mini-batches - for batch=1:batch_size:n - if batch + batch_size <= n - - % Set values of visible nodes - vis1 = double(X(ind(batch:min([batch + batch_size - 1 n])),:)); - - % Compute probabilities for hidden nodes - hid1 = 1 ./ (1 + exp(-bsxfun(@plus, vis1 * machine.W, machine.bias_upW))); - - % Sample states for hidden nodes - hid_states = hid1 > rand(size(hid1)); - - % Compute probabilities for visible nodes - vis2 = 1 ./ (1 + exp(-(bsxfun(@plus, hid_states * machine.W', machine.bias_downW)))); - - % Compute probabilities for hidden nodes - hid2 = 1 ./ (1 + exp(-(bsxfun(@plus, vis2 * machine.W, machine.bias_upW)))); - - % Now compute the weights update - posprods = vis1' * hid1; - negprods = vis2' * hid2; - deltaW = momentum * deltaW + (eta ./ batch_size) * ((posprods - negprods) - (weight_cost * machine.W)); - deltaBias_upW = momentum * deltaBias_upW + (eta ./ batch_size) * (sum(hid1, 1) - sum(hid2, 1)); - deltaBias_downW = momentum * deltaBias_downW + (eta ./ batch_size) * (sum(vis1, 1) - sum(vis2, 1)); - - % Update the network weights - machine.W = machine.W + deltaW; - machine.bias_upW = machine.bias_upW + deltaBias_upW; - machine.bias_downW = machine.bias_downW + deltaBias_downW; - end - end - - % Estimate error and plot some of the receptive fields - siz = min([n 5000]); - err = compute_recon_err(machine, X(1:siz,:)); - disp(['Iteration ' num2str(iter) ' (rec. error = ' num2str(err) ')...']); - end - disp(' '); diff --git a/code/dimReducMethods/tsne.m b/code/dimReducMethods/tsne.m deleted file mode 100644 index 6875024..0000000 --- a/code/dimReducMethods/tsne.m +++ /dev/null @@ -1,91 +0,0 @@ -function ydata = tsne(X, labels, no_dims, initial_dims, perplexity) -%TSNE Performs symmetric t-SNE on dataset X -% -% mappedX = tsne(X, labels, no_dims, initial_dims, perplexity) -% mappedX = tsne(X, labels, initial_solution, perplexity) -% -% The function performs symmetric t-SNE on the NxD dataset X to reduce its -% dimensionality to no_dims dimensions (default = 2). The data is -% preprocessed using PCA, reducing the dimensionality to initial_dims -% dimensions (default = 30). Alternatively, an initial solution obtained -% from an other dimensionality reduction technique may be specified in -% initial_solution. The perplexity of the Gaussian kernel that is employed -% can be specified through perplexity (default = 30). The labels of the -% data are not used by t-SNE itself, however, they are used to color -% intermediate plots. Please provide an empty labels matrix [] if you -% don't want to plot results during the optimization. -% The low-dimensional data representation is returned in mappedX. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('labels', 'var') - labels = []; - end - if ~exist('no_dims', 'var') || isempty(no_dims) - no_dims = 2; - end - if ~exist('initial_dims', 'var') || isempty(initial_dims) - initial_dims = min(50, size(X, 2)); - end - if ~exist('perplexity', 'var') || isempty(perplexity) - perplexity = 30; - end - - % First check whether we already have an initial solution - if numel(no_dims) > 1 - initial_solution = true; - ydata = no_dims; - no_dims = size(ydata, 2); - perplexity = initial_dims; - else - initial_solution = false; - end - - % Normalize input data - X = X - min(X(:)); - X = X / max(X(:)); - X = bsxfun(@minus, X, mean(X, 1)); - - % Perform preprocessing using PCA - if ~initial_solution - disp('Preprocessing data using PCA...'); - if size(X, 2) < size(X, 1) - C = X' * X; - else - C = (1 / size(X, 1)) * (X * X'); - end - [M, lambda] = eig(C); - [lambda, ind] = sort(diag(lambda), 'descend'); - M = M(:,ind(1:initial_dims)); - lambda = lambda(1:initial_dims); - if ~(size(X, 2) < size(X, 1)) - M = bsxfun(@times, X' * M, (1 ./ sqrt(size(X, 1) .* lambda))'); - end - X = X * M; - clear M lambda ind - end - - % Compute pairwise distance matrix - sum_X = sum(X .^ 2, 2); - D = bsxfun(@plus, sum_X, bsxfun(@plus, sum_X', -2 * (X * X'))); - - % Compute joint probabilities - P = d2p(D, perplexity, 1e-5); % compute affinities using fixed perplexity - clear D - - % Run t-SNE - if initial_solution - ydata = tsne_p(P, labels, ydata); - else - ydata = tsne_p(P, labels, no_dims); - end - \ No newline at end of file diff --git a/code/dimReducMethods/tsne_d.m b/code/dimReducMethods/tsne_d.m deleted file mode 100644 index c0df717..0000000 --- a/code/dimReducMethods/tsne_d.m +++ /dev/null @@ -1,58 +0,0 @@ -function ydata = tsne_d(D, labels, no_dims, perplexity) -%TSNE_D Performs symmetric t-SNE on the pairwise Euclidean distance matrix D -% -% mappedX = tsne_d(D, labels, no_dims, perplexity) -% mappedX = tsne_d(D, labels, initial_solution, perplexity) -% -% The function performs symmetric t-SNE on the NxN pairwise Euclidean -% distance matrix D to construct an embedding with no_dims dimensions -% (default = 2). An initial solution obtained from an other dimensionality -% reduction technique may be specified in initial_solution. -% The perplexity of the Gaussian kernel that is employed can be specified -% through perplexity (default = 30). The labels of the data are not used -% by t-SNE itself, however, they are used to color intermediate plots. -% Please provide an empty labels matrix [] if you don't want to plot -% results during the optimization. -% The data embedding is returned in mappedX. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('labels', 'var') - labels = []; - end - if ~exist('no_dims', 'var') || isempty(no_dims) - no_dims = 2; - end - if ~exist('perplexity', 'var') || isempty(perplexity) - perplexity = 30; - end - - % First check whether we already have an initial solution - if numel(no_dims) > 1 - initial_solution = true; - ydata = no_dims; - no_dims = size(ydata, 2); - else - initial_solution = false; - end - - % Compute joint probabilities - D = D / max(D(:)); % normalize distances - P = d2p(D .^ 2, perplexity, 1e-5); % compute affinities using fixed perplexity - - % Run t-SNE - if initial_solution - ydata = tsne_p(P, labels, ydata); - else - ydata = tsne_p(P, labels, no_dims); - end - \ No newline at end of file diff --git a/code/dimReducMethods/tsne_p.m b/code/dimReducMethods/tsne_p.m deleted file mode 100644 index fadd79b..0000000 --- a/code/dimReducMethods/tsne_p.m +++ /dev/null @@ -1,118 +0,0 @@ -function ydata = tsne_p(P, labels, no_dims) -%TSNE_P Performs symmetric t-SNE on affinity matrix P -% -% mappedX = tsne_p(P, labels, no_dims) -% -% The function performs symmetric t-SNE on pairwise similarity matrix P -% to create a low-dimensional map of no_dims dimensions (default = 2). -% The matrix P is assumed to be symmetric, sum up to 1, and have zeros -% on the diagonal. -% The labels of the data are not used by t-SNE itself, however, they -% are used to color intermediate plots. Please provide an empty labels -% matrix [] if you don't want to plot results during the optimization. -% The low-dimensional data representation is returned in mappedX. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - - if ~exist('labels', 'var') - labels = []; - end - if ~exist('no_dims', 'var') || isempty(no_dims) - no_dims = 2; - end - - % First check whether we already have an initial solution - if numel(no_dims) > 1 - initial_solution = true; - ydata = no_dims; - no_dims = size(ydata, 2); - else - initial_solution = false; - end - - % Initialize some variables - n = size(P, 1); % number of instances - momentum = 0.5; % initial momentum - final_momentum = 0.8; % value to which momentum is changed - mom_switch_iter = 250; % iteration at which momentum is changed - stop_lying_iter = 100; % iteration at which lying about P-values is stopped - max_iter = 1000; % maximum number of iterations - epsilon = 500; % initial learning rate - min_gain = .01; % minimum gain for delta-bar-delta - - % Make sure P-vals are set properly - P(1:n + 1:end) = 0; % set diagonal to zero - P = 0.5 * (P + P'); % symmetrize P-values - P = max(P ./ sum(P(:)), realmin); % make sure P-values sum to one - const = sum(P(:) .* log(P(:))); % constant in KL divergence - if ~initial_solution - P = P * 4; % lie about the P-vals to find better local minima - end - - % Initialize the solution - if ~initial_solution - ydata = .0001 * randn(n, no_dims); - end - y_incs = zeros(size(ydata)); - gains = ones(size(ydata)); - - % Run the iterations - for iter=1:max_iter - - % Compute joint probability that point i and j are neighbors - sum_ydata = sum(ydata .^ 2, 2); - num = 1 ./ (1 + bsxfun(@plus, sum_ydata, bsxfun(@plus, sum_ydata', -2 * (ydata * ydata')))); % Student-t distribution - num(1:n+1:end) = 0; % set diagonal to zero - Q = max(num ./ sum(num(:)), realmin); % normalize to get probabilities - - % Compute the gradients (faster implementation) - L = (P - Q) .* num; - y_grads = 4 * (diag(sum(L, 1)) - L) * ydata; - - % Update the solution - gains = (gains + .2) .* (sign(y_grads) ~= sign(y_incs)) ... % note that the y_grads are actually -y_grads - + (gains * .8) .* (sign(y_grads) == sign(y_incs)); - gains(gains < min_gain) = min_gain; - y_incs = momentum * y_incs - epsilon * (gains .* y_grads); - ydata = ydata + y_incs; - ydata = bsxfun(@minus, ydata, mean(ydata, 1)); - - % Update the momentum if necessary - if iter == mom_switch_iter - momentum = final_momentum; - end - if iter == stop_lying_iter && ~initial_solution - P = P ./ 4; - end - - % Print out progress - if ~rem(iter, 10) - cost = const - sum(P(:) .* log(Q(:))); - disp(['Iteration ' num2str(iter) ': error is ' num2str(cost)]); - end - - % Display scatter plot (maximally first three dimensions) - if ~isempty(labels) - if no_dims == 1 - scatter(ydata, ydata, 9, labels, 'filled'); - elseif no_dims == 2 - scatter(ydata(:,1), ydata(:,2), 9, labels, 'filled'); - else - scatter3(ydata(:,1), ydata(:,2), ydata(:,3), 40, labels, 'filled'); - end - axis equal tight -% axis off - drawnow - end - end - \ No newline at end of file diff --git a/code/dimReducMethods/welcome.m b/code/dimReducMethods/welcome.m deleted file mode 100644 index c996574..0000000 --- a/code/dimReducMethods/welcome.m +++ /dev/null @@ -1,25 +0,0 @@ -function welcome -%WELCOME Displays DR Toolbox version information -% -% welcome -% -% Displays DR Toolbox version information. - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - global DR_WELCOME; - if isempty(DR_WELCOME) - disp(' '); - disp(' Welcome to the Matlab Toolbox for Dimensionality Reduction, version 0.8b (18-April-2012).'); - disp(' You are free to modify or redistribute this code (for non-commercial purposes), as long as a reference'); - disp(' to the original author (Laurens van der Maaten, Delft University of Technology) is retained.'); - disp(' For more information, please visit http://homepage.tudelft.nl/19j49'); - disp(' '); - DR_WELCOME = 1; - end diff --git a/code/dimReducMethods/writesdpa.m b/code/dimReducMethods/writesdpa.m deleted file mode 100644 index 9b697d7..0000000 --- a/code/dimReducMethods/writesdpa.m +++ /dev/null @@ -1,403 +0,0 @@ -function ret=writesdpa(fname,A,b,c,K,pars) -%WRITESDPA Take a problem in SeDuMi format and writes it in SDPA format -% -% Usage: -% -% ret=writesdpa(fname,A,b,c,K,pars) -% -% fname Name of SDPpack file, in quotes -% A,b,c,K Problem in SeDuMi form -% pars Optional parameters. -% pars.printlevel=0 No printed output -% pars.printlevel=1 (default) Some printed output. -% -% ret ret=0 on success, ret=1 on failure. -% -% Notes: -% -% Problems with complex data are not allowed. -% -% Quadratic cone and rotated cone constraints are not supported. -% -% Nonsymmetric A.s and C.s matrices are symmetrized with A=(A+A')/2 -% a warning is given when this happens. -% -% Free variables are not supported. -% -% Floating point numbers are written out with 18 decimal digits for -% accuracy. -% -% Please contact the author (Brian Borchers, borchers@nmt.edu) with any -% questions or bug reports. -% -% Third Version: 3/3/06. Corrected a bug in the handling of -% nonsymmetric constraint matrices. -% -% Second Version: 7/14/04. Modified to vastly speed up operations on sparse -% matrices. On some problems, this version is 100 times -% faster! -% -% First Version: 7/14/03. Modified from old writesdp.m which wrote problems -% in SDPPack format. -% -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - -% -% First, check to see whether or not we should be quiet. -% -if (nargin > 5) - if (isfield(pars,'printlevel')) - if (pars.printlevel == 0) - quiet=1; - else - quiet=0; - end - else - quiet=0; - end -else - pars.printlevel=1; - quiet=0; -end -% -% First, check for complex numbers in A, b, or c. -% -if (isreal(A) ~= 1) - if (quiet == 0) - fprintf('A is not real!\n'); - end - ret=1; - return -end -if (isreal(b) ~= 1) - if (quiet == 0) - fprintf('b is not real!\n'); - end - ret=1; - return -end -if (isreal(c) ~= 1) - if (quiet == 0) - fprintf('c is not real!\n'); - end - ret=1; - return -end -% -% Check for any quadratic cone constraints. -% -if (isfield(K,'q')) - if ((~isempty(K.q)) & (K.q ~= 0)) - if (quiet == 0) - fprintf('quadratic cone constraints are not supported.\n'); - end - ret=1; - return - end -end -% -% Check for any rotated cone constraints. -% -if (isfield(K,'r')) - if ((~isempty(K.r)) & (K.r ~= 0)) - if (quiet == 0) - fprintf('rotated cone constraints are not supported.\n'); - end - ret=1; - return - end -end -% -% Check for any free variables. -% -if (isfield(K,'f')) - if ((~isempty(K.f)) & (K.f ~= 0)) - if (quiet == 0) - fprintf('Free variables are not supported.\n'); - end - ret=1; - return - end -end -% -% Find the number of constraints. -% -m=length(b); -% -% Deal with the following special case. If A is transposed, transpose -% it again so that it is of the right size. -% -[Am,An]=size(A); -if (Am ~= m) - if (An == m) - if (quiet==0) - fprintf('Transposing A to match b \n'); - end - AT=A; - A=A'; -% -% Also swap Am and An so that they're correct. -% - temp=Am; - Am=An; - An=temp; - else -% -% In this case, A is just plain the wrong size. -% - if (quiet==0) - fprintf('A is not of the correct size to match b \n'); - end - ret=1; - return - end -else -% -% No need to transpose A, but we'll need AT. -% - AT=A'; -end -% -% Deal with the following special case: if c==0, then c should really -% be a zero vector of the appropriate size. -% -if (c == 0) - if (quiet==0) - fprintf('Expanding c to the appropriate size\n'); - end - c=sparse(An,1); -end -% -% If c is empty, then act as if it was zero. -% -if (isempty(c)) - if (quiet==0) - fprintf('Expanding empty c to zeros of the appropriate size\n'); - end - c=sparse(An,1); -end -% -% If c is a row vector, make it a column vector. -% -[cm,cn]=size(c); -if (cn > cm) - c=c'; -end -% -% Get the size data. -% -% -% First, the size of the LP block. -% -if (isfield(K,'l')) - nlin=K.l; - sizelin=nlin; - if (isempty(sizelin)) - sizelin=0; - nlin=0; - end - if (K.l == 0) - nlin=0; - sizelin=0; - end -else - nlin=0; - sizelin=0; -end -% -% Get the sizes of the SDP blocks. -% -if (isfield(K,'s')) - nsdpblocks=length(K.s); - sizesdp=sum((K.s).^2); - if (isempty(sizesdp)) - sizesdp=0; - nsdpblocks=0; - end - if (K.s == 0) - nsdpblocks=0; - sizesdp=0; - end -else - sizesdp=0; - nsdpblocks=0; -end -% -% Figure out the number of blocks. -% -nblocks=nsdpblocks; -if (nlin>0) - nblocks=nblocks+1; -end -% -% print out some size information -% -if (quiet==0) - fprintf('Number of constraints: %d \n',m); - fprintf('Number of SDP blocks: %d \n',nsdpblocks); - fprintf('Number of LP vars: %d \n',nlin); -end -% -% Open up the file for writing. -% -fid=fopen(fname,'w'); -if (fid==-1) - if (quiet==0) - fprintf('Could not open file for output!'); - end - ret=1; - return -end -% -% Print out m, the number of constraints. -% -fprintf(fid,'%d \n',m); -% -% Next, the number of blocks. -% -fprintf(fid,'%d \n',nblocks); -% -% Print out the block structure. -% -if (K.s > 0) - fprintf(fid,'%d ',K.s); -end -if (nlin > 0) - fprintf(fid,'%d ',-nlin); -end -fprintf(fid,'\n'); -% -% Next, b, with all on one line. -% -fprintf(fid,'%.18e ',full(b)); -fprintf(fid,'\n'); -% -% First, the C matrix. -% -% -% First, calculate where in c things start. -% -base=sizelin+1; -% -% Next, work through the SDP blocks. -% -for i=1:nsdpblocks -% -% Get the current block of C. -% - I=find(c); - II=find(I>=base); - I=I(II); - II=find(I<=base+K.s(i)^2-1); - I=I(II); - II=I-(base-1)*ones(size(I)); - work=sparse(II,ones(size(II)),c(I),K.s(i)^2,1); - work=reshape(work,K.s(i),K.s(i)); - -% -% Check this block for symmetry. -% -if (norm(work-work','fro') ~= 0) - if (quiet==0) - fprintf('Non symmetric C.s matrix!\n'); - end - work=(work+work')/2; -end -% -% Write out the C.s matrix. -% - work=triu(work); - [II,JJ,V]=find(work); - cnt=length(II); - if (cnt ~= 0) - fprintf(fid,'%d %d %d %d %.18e\n',[zeros(size(II)) i*ones(size(II)) II JJ -V]'); - end - -% -% Next, update to the next base. -% - base=base+K.s(i)^2; -end -% -% Print out the coefficients for the linear block of C. -% -for i=1:nlin - if (c(i) ~= 0.0) - fprintf(fid,'%d %d %d %d %.18e\n',[0 nsdpblocks+1 i i -full(c(i))]); - end -end - -% -% Now, loop through the constraints, one at a time. -% -for cn=1:m -% -% Print out the SDP part of constraint cn. -% - base=sizelin+1; - rowcn=AT(:,cn); - for i=1:nsdpblocks - I=find(rowcn); - II=find(I>=base); - I=I(II); - II=find(I<=(base+K.s(i)^2-1)); - I=I(II); - II=I-(base-1)*ones(size(I)); - work=sparse(II,ones(size(II)),rowcn(I),K.s(i)^2,1); - - work=reshape(work,K.s(i),K.s(i)); - - if (norm(work-work','fro') ~= 0) - if (quiet==0) - fprintf('Non symmetric A.s matrix! \n'); - end - work=(work+work')/2; - end -% -% Ignore the lower left triangle. -% - work=triu(work); -% -% Get the nonzero entries. -% - [II,JJ,V]=find(work); - cnt=length(II); - if (cnt ~= 0) - fprintf(fid,'%d %d %d %d %.18e\n',[cn*ones(size(II)) i*ones(size(II)) II JJ V]'); - end -% -% Next, update to the next base. -% - base=base+K.s(i)^2; - end -% -% Finally, the linear part. -% - I=find(rowcn); - II=find(I<=nlin); - I=I(II); - workrow=sparse(I,ones(size(I)),rowcn(I),nlin,1); - [II,JJ,V]=find(workrow); - if (length(II) > 0) - fprintf(fid,'%d %d %d %d %.18e\n',[cn*ones(length(II),1) (nsdpblocks+1)*ones(length(II),1) II II V]'); - end -end -% -% Close the file. -% -fclose(fid); -% -% Return success -% -ret=0; -return diff --git a/code/dimReducMethods/x2p.m b/code/dimReducMethods/x2p.m deleted file mode 100644 index e4611ec..0000000 --- a/code/dimReducMethods/x2p.m +++ /dev/null @@ -1,104 +0,0 @@ -function [P, beta] = x2p(X, u, tol) -%X2P Identifies appropriate sigma's to get kk NNs up to some tolerance -% -% [P, beta] = x2p(xx, kk, tol) -% -% Identifies the required precision (= 1 / variance^2) to obtain a Gaussian -% kernel with a certain uncertainty for every datapoint. The desired -% uncertainty can be specified through the perplexity u (default = 15). The -% desired perplexity is obtained up to some tolerance that can be specified -% by tol (default = 1e-4). -% The function returns the final Gaussian kernel in P, as well as the -% employed precisions per instance in beta. -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('u', 'var') || isempty(u) - u = 15; - end - if ~exist('tol', 'var') || isempty(tol) - tol = 1e-4; - end - - % Initialize some variables - n = size(X, 1); % number of instances - P = zeros(n, n); % empty probability matrix - beta = ones(n, 1); % empty precision vector - logU = log(u); % log of perplexity (= entropy) - - % Compute pairwise distances -% disp('Computing pairwise distances...'); - D = squareform(pdist(X, 'euclidean') .^ 2); - - % Run over all datapoints -% disp('Computing P-values...'); - for i=1:n - -% if ~rem(i, 500) -% disp(['Computed P-values ' num2str(i) ' of ' num2str(n) ' datapoints...']); -% end - - % Set minimum and maximum values for precision - betamin = -Inf; - betamax = Inf; - - % Compute the Gaussian kernel and entropy for the current precision - Di = D(i, [1:i-1 i+1:end]); - [H, thisP] = Hbeta(Di, beta(i)); - - % Evaluate whether the perplexity is within tolerance - Hdiff = H - logU; - tries = 0; - while abs(Hdiff) > tol && tries < 50 - - % If not, increase or decrease precision - if Hdiff > 0 - betamin = beta(i); - if isinf(betamax) - beta(i) = beta(i) * 2; - else - beta(i) = (beta(i) + betamax) / 2; - end - else - betamax = beta(i); - if isinf(betamin) - beta(i) = beta(i) / 2; - else - beta(i) = (beta(i) + betamin) / 2; - end - end - - % Recompute the values - [H, thisP] = Hbeta(Di, beta(i)); - Hdiff = H - logU; - tries = tries + 1; - end - - % Set the final row of P - P(i, [1:i - 1, i + 1:end]) = thisP; - end -% disp(['Mean value of sigma: ' num2str(mean(sqrt(1 ./ beta)))]); -% disp(['Minimum value of sigma: ' num2str(min(sqrt(1 ./ beta)))]); -% disp(['Maximum value of sigma: ' num2str(max(sqrt(1 ./ beta)))]); -end - - - -% Function that computes the Gaussian kernel values given a vector of -% squared Euclidean distances, and the precision of the Gaussian kernel. -% The function also computes the perplexity of the distribution. -function [H, P] = Hbeta(D, beta) - P = exp(-D * beta); - sumP = sum(P); - H = log(sumP) + beta * sum(D .* P) / sumP; - P = P / sumP; -end - diff --git a/code/neumapper/ballMapper.m b/code/neumapper/ballMapper.m deleted file mode 100644 index f490c3f..0000000 --- a/code/neumapper/ballMapper.m +++ /dev/null @@ -1,66 +0,0 @@ -function [pts_in_bigBin, idx_bigBin] = ballMapper(dX,options) -% Function ballMapper -% Implements (a version of) the ball mapper algorithm on data -% -% Input: - -% options -- struct containing resolution and gain -% dfX -- distance matrix (possibly after some filtering) - -% Output: -% pts_in_bigBin -- a collection of bigBins corresponding to a cover of X -% idx_bigBin -- indices of the chosen landmarks/bigBins in X - -% Dependencies: -% -- Laurens van der Maaten's isomap code and related subdependencies. -% -- Vin de Silva's FPS code (px_maxmin.m) - - -% Procedure: - -% -- Perform farthest point sampling. Number of landmarks for FPS -% is determined by resolution parameter. Output of this process is an -% epsilon-cover of X. -% -- Create cover (using gain parameter along with the epsilon obtained in -% the FPS step). Return points in each element of the cover. - -%% Check inputs - -if nargin < 2 - error('Not enough inputs for BallMapper') -end - -%% Obtain options. If a parameter is missing, switch to a default value. - -resolution = getoptions(options,'resolution',30); -gain = getoptions(options,'gain',50); - - -%% Check that helper files have been loaded - -if ~exist('px_maxmin.m','file') - error('Load the "tools" folder') -end - - - -%% FPS -[landmk_idx, dist_to_landmk, epsilon] = px_maxmin(dX,'metric',resolution,'n', 1,'seeds'); - - -%% Add points to bigBins - -pts_in_bigBin = cell(resolution,1); - -for ii = 1:resolution - tmp = dist_to_landmk(ii,:); - pt_idx = tmp < max((gain/100)*(4*epsilon), eps); - % Gain should be at least 25 to make sure we're covering the dataset - pts_in_bigBin{ii} = find(pt_idx); -end - -idx_bigBin = landmk_idx; - - -end - diff --git a/code/neumapper/bdl_binning.m b/code/neumapper/bdl_binning.m deleted file mode 100644 index 89317da..0000000 --- a/code/neumapper/bdl_binning.m +++ /dev/null @@ -1,204 +0,0 @@ -function [pts_in_bigBin, bin_indices] = bdl_binning(filter_X, resolution, gain, nsides, display) -% Function bdl_binning -% Input: n-dimensional embedding of data, resolution and gain parameters -% Output: a cell array of bigBins along with indices of the data points -% in each bin. The bigBins constitute the first binning step of mapper. - -% @Samir Chowdhury -% Adapted from mapper2d_bdl_nonmetric. The "levels" in that function -% correspond to "bigBins" in this function. Note that "smallBins" is what -% we will obtain after applying partial clustering to bigBins - -% @braindynamicslab [07.25.2019] -% Adapted from bdl_binning_2d_v0. -% CHANGES: -% - allow an arbitrary number of dimensions in the filter -% TODO: -% - generalize to handle future extentions (i.e. disks based on -% the notion of "centers") -% - update comments from 2d case to Nd case - -% @daniel hasegan [11/02/2021] -% Adapted from bdl_binning_v0 and from Manish's mapper2d_bdl_hex_binning.m -% Changes: -% - allow for non-square 2d bins - -if nargin < 4 - nsides = 4; -end -if nargin < 5 - display = 0; -end - -num_intervals = resolution; % Number of intervals in each of 2 dimensions -percent_overlap = gain; % Amount of overlap between intervals -verbose = 1; % TODO: make this an option - -% This function assumes that each observation in X corresponds to a 2d -% filter value. -filter_values = filter_X; - -% Obtain the number of points and number of filters -% (i.e. number of rows, columns in filter_values) -num_filters = size(filter_values, 2); - -if nsides ~= 4 - assert(num_filters == 2, 'Can only specify nsides for dims=2'); -end - -% Obtain bounds (i.e. min, max) along all filters -filter_min = min(filter_values); -filter_max = max(filter_values); - -% Check that num_intervals has same shape as num_filters -if size(num_intervals,2) < num_filters - num_intervals = repmat(num_intervals,1,num_filters); - if verbose > 2 - disp(['num_intervals = ',num2str(num_intervals)]); - end -end - -% Check that percent_overlap has same shape as num_filters -if size(percent_overlap,2) < num_filters - percent_overlap = repmat(percent_overlap,1,num_filters); - if verbose > 2 - disp(['percent_overlap = ',num2str(percent_overlap)]); - end -end - -if nsides ~= 4 - percent_overlap = find_perc_overlap(percent_overlap, nsides, display) * 100; -end - - -% Initialize empty matrix of effective interval lengths, step_sizes -filter_length = diff([filter_min; filter_max]); -num_effective = num_intervals - (num_intervals - 1) .* percent_overlap/100; -interval_length = filter_length ./ num_effective; - -% This part says how far you move from the left endpoint of one interval -% towards the right before hitting the left endpoint of the overlapping -% interval -step_size = interval_length .* (1 - percent_overlap/100); - - - -% Initialize a variable to hold n-dimensional bin indices -dim_bin_indices = cell(size(num_intervals)); - -% Loop over each dim, tile the bin inds to match all other dimensions -for dim = 1:num_filters - mask_dims = eye(num_filters); - mask_dim = mask_dims(dim, :); - new_size = mask_dim - (mask_dim - 1) .* num_intervals; - dim_indices = repmat(1:num_intervals(dim), new_size); - dim_bin_indices{dim} = dim_indices; -end - -% now convert to matrix, then sort rows => [1 1; 1 2] => [1 1; 2 1] -dim_bin_indices = cellfun(@(x) x(:), dim_bin_indices, 'UniformOutput', false); -bin_dim_indices = cell2mat(dim_bin_indices); - - -% Initialize some variables to hold num bins, bin points, etc. -num_bigBins = prod(num_intervals); -pts_in_bigBin = cell(num_bigBins,1); -bin_indices = zeros(num_bigBins, num_filters); - -if display - figure -end - -% Loop over the bigBins to get the points in each bigBin -for bin = 1:num_bigBins - - % select a particular bigBin, i.e., 2 => [1 1 2] - bin_ind = bin_dim_indices(bin,:); - - % get bounding coordinates of bigBin - min_val_bin = filter_min + (bin_ind - 1) .* step_size; - max_val_bin = min_val_bin + interval_length; - - if num_filters ~= 2 - % find the indices of the points in this bigBin - % 1. compare values to [min; max] across dimensions - % 2. mask points where this is true for every dimension - pts_bin = (filter_values >= min_val_bin) & ... - (filter_values <= max_val_bin); - - % find points where no value falls outside the bin in any dimension - pts_bin = all(pts_bin, 2); - else - % Create a polygon - center_point = (min_val_bin+max_val_bin)./2; - poly = nsidedpoly(nsides, 'Center', [0, 0], 'SideLength', 1); - poly.Vertices = poly.Vertices .* interval_length + center_point; - if display - plot(poly) - hold on - end - - % Find all the points that lie inside the polygon - pts_bin = isinterior(poly, filter_values); - end - - % display progress - if verbose > 2 - fprintf(' > Found %2d points in bin |%s|\n', sum(pts_bin), num2str(bin_ind)); - end - - % continue if no points found - if sum(pts_bin) < 1 - continue; - end - - % num_pts_bin = sum(pts_bin); - pts_in_bigBin{bin} = find(pts_bin); - bin_indices(bin,:) = bin_ind; - -end - -end - -% Iteratively find the percentage overlap for a polygon of sides. -function sides_perc_overlap = find_perc_overlap(target_percent_overlap, sides, display) - EPS = 1e-10; - iter_steps = 100; - - if nargin < 3 - display = 0; - end - - % binary search to find the step size - poly1 = nsidedpoly(sides, 'Center', [0, 0], 'SideLength', 1); - - I = eye(2); - res = zeros(1,2); - for d=1:2 - smin = 0; - smax = ceil(1 / sin(pi / sides)); - smid = 0; - for i = 1:iter_steps - smid = (smin + smax) / 2; - C2 = I(d, :) * smid; - poly2 = nsidedpoly(sides, 'Center', C2, 'SideLength', 1); - pinter = intersect(poly1, poly2); - percent = area(pinter) / area(poly1); - if abs(percent - target_percent_overlap(d) / 100) < EPS - if display - disp(['Found at iter ', num2str(i)]) - end - break - end - if percent > target_percent_overlap(d) / 100 - smin = smid; - else - smax = smid; - end - end - res(d) = smid; - end - sides_perc_overlap = 1 - res; -end - - diff --git a/code/neumapper/bdl_corr_isomap.m b/code/neumapper/bdl_corr_isomap.m deleted file mode 100644 index 2f1409d..0000000 --- a/code/neumapper/bdl_corr_isomap.m +++ /dev/null @@ -1,42 +0,0 @@ -function embed_fX = bdl_corr_isomap(X, L, num_k, dim_embed) -% Function bdl_corr_isomap -% Inputs: -% X is an n x p data matrix. Rows are observations, columns are -% variables/features -% L is a subset of {1,2,...,p} -- the collection of landmarks. It is a -% subset of the features of X. -% num_k is the number of nearest neighbors used for the isomap portion -% dim_embed is the embedding dimension used in the isomap portion - -% Procedure: -% - Compute p x p matrix of correlations between features of X -% - For each feature, create a vector listing its correlations to the -% landmark features. This is an |L| x 1 vector. -% - Compute the "landmark-correlated" distance between the features. -% Specifically, given the p x |L| matrix constructed above, compute a p x p -% distance matrix using pdist2. -% - According to this distance matrix, two points are "close" if they have -% the same correlations to all the landmark points. Note that two highly -% correlated points may be "far apart" in this lens, if they have different -% correlations to the landmarks. -% - The landmarks form a "trusted set" -- they decide which features are -% similar - -% - Next the p x p distance matrix is passed to isomap for dimension -% reduction - -% Output: -% embed_fX -- a p x dim_embed matrix giving an embedding of the features of -% the data matrix X - -cX = corr(X); -corr_to_landmarks = cX(:,L); -landmark_corr_dist = pdist2(corr_to_landmarks,corr_to_landmarks); - -embed_fX = isomap(landmark_corr_dist, dim_embed, num_k); - -end - - - - diff --git a/code/neumapper/bdl_isomap.m b/code/neumapper/bdl_isomap.m deleted file mode 100644 index 47849a4..0000000 --- a/code/neumapper/bdl_isomap.m +++ /dev/null @@ -1,78 +0,0 @@ -function [embed_X, mapping] = bdl_isomap(distMat,dim_embed,num_k,pknng) -% Function bdl_isomap - -% Two key procedural differences between this code and van der Maaten's -% isomap.m: -% -- this code builds a penalized knn graph, instead of a standard knn -% graph -% -- if there are multiple components in the knn graph, connections are -% forced to produce a single component. In contrast, van der Maaten's -% isomap will retain only the largest component and drop the others - -% Input: -% distMat -- distances computed on Dataset. -% num_k -- k parameter for knn graph -% dim_embed -- embedding dimension -% pknng -- use weighted PKNNG - - -% Output: -% embed_X -- data matrix embedded in dim_embed dimensions -% mapping -- struct containing knn graph and geodesic distances - - - - -% Build distance matrix from X (default is Euclidean) -%if nargin < 5 -% dist = 'euclidean'; -%end -% -%distMat = pdist2(X,X,dist); - -% create penalized knn graph -% slight change here from bdl_isomap_v0 to current version: now using the -% binary adjacency matrix instead of the weighted adj matrix for more -% interpretability -% -% nevermind, this is now an option as of September 27, 2019 -% -[~,~,~,knn_g_bin,knn_g_wtd] = createPKNNG(distMat, num_k); -if ~pknng - knn_g = graph(knn_g_bin); % build graph from binary adj matrix -else - knn_g = graph(knn_g_wtd); % build graph from weighted adj matrix -end - -% estimate geodesic distances -%dist_geo_bin = round(distances(knn_g_bin,'Method','positive')); -%dist_geo_wtd = round(distances(knn_g_wtd,'Method','positive')); -%dist_geo_wtd = round(distances(knn_g_bin)); - - -%dist_geo = round(distances(knn_g,'Method','positive')); %edited 10/22/2019 -dist_geo = knn_g.distances; - -% symmetrize to prevent rounding error -dist_geo = (dist_geo + dist_geo')/2; - -% set mapping -mapping.graph = knn_g; -mapping.graphDist = dist_geo; - -% embed using cmdscale -[y,E] = cmdscale(dist_geo); - -mapping.mdsEvals = E; - -% get embedding in dimensions specified by dim_embed - -%embed_X = y(:,1:3); - -embed_X = y(:,1:dim_embed); - -%maxerr = max(max(abs(distMat - pdist2(embed_X,embed_X)))) - - -end - diff --git a/code/neumapper/buildDist.m b/code/neumapper/buildDist.m deleted file mode 100644 index 2c80642..0000000 --- a/code/neumapper/buildDist.m +++ /dev/null @@ -1,33 +0,0 @@ -function dX = buildDist(X,options) -% Function buildDist -% Create a distance matrix from data matrix X - - -% Options for metric -dXtype = getoptions(options,'dXtype','euclidean'); -dXgeod = getoptions(options,'dXgeod',true); -num_k = getoptions(options,'knnparam',6); -pknng = getoptions(options,'pknng',true); - - -tmpdx = pdist2(X,X,dXtype); %use for normalization -% force symmetrization; sometimes Matlab has round-off errors -tmpdx = (tmpdx + tmpdx')/2; - -diam = max(max(tmpdx)); - -if dXgeod - %fprintf("Computing geodesic distances...\n"); - %[~, mapping] = bdl_isomap(X,2,num_k,pknng,dXtype); - [~, mapping] = bdl_isomap(tmpdx,2,num_k,pknng); % Oct 8, 2019 - - dX = mapping.graphDist; - % normalize to have original diameter - graphDiam = max(max(dX)); - tmp = graphDiam/diam; - dX = dX./tmp; -else - %fprintf("Using non-geodesic distances (metric = %s)\n", dXtype); - dX = tmpdx; -end - diff --git a/code/neumapper/cbMapper.m b/code/neumapper/cbMapper.m deleted file mode 100644 index 7055244..0000000 --- a/code/neumapper/cbMapper.m +++ /dev/null @@ -1,51 +0,0 @@ -function [pts_in_smallBin, pts_in_bigBin, hrfdur_stat] = cbMapper(X,dX,options) -% Function cbMapper = connected b-Mapper -% Takes a distance matrix as input, builds a knn graph, and -% returns a cover of the graph. The cover includes disconnected pieces of -% the knn graph. -% -% Input includes data and fixed r,k,g values. For optimization, look at -% optim_cbMapper -% -% Apr 13, 2020 -% samirc@stanford.edu - -%% Obtain options. If a parameter is missing, switch to a default value. -resolution = getoptions(options,'resolution',30); -gain = getoptions(options,'gain',25); -k = getoptions(options,'knnparam',3); -hrfdur = getoptions(options,'hrfdur',11); -hrfdurprc = getoptions(options,'hrfdurprc',0.3); -tr = getoptions(options,'tr',1.5); -dfXtype = getoptions(options,'dfXtype','cityblock'); -sl_histo_bins = getoptions(options,'sl_histo_bins',10); - -%% For while loop used below, check that exit conditions are okay -if max(hrfdurprc) > 1 - error('Check hrfdurprc') -end - -%% Check that helper files have been loaded -if ~exist('px_maxmin.m','file') - error('Load the "tools" folder') -end - -%% Compute cbMapper - -%hrfdur = 11; %seconds. hrfdurpc % bins have two nodes that are at least hrfdur s apart -% tr = 1.5; - -rad = ceil(hrfdur/tr); - -% ev_help = @(v) find(v,1,'last') - find(v,1,'first'); -cv_help = @(v) max(v) - min(v); - -memberMat = construct_cover(X,resolution,gain,k,dfXtype);%first pass -pts_in_bigBin = cellfun(@find,num2cell(memberMat,2),'UniformOutput',false); -pts_in_smallBin = pc_sl_hist(pts_in_bigBin,dX,sl_histo_bins);%second pass -cover_width = cellfun(cv_help,pts_in_smallBin); -hrfdur_stat = sum(cover_width > rad)/length(cover_width); - -end - - diff --git a/code/neumapper/createPKNNG.m b/code/neumapper/createPKNNG.m deleted file mode 100644 index f466413..0000000 --- a/code/neumapper/createPKNNG.m +++ /dev/null @@ -1,123 +0,0 @@ -% WGGGG -% -% aim - to code neighborhood based filter function in Matlab -% author - saggar@stanford.edu (7.11.2019) -% -% -% output: knnGraph (as a table, binary and weighted versions) -% -% inspired by the paper on penalized KNN graph in Baya & Granitto 2011 BMC -% Bioinformatics -% -% Version History -% - [7.11.19] Wrote it to perform knn graph construction with outlier -% removal and penalized edges to construct a single connected component -% -% *** DISCLAIMER & NOTICE *** -% - Please DON'T SHARE this code yet, mainly because we still need to make sure -% it is valid and free of bugs. -% -function [knnGraphTbl, knnGraph_dense_bin, knnGraph_dense_wtd, knnGraph_dense_bin_conn, knnGraph_dense_wtd_conn]= createPKNNG(distMat, num_k) - % create neighborhood graph - knnGraphTbl = zeros(size(distMat,1), num_k); - knnGraph_bin = zeros(size(distMat)); - knnGraph_wtd = zeros(size(distMat)); - for n = 1:1:size(distMat,1) - [tmp idx] = sort(distMat(n,:),'ascend'); - knnGraphTbl(n,:) = idx(2:2+num_k-1); - for l = 1:1:num_k - knnGraph_bin(n, knnGraphTbl(n,l)) = 1; - knnGraph_wtd(n, knnGraphTbl(n,l)) = distMat(n,knnGraphTbl(n,l)); - - end - end - - % remove outliers in knn graph to find densely connected subgraphs - % first remove non-reciprocal connections - % - % TODO: remove outlier arc lengths; - % - % See excerpt from paper listed above: - % "[...] and the length of the arc is an out-lier of its own distribution - % (i.e. if its length is larger than the 3rd quartile plus 1.5 times - % the inter-quartile distance of the distribution of the lengths of - % all the edges in the graph)." - Baya & Granitto, 2011 - % - knnGraph_dense_bin = knnGraph_bin; - knnGraph_dense_wtd = knnGraph_wtd; - for n = 1:1:size(distMat,1) - tmp = knnGraphTbl(n,:); - for l = 1:1:num_k - if ~ismember(n,knnGraphTbl(tmp(l),:)) - knnGraph_dense_bin(n,tmp(l)) = 0; - knnGraph_dense_bin(tmp(l),n) = 0; - - knnGraph_dense_wtd(n,tmp(l)) = 0; - knnGraph_dense_wtd(tmp(l),n) = 0; - - end - - end - - end - - % connect disconnected components of the graph - % - % TODO: bound the weights so that distances do not explode? - % (see the Baya 2016 paper on PK-D adaptation of PKNNG) - % - g = graph(knnGraph_dense_wtd); - knnGraph_dense_wtd_conn = knnGraph_dense_wtd; - knnGraph_dense_bin_conn = knnGraph_dense_bin; - bins = conncomp(g); - nComp = max(bins); - if nComp > 1 - for c = 1:1:nComp - for d = c+1:1:nComp - nodes_c = find(bins==c); - nodes_d = find(bins==d); - max_edge_c = max(max(knnGraph_dense_wtd(nodes_c, nodes_c))); - max_edge_d = max(max(knnGraph_dense_wtd(nodes_d, nodes_d))); - if length(nodes_d) == 1 - [val, best_nodes_c] = min(distMat(nodes_d, nodes_c)); - % [samir] added this to fix indexing - best_nodes_c = nodes_c(best_nodes_c); - - % [samir] added Oct 31: divide by zero error if nodes_c is a - % singleton, so add a conditional. - if length(nodes_c) > 1 - knnGraph_dense_wtd_conn(nodes_d, best_nodes_c) = val * exp(val/max_edge_c); - else - % normalize using max edge weight in the full graph - knnGraph_dense_wtd_conn(nodes_d, best_nodes_c) = val * exp(val/max(max(knnGraph_dense_wtd))); - end - knnGraph_dense_wtd_conn(best_nodes_c, nodes_d) = knnGraph_dense_wtd_conn(nodes_d, best_nodes_c); - knnGraph_dense_bin_conn(nodes_d, best_nodes_c) = 1; - knnGraph_dense_bin_conn(best_nodes_c, nodes_d) = 1; - elseif length(nodes_c) == 1 - [val, best_nodes_d] = min(distMat(nodes_c, nodes_d)); - best_nodes_d = nodes_d(best_nodes_d); - - knnGraph_dense_wtd_conn(nodes_c, best_nodes_d) = val * exp(val/max_edge_d); - knnGraph_dense_wtd_conn(best_nodes_d, nodes_c) = knnGraph_dense_wtd_conn(nodes_c, best_nodes_d); - knnGraph_dense_bin_conn(nodes_c, best_nodes_d) = 1; - knnGraph_dense_bin_conn(best_nodes_d, nodes_c) = 1; - else % find the best pair of nodes between nodes_c and nodes_d that can be connected - tmp = distMat(nodes_c, nodes_d); - val = min(tmp(:)); - [nodes_c_min, nodes_d_min] = find(tmp==val); - nodes_c_min = nodes_c(nodes_c_min); - nodes_d_min = nodes_d(nodes_d_min); - knnGraph_dense_wtd_conn(nodes_c_min, nodes_d_min) = val * exp(val/max(max_edge_c,max_edge_d)); - knnGraph_dense_wtd_conn(nodes_d_min, nodes_c_min) = knnGraph_dense_wtd_conn(nodes_c_min, nodes_d_min); - knnGraph_dense_bin_conn(nodes_c_min, nodes_d_min) = 1; - knnGraph_dense_bin_conn(nodes_d_min, nodes_c_min) = 1; - end - - end - - end - end - - -end \ No newline at end of file diff --git a/code/neumapper/create_pruned_graph.m b/code/neumapper/create_pruned_graph.m deleted file mode 100644 index bd82fed..0000000 --- a/code/neumapper/create_pruned_graph.m +++ /dev/null @@ -1,19 +0,0 @@ -function [adja_pruned, prunedMat, prunedBins] = create_pruned_graph(memberMat) - -%% Find identical rows -prunedMat = unique(memberMat,'rows'); - -%% Create weighted adjacency matrix -n = size(prunedMat,1); -adja_pruned = zeros(n); - -for ii = 1:n - for jj = ii+1:n - adja_pruned(ii,jj) = double(prunedMat(ii,:))*double(prunedMat(jj,:))'; - end -end -adja_pruned = adja_pruned + adja_pruned'; - -prunedBins = cellfun(@find,num2cell(prunedMat,2),'UniformOutput',false); - -end \ No newline at end of file diff --git a/code/neumapper/create_pruned_graph_fast.m b/code/neumapper/create_pruned_graph_fast.m deleted file mode 100644 index 58540c3..0000000 --- a/code/neumapper/create_pruned_graph_fast.m +++ /dev/null @@ -1,26 +0,0 @@ -function [adja_pruned, prunedMat, prunedBins] = create_pruned_graph_fast(memberMat) -% Input: -% - memberMat: matrix of nr small bins by nr datapoints. 1 if datapoint in -% smallbin - -%% Find identical rows -prunedMat = unique(memberMat,'rows'); - -%% Create weighted adjacency matrix -n = size(prunedMat,1); - -% adja_pruned = zeros(n); -% for ii = 1:n -% for jj = ii+1:n -% adja_pruned(ii,jj) = double(prunedMat(ii,:))*double(prunedMat(jj,:))'; -% end -% end -% adja_pruned = adja_pruned + adja_pruned'; - -% we can speed up the loop above by doing a single dot product -adja_pruned = double(prunedMat) * double(prunedMat)' ; -adja_pruned = adja_pruned .* (1-eye(n)); % zero-out diagonal - -prunedBins = cellfun(@find,num2cell(prunedMat,2),'UniformOutput',false); - -end \ No newline at end of file diff --git a/code/neumapper/get_cluster_bins.m b/code/neumapper/get_cluster_bins.m new file mode 100644 index 0000000..9e82ef7 --- /dev/null +++ b/code/neumapper/get_cluster_bins.m @@ -0,0 +1,60 @@ +function [pts_in_clusterBins, memberMat] = get_cluster_bins(pts_in_coverBins,dX) +% Function get_cluster_bins +% +% Inputs: +% pts_in_coverBins : cell array of cover bin membership +% dX : distance matrix in native space +% +% Outputs: +% pts_in_clusterBins : cell array of cluster bin membership +% memberMat : cluster bin membership matrix +% +% Notes: +% Loop through each cover bin, cluster when needed + +num_coverBins = length(pts_in_coverBins); + +% Store indices of the cluster bins in each cover bin +% indices_clusterBins_in_coverBin = cell(num_covBins,1); + +% Initialize list of cover bins +coverBin_index = 0; +pts_in_clusterBins= []; + +% Loop over cover bins. Inside each cover bin, create new cluster bins +% as needed. Extra variables defined here: +% +% cluster_indices_within_coverBin : cluster membership in a cover bin +% +for bin = 1:num_coverBins + len = length(pts_in_coverBins{bin}); + + % Split into cluster bins if needed + if len == 0 + continue; % Pass control to next loop iteration + elseif len == 1 + cluster_indices_within_coverBin = [1]; % single cluster + elseif len > 1 + % Restrict distance matrix to this cover element + coverBin_dX = dX(pts_in_coverBins{bin}, pts_in_coverBins{bin}); + % Perform clustering + [Z, cutoff] = find_cluster_cutoff(coverBin_dX, 10, 'single'); + cluster_indices_within_coverBin = cluster(Z, 'cutoff',cutoff, 'criterion','distance'); + num_clusterBins_in_coverBin = max(cluster_indices_within_coverBin); + end + + % Create cluster bins, using a separate pointer for cluster bin indices + for j = 1:num_clusterBins_in_coverBin + coverBin_index = coverBin_index + 1; + pts_in_clusterBins{coverBin_index} = pts_in_coverBins{bin}(cluster_indices_within_coverBin==j); + end + +end + +% Convert into membership matrix +memberMat = false(length(pts_in_clusterBins),size(dX,1)); +for ii = 1:size(memberMat,1) + memberMat(ii,pts_in_clusterBins{ii}) = true; +end + +end diff --git a/code/neumapper/construct_cover.m b/code/neumapper/get_cover_bins.m similarity index 62% rename from code/neumapper/construct_cover.m rename to code/neumapper/get_cover_bins.m index bed0e08..81a84be 100644 --- a/code/neumapper/construct_cover.m +++ b/code/neumapper/get_cover_bins.m @@ -1,22 +1,19 @@ -function memberMat = construct_cover(X,resolution,gain,k,dfXtype) - -%% Build knn graph with reciprocal connections. -[nnid,~] = knnsearch(X,X,'K',k,'Distance',dfXtype); -n = size(nnid,1); -g = graph; -g = addnode(g,n); -for ii = 1:size(nnid,1) - v = nnid(ii,:); %get vertices that ii points to - w = max(nnid(v,:)==ii,[],2); %get vertices that also point back to ii - e = [repmat(ii,sum(w),1),v(w)']; %build edges - g = addedge(g,e(:,1),e(:,2)); -end -g = simplify(g); % remove self loops - -%% Now create a cover. -% The number of landmarks is divided proportional to -% the size of each connected component. +function memberMat = get_cover_bins(g,resolution,gain) +% Function get_cover_bins +% +% Inputs: +% g : rkNN graph +% resolution : int, number of landmarks for farthest point sampling +% gain : int, used to create overlaps +% +% Outputs: +% memberMat : cover bin membership matrix +% +% Notes: +% For disconnected rkNN graphs, the number of landmarks is divided +% proportional to the size of each connected component. +n = g.numnodes; [cc,ccs] = conncomp(g); binAlloc = ceil((ccs/n)*resolution); %grab extra landmarks if needed @@ -48,5 +45,4 @@ curr_col = next_col + 1; end - end \ No newline at end of file diff --git a/code/neumapper/get_mapper_graph.m b/code/neumapper/get_mapper_graph.m new file mode 100644 index 0000000..b08d134 --- /dev/null +++ b/code/neumapper/get_mapper_graph.m @@ -0,0 +1,25 @@ +function [adjacency, memberMat, pts_in_clusterBins] = get_mapper_graph(memberMat) +% Function get_mapper_graph +% +% Inputs: +% memberMat : membership matrix of cluster bins +% +% Outputs: +% adjacency : adjacency matrix of Mapper graph +% memberMat : cluster bin membership matrix; identical rows removed +% pts_in_clusterBins : points in cluster bins with identical bins removed +% + + +%% Find identical rows +memberMat = unique(memberMat,'rows'); + +%% Create weighted adjacency matrix +n = size(memberMat,1); + +adjacency = double(memberMat) * double(memberMat)' ; +adjacency = adjacency .* (1-eye(n)); % zero-out diagonal + +pts_in_clusterBins = cellfun(@find,num2cell(memberMat,2),'UniformOutput',false); + +end \ No newline at end of file diff --git a/code/neumapper/get_rknn.m b/code/neumapper/get_rknn.m new file mode 100644 index 0000000..000a9ec --- /dev/null +++ b/code/neumapper/get_rknn.m @@ -0,0 +1,25 @@ +function g = get_rknn(X,options) +% Function get_rknn +% Inputs: +% +% X : (num_obs, num_features) data matrix. +% options : struct containing several parameters. +% - metric : 'euclidean', 'cityblock', etc (see choices for pdist) +% - k : int, parameter for reciprocal nearest neighbor graphs +% +% Outputs: +% g : reciprocal kNN graph. + + +[nnid,~] = knnsearch(X,X,'K',options.k,'Distance',options.metric); +n = size(nnid,1); +g = graph; +g = addnode(g,n); +for ii = 1:size(nnid,1) + v = nnid(ii,:); %get vertices that ii points to + w = max(nnid(v,:)==ii,[],2); %get vertices that also point back to ii + e = [repmat(ii,sum(w),1),v(w)']; %build edges + g = addedge(g,e(:,1),e(:,2)); +end +g = simplify(g); % remove self loops +end \ No newline at end of file diff --git a/code/neumapper/neumapper.m b/code/neumapper/neumapper.m index 89d10f1..a0bd119 100644 --- a/code/neumapper/neumapper.m +++ b/code/neumapper/neumapper.m @@ -1,803 +1,79 @@ -function res = neumapper(X,options) +function [res,h] = neumapper(X,options) % Function neumapper % authors: Samir Chowdhury, Caleb Geniesse, Manish Saggar % % Inputs: -% (0) X is the data (rows are observations, columns are variables) -% (1) options contains the different parameters - -% Notes on input options: -% - An important idea in Mapper is that there are two metric spaces -% involved: (X,dX) and (fX,dfX). Here X is the original data, and is the -% only object supplied to the user. - -% - The user chooses dX, the metric with -% which to endow the original data. Choices include: lp-metrics, -% correlation, cosine, etc. For each of these choices, the user can -% additionally choose to build a knn-graph to approximate -% geodesic distances. -% - The choice of dX is necessary in the partial clustering step, which -% happens at the level of (X,dX). - -% - The user chooses how to obtain fX, which is a "filtered" version of the -% data. One method would be to apply a dimension reduction technique to X -% to get fX. - -% - Finally, the user chooses dfX, the metric on the filtered data. The -% choices here are the same as those encountered when choosing dX. -% - The choice of dfX is necessary in the binning stage. - -% Choices of dXtype/dfXtype: - - % 'euclidean' - Euclidean distance (default) - % 'squaredeuclidean' - Squared Euclidean distance - % 'seuclidean' - Standardized Euclidean distance. Each - % coordinate difference between rows in X and Y - % is scaled by dividing by the corresponding - % element of the standard deviation computed - % from X, S=NANSTD(X). To specify another value - % for S, use - % D = pdist2(X,Y,'seuclidean',S). - % 'cityblock' - City Block distance - % 'minkowski' - Minkowski distance. The default exponent is 2. - % To specify a different exponent, use - % D = pdist2(X,Y,'minkowski',P), where the - % exponent P is a scalar positive value. - % 'chebychev' - Chebychev distance (maximum coordinate - % difference) - % 'mahalanobis' - Mahalanobis distance, using the sample - % covariance of X as computed by NANCOV. To - % compute the distance with a different - % covariance, use - % D = pdist2(X,Y,'mahalanobis',C), where the - % matrix C is symmetric and positive definite. - % 'cosine' - One minus the cosine of the included angle - % between observations (treated as vectors) - % 'correlation' - One minus the sample linear correlation - % between observations (treated as sequences of - % values). - % 'spearman' - One minus the sample Spearman's rank - % correlation between observations (treated as - % sequences of values) - % 'hamming' - Hamming distance, percentage of coordinates - % that differ - % 'jaccard' - One minus the Jaccard coefficient, the - % percentage of nonzero coordinates that differ - - -% Implementation notes: -% (0) Start with dataset X (rows are observations, columns are variables). -% A distance matrix is needed for clustering, although this condition can -% be relaxed (ask Samir) - -% (1) Optionally perform dimension reduction (see (2a) below). - -% (2) Define a filter function on the data. Here are some ways to do this: -% (2a) Dimension filtration: embed the data into a lower dimensional space, -% e.g. 2d space, and then compose the dimension reduction with the identity -% function. The composed map has the form X --> R^2. -% -- this can be viewed as time x space - - -% (3) First partitioning step/"big" binning: Use a cover of the codomain to -% obtain a relaxed partition of (the rows of) X into bigBins. Each row of X -% can belong to multiple bigBins. Here a "relaxed" partition means that -% overlaps are allowed. -% -- the resolution and gain parameters are used here - - -% (4) Second partitioning step/"small" binning: for each bigBin, restrict -% the distance matrix and do some clustering step to obtain a refined (but -% still relaxed) partition into smallBins. Each row of X can belong to -% multiple smallBins -% -- the pcparam parameter is used here - -% (*) Pruning step: if two smallBins are identical, remove one of them - -% (5) Graph creation: -% (5a) Nodes are rows -% (5b) Two nodes form an edge if they belong to the same smallBin -% (5c) Color by the colors parameter - - -%% Obtain options. If a parameter is missing, switch to a default value. - -filename = getoptions(options,'filename','Unspecified data'); -dimreduce = getoptions(options,'dimreduce','none'); % 'bdl_isomap' -filter = getoptions(options,'filter','identity'); -binning = getoptions(options,'binning','cball'); % 'Nd' -resolution = getoptions(options,'resolution',nan); -gain = getoptions(options,'gain',nan); -clustering = getoptions(options,'clustering','sl_histo'); -colors = getoptions(options,'colors', X(:,1)); -labels = getoptions(options,'labels', []); -lens = getoptions(options,'lens', []); - -save_to = getoptions(options,'save_to',['res_',filename]); - -% 9.30.2020 plotting options to save memory and speed up -low_mem = getoptions(options,'low_mem',true); -plot_graph = getoptions(options,'plot_graph',true); -show_embed = getoptions(options,'show_embed',true); -use_layout = getoptions(options,'use_layout','force'); -save_plot = getoptions(options,'save_plot',false); - -% Options for metrics -dXtype = getoptions(options,'dXtype','euclidean'); -dXgeod = getoptions(options,'dXgeod',true); -dfXtype = getoptions(options,'dfXtype','euclidean'); -dfXgeod = getoptions(options,'dfXgeod',true); -pknng = getoptions(options,'pknng',true); - - -% Parameters for dimension reduction techniques -num_k = getoptions(options,'knnparam',nan); -maxiter = getoptions(options,'maxiter',200); -perplexity = getoptions(options,'perplexity',30); -dim_embed = getoptions(options,'dim_embed',2); - -% If clustering using 'sl_histo', specify number of bins for histogram -sl_histo_bins = getoptions(options,'sl_histo_bins',10); - - -% New options for preprocessing -preprocess = getoptions(options,'preprocess','none'); -initial_dims = getoptions(options,'initial_dims', size(X,2)); -if (initial_dims < 1) || isnan(initial_dims) - initial_dims = size(X,2); -end - -lens_preprocess = getoptions(options,'lens_preprocess','none'); -lens_initial_dims = getoptions(options,'lens_initial_dims', size(lens,2)); -if (lens_initial_dims < 1) || isnan(lens_initial_dims) - lens_initial_dims = max([size(lens,2),initial_dims]); -end - - - -%% Preprocess data (output will be used for partial clustering) -% Output: a preprocessed version of X, with dim_init - -switch preprocess - - case 'none' - disp('No preprocessing') - preprocessed_X = X; - - case 'MDS' - disp('Performing MDS') - preprocessed_X = compute_mapping(X,preprocess,initial_dims); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'nMDS' - % compute distance matrix based on input X - metric_options.dXtype = getoptions(options,'dXtype','euclidean'); - metric_options.dXgeod = getoptions(options,'dXgeod',false); - metric_options.knnparam = getoptions(options,'knnparam',6); - metric_options.pknng = getoptions(options,'pknng',true); % TODO: should we accept dXpknng, dfXpknng ? - dX_input = buildDist(X,metric_options); - - disp('Performing non-metric MDS') - % remove dimension reduction path; force matlab to use pca from - % stats toolbox (this is a subroutine in mdscale) - rmpath(genpath('../../dimReducMethods/')); - preprocessed_X = mdscale(dX_input, initial_dims); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'PCA' - disp('Performing PCA') - preprocessed_X = compute_mapping(X,preprocess,initial_dims); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'DiffusionMaps' - disp('Performing diffusion map embedding') - preprocessed_X = compute_mapping(X,preprocess,initial_dims); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'ManifoldChart' - disp('Performing manifold charting') - preprocessed_X = compute_mapping(X,preprocess,initial_dims); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - - -% Methods using k nearest neighbors - - case 'bdl_isomap' - - % compute distance matrix based on input X - metric_options.dXtype = getoptions(options,'dXtype','euclidean'); - metric_options.dXgeod = getoptions(options,'dXgeod',false); - metric_options.knnparam = getoptions(options,'knnparam',6); - metric_options.pknng = getoptions(options,'pknng',true); % TODO: should we accept dXpknng, dfXpknng ? - dX_input = buildDist(X,metric_options); - - fprintf(1,'Performing bdl_isomap with %d nearest neighbors \n',num_k) - preprocessed_X = bdl_isomap(dX_input,initial_dims,num_k,pknng); % Oct 8, 2019 - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'Isomap' - fprintf(1,'Performing Isomap with %d nearest neighbors \n',num_k) - preprocessed_X = compute_mapping(X,preprocess,initial_dims,num_k); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'LLE' - fprintf(1,'Performing locally linear embedding with %d nearest neighbors \n',num_k) - preprocessed_X = compute_mapping(X,preprocess,initial_dims,num_k); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'HessianLLE' - fprintf(1,'Performing Hessian locally linear embedding with %d nearest neighbors \n',num_k) - preprocessed_X = compute_mapping(X,preprocess,initial_dims,num_k); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'Laplacian' - fprintf(1,'Performing Laplacian eigenmap embedding with %d nearest neighbors \n',num_k) - preprocessed_X = compute_mapping(X,preprocess,initial_dims,num_k); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'LTSA' - fprintf(1,'Performing local tangent space alignment embedding with %d nearest neighbors \n',num_k) - preprocessed_X = compute_mapping(X,preprocess,initial_dims,num_k); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - -% Iterative methods - - case 'ProbPCA' - fprintf(1,'Performing Probabilistic PCA using %d iterations \n',options.maxiter) - preprocessed_X = compute_mapping(X,preprocess,initial_dims,options.maxiter); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - -% SNE-type methods - - case 'SNE' - fprintf(1,'Performing stochastic neighborhood embedding with perplexity %d \n',perplexity) - preprocessed_X = compute_mapping(X,preprocess,initial_dims,perplexity); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - case 'tSNE' - fprintf(1,'Performing tSNE with perplexity %d \n',perplexity) - %embed_X = compute_mapping(X,dimreduce,initial_dims,perplexity); - preprocessed_X = tsne(X, [], initial_dims, size(X,2), perplexity); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - -% Trajectory-focused methods - case 'bdl_corr_isomap' - % currently this is specialized to the winding trefoil case - %landmarks = 1:size(X,1); - landmarks = [200;1500;1800]; - fprintf(1,'Performing bdl_corr_isomap with %d nearest neighbors and %d landmarks \n',num_k,length(landmarks)) - X = X'; - preprocessed_X = bdl_corr_isomap(X,landmarks,num_k, initial_dims); - fprintf(1,'Data has been preprocessed (initial_dims = %d) \n',initial_dims); - - - otherwise - error('Did not recognize dimension reduction method') -end - - - - - - - - -%% Obtain metric at the data level -% Output: distance matrix dX on original data space, eventually -% used for partial clustering -metric_options.dXtype = getoptions(options,'dXtype','euclidean'); -metric_options.dXgeod = getoptions(options,'dXgeod',false); -metric_options.knnparam = getoptions(options,'knnparam',6); -metric_options.pknng = getoptions(options,'pknng',true); % TODO: should we accept dXpknng, dfXpknng ? - -dX = buildDist(preprocessed_X,metric_options); - - - - - -%% Prepare lens (i.e., data that will be embedded below) -% -% if user provided a lens, use that for dim reduction -% ... and compute new distance matrix based on the lens - -% use preprocessed_X and dX as lens_X and dX_lens -lens_X = preprocessed_X; -dX_lens = dX; - -% check for valid lens provided by the user -if ~isempty(lens) - - % use lens as lens_X - disp('Using lens provided by the user'); - lens_X = lens; - -end - - - - -%% Preprocess lens (output will be used for dim reduction and binning) -% Output: a preprocessed version of lens_X, with lens_initial_dims - -switch lens_preprocess - - case 'none' - disp('No lens preprocessing') - lens_X = lens_X; - - case 'MDS' - disp('Performing MDS on lens') - lens_X = compute_mapping(lens_X,lens_preprocess,initial_dims); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'nMDS' - % compute distance matrix based on input X - metric_options.dXtype = getoptions(options,'dXtype','euclidean'); - metric_options.dXgeod = getoptions(options,'dXgeod',false); - metric_options.knnparam = getoptions(options,'knnparam',6); - metric_options.pknng = getoptions(options,'pknng',true); % TODO: should we accept dXpknng, dfXpknng ? - dX_lens_input = buildDist(lens_X,metric_options); - - disp('Performing non-metric MDS on lens') - % remove dimension reduction path; force matlab to use pca from - % stats toolbox (this is a subroutine in mdscale) - rmpath(genpath('../../dimReducMethods/')); - lens_X = mdscale(dX_lens_input, lens_initial_dims); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'PCA' - disp('Performing PCA on lens') - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'DiffusionMaps' - disp('Performing diffusion map embedding on lens') - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'ManifoldChart' - disp('Performing manifold charting on lens') - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - - -% Methods using k nearest neighbors - - case 'bdl_isomap' - - % compute distance matrix based on input X - metric_options.dXtype = getoptions(options,'dXtype','euclidean'); - metric_options.dXgeod = getoptions(options,'dXgeod',false); - metric_options.knnparam = getoptions(options,'knnparam',6); - metric_options.pknng = getoptions(options,'pknng',true); % TODO: should we accept dXpknng, dfXpknng ? - dX_lens_input = buildDist(lens_X,metric_options); - - fprintf(1,'Performing bdl_isomap on lens with %d nearest neighbors \n',num_k) - lens_X = bdl_isomap(dX_lens_input,lens_initial_dims,num_k,pknng); % Oct 8, 2019 - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'Isomap' - fprintf(1,'Performing Isomap on lens with %d nearest neighbors \n',num_k) - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims,num_k); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'LLE' - fprintf(1,'Performing locally linear embedding on lens with %d nearest neighbors \n',num_k) - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims,num_k); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'HessianLLE' - fprintf(1,'Performing Hessian locally linear embedding on lens with %d nearest neighbors \n',num_k) - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims,num_k); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'Laplacian' - fprintf(1,'Performing Laplacian eigenmap embedding on lens with %d nearest neighbors \n',num_k) - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims,num_k); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'LTSA' - fprintf(1,'Performing local tangent space alignment embedding on lens with %d nearest neighbors \n',num_k) - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims,num_k); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - -% Iterative methods - - case 'ProbPCA' - fprintf(1,'Performing Probabilistic PCA on lens using %d iterations \n',options.maxiter) - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims,options.maxiter); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - -% SNE-type methods - - case 'SNE' - fprintf(1,'Performing stochastic neighborhood embedding on lens with perplexity %d \n',perplexity) - lens_X = compute_mapping(lens_X,lens_preprocess,lens_initial_dims,perplexity); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - case 'tSNE' - fprintf(1,'Performing tSNE on lens with perplexity %d \n',perplexity) - lens_X = tsne(lens_X, [], lens_initial_dims, size(lens_X,2), perplexity); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - -% Trajectory-focused methods - case 'bdl_corr_isomap' - % currently this is specialized to the winding trefoil case - %landmarks = 1:size(lens_X,1); - landmarks = [200;1500;1800]; - fprintf(1,'Performing bdl_corr_isomap on lens with %d nearest neighbors and %d landmarks \n',num_k,length(landmarks)) - lens_X = lens_X'; - lens_X = bdl_corr_isomap(lens_X,landmarks,num_k, lens_initial_dims); - fprintf(1,'Lens has been preprocessed (lens_initial_dims = %d) \n',lens_initial_dims); - - - otherwise - error('Did not recognize dimension reduction method') -end - - - - - - - -%% compute new distance matrix based on the lens (unless no lens or lens_preprocess) -if ~(isempty(lens) && strcmp(lens_preprocess, 'none')) - - disp('Computing distance matrix based on the (preprocessed) lens'); - metric_options.dXtype = getoptions(options,'dXtype','euclidean'); - metric_options.dXgeod = getoptions(options,'dXgeod',false); - metric_options.knnparam = getoptions(options,'knnparam',6); - metric_options.pknng = getoptions(options,'pknng',true); % TODO: should we accept dXpknng, dfXpknng ? - - dX_lens = buildDist(lens_X,metric_options); - -end - - - - - - - - -%% Dimension reduction -% Output: a low dimensional embedding, stored in embed_X - -switch dimreduce - - case 'none' - disp('No dimension reduction') - embed_X = lens_X; - - case 'MDS' - disp('Performing MDS') - embed_X = compute_mapping(lens_X,dimreduce,dim_embed); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'nMDS' - disp('Performing non-metric MDS') - % remove dimension reduction path; force matlab to use pca from - % stats toolbox (this is a subroutine in mdscale) - rmpath(genpath('../../dimReducMethods/')); - embed_X = mdscale(dX_lens, dim_embed); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'PCA' - disp('Performing PCA') - embed_X = compute_mapping(lens_X,dimreduce,dim_embed); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'DiffusionMaps' - disp('Performing diffusion map embedding') - embed_X = compute_mapping(lens_X,dimreduce,dim_embed); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'ManifoldChart' - disp('Performing manifold charting') - embed_X = compute_mapping(lens_X,dimreduce,dim_embed); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - - -% Methods using k nearest neighbors - - case 'bdl_isomap' - fprintf(1,'Performing bdl_isomap with %d nearest neighbors \n',num_k) - embed_X = bdl_isomap(dX_lens,dim_embed,num_k,pknng); % Oct 8, 2019 - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'Isomap' - fprintf(1,'Performing Isomap with %d nearest neighbors \n',num_k) - embed_X = compute_mapping(lens_X,dimreduce,dim_embed,num_k); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'LLE' - fprintf(1,'Performing locally linear embedding with %d nearest neighbors \n',num_k) - embed_X = compute_mapping(lens_X,dimreduce,dim_embed,num_k); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'HessianLLE' - fprintf(1,'Performing Hessian locally linear embedding with %d nearest neighbors \n',num_k) - embed_X = compute_mapping(lens_X,dimreduce,dim_embed,num_k); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'Laplacian' - fprintf(1,'Performing Laplacian eigenmap embedding with %d nearest neighbors \n',num_k) - embed_X = compute_mapping(lens_X,dimreduce,dim_embed,num_k); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'LTSA' - fprintf(1,'Performing local tangent space alignment embedding with %d nearest neighbors \n',num_k) - embed_X = compute_mapping(lens_X,dimreduce,dim_embed,num_k); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - -% Iterative methods - - case 'ProbPCA' - fprintf(1,'Performing Probabilistic PCA using %d iterations \n',options.maxiter) - embed_X = compute_mapping(lens_X,dimreduce,dim_embed,options.maxiter); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - -% SNE-type methods - - case 'SNE' - fprintf(1,'Performing stochastic neighborhood embedding with perplexity %d \n',perplexity) - embed_X = compute_mapping(lens_X,dimreduce,dim_embed,perplexity); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - case 'tSNE' - fprintf(1,'Performing tSNE with perplexity %d \n',perplexity) - %embed_X = compute_mapping(lens_X,dimreduce,dim_embed,perplexity); - embed_X = tsne(lens_X, [], dim_embed, size(lens_X,2), perplexity); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - -% Trajectory-focused methods - case 'bdl_corr_isomap' - % currently this is specialized to the winding trefoil case - %landmarks = 1:size(lens_X,1); - landmarks = [200;1500;1800]; - fprintf(1,'Performing bdl_corr_isomap with %d nearest neighbors and %d landmarks \n',num_k,length(landmarks)) - lens_X = lens_X'; - embed_X = bdl_corr_isomap(lens_X,landmarks,num_k, dim_embed); - fprintf(1,'Data has been embedded into %d dimensions \n',dim_embed); - - - otherwise - error('Did not recognize dimension reduction method') -end - - - - - - - - - - - -%% Filter function -% Output: a (possibly lower) dimensional projection, stored in filter_X +% X : (num_obs, num_features) data matrix. +% Although not a requirement, NeuMapper is best used for data +% with num_features > 5 +% options : struct containing several parameters. +% - metric : 'euclidean', 'cityblock', etc (see choices for pdist) +% - k : int, parameter for reciprocal nearest neighbor graphs +% - resolution : int, resolution parameter used during farthest point sampling +% - gain : int, gain parameter used when building cover bins +% - labels : (num_obs,1) vector of data point labels +% +% Outputs: +% res : struct containing the NeuMapper graph. +% h : figure handle -switch filter - case 'identity' - disp('Using identity filtration') - - filter_X = embed_X; - - case 'time' - disp('Incorporating time in the filtration') - times = linspace(mean(min(embed_X)), mean(max(embed_X)), size(embed_X,1)); - %times = 1:size(embed_X,1); - filter_X = [embed_X, times']; - - otherwise - error('Did not recognize filter function') +%% Set up options +if ~isfield(options,'metric') + options.metric = 'cityblock'; % Default to Euclidean end - - -%% Obtain metric at the filtered data level -% Output: distance matrix dfX on filtered data space, -% used for partial clustering -if strcmp(binning, 'ball') - metric_options.dXtype = getoptions(options,'dfXtype','euclidean'); - metric_options.dXgeod = getoptions(options,'dfXgeod',false); - metric_options.knnparam = getoptions(options,'knnparam',6); - metric_options.pknng = getoptions(options,'pknng',true); % TODO: should we accept dXpknng, dfXpknng ? - - disp('Computing dfX') - dfX = buildDist(filter_X,metric_options); +if ~isfield(options,'k') + options.k = 12; end - - - -%% Binning: first pass -% Output: a cell array called pts_in_bigBin that comprises bins with -% indices of observations in each bin - -switch binning - case 'Nd' - disp('Using Nd binning') - - nsides = getoptions(options, 'nsides', 4); - pts_in_bigBin = bdl_binning(filter_X, resolution, gain, nsides); - fprintf(1,'First binning stage produced %d bigBins \n', ... - length(pts_in_bigBin)); - - case 'ball' - disp('Using ball mapper') - - [pts_in_bigBin, ~] = ballMapper(dfX, options); - - case 'cball' - disp('Using connected ball mapper with fixed values') - [pts_in_smallBin, pts_in_bigBin, hrfdurstat] = cbMapper(filter_X,dX,options); - -% if ~isnan(resolution) && ~isnan(gain) && ~isnan(num_k) -% disp('Using connected ball mapper with fixed values') -% [pts_in_smallBin, pts_in_bigBin, hrfdurstat] = cbMapper(filter_X,dX,options); -% else -% disp('Using connected ball mapper with optimization') -% [pts_in_smallBin, pts_in_bigBin, rkg, hrfdurstats] = optim_cbMapper(filter_X,dX,options); -% end - - otherwise - error('Did not recognize binning strategy') +if ~isfield(options,'resolution') + options.resolution = floor(0.25*size(X,1)); end -%% Binning: second pass//partial clustering -% Output: a refined cell array called pts_in_smallBin comprising of bins -% with indices of observations in each bin - -if ~exist('pts_in_smallBin','var') - -switch clustering - case 'sl_histo' - disp('Partial clustering with single linkage and histograms') - pts_in_smallBin = pc_sl_hist(pts_in_bigBin,dX, ... - sl_histo_bins); - case 'avel_histo' - disp('Partial clustering with average linkage and histograms') - pts_in_smallBin = pc_avel_hist(pts_in_bigBin,dX, ... - sl_histo_bins); - - case 'cl_histo' - disp('Partial clustering with complete linkage and histograms') - pts_in_smallBin = pc_cl_hist(pts_in_bigBin,dX, ... - sl_histo_bins); - - otherwise - error('Did not recognize partial clustering method') -end +if ~isfield(options,'gain') + options.gain = 50; end -%% Create membership matrix prior to pruning -memberMat = false(length(pts_in_smallBin),size(lens_X,1)); -for ii = 1:size(memberMat,1) - memberMat(ii,pts_in_smallBin{ii}) = true; +if options.gain < 25 + fprintf('Gain should be at least 25, updating\n') + options.gain = 25; end -%% Pruned graph creation -% Output: -% - remove smallBins that are identical -% - create weighted adjacency matrix where weights are proportional to size -% of intersection - -fprintf(1,'Pruning Mapper nodes\n'); -[adja_pruned, memberMat, pts_in_smallBin_pruned] = create_pruned_graph_fast(memberMat); - - -%% Start storing all results in a struct -% Output: a struct which contains the dataset name, all mapper parameters -% used in the analysis, as well as outputs in each layer of the mapper -% pipeline. - -res = struct; -res.filename = filename; -res.options = options; - -% need to store filter_X for plotting -res.filter_X = filter_X; - -% store other variables here -% res.bigBin = pts_in_bigBin; -% res.smallBin = pts_in_smallBin; -res.smallBinPruned = pts_in_smallBin_pruned; -res.memberMat = sparse(memberMat); -res.adja_pruned = adja_pruned; - -% res.opt_gain = opt_gain; -% res.opt_k = opt_k; -if exist('hrfdurstat', 'var') - res.hrfdurstat = hrfdurstat; +if ~isfield(options,'labels') + options.labels = (1:size(X,1))'; end -%% Plot graphs -% 9.30.2020 plotting takes a lot of time, make it optional - -if plot_graph | show_embed | save_plot - - % create filename for saving (and title) - [save_path,save_name,~] = fileparts(save_to); - title_text = save_name; +%% Generate initial distance matrix - if save_plot & ~ischar(save_plot) & ~isstring(save_plot) - save_plot = fullfile(save_path,strcat('plotGraph_',save_name,'.png')); - fprintf(1,['Figure saved as ',save_plot,'\n']); - end - - % visualize - fprintf(1,'Visualizing force layout of graph\n'); - [graph, h, node_sizes, node_colors] = replotGraph(res,colors,labels,title_text,show_embed,use_layout,save_plot); +dX = pdist2(X,X,options.metric); +dX = (dX+dX')/2; % force symmetrization to avoid round-off errors -else - - % skip plotting, but process graph, node_sizes, node-colors, etc. - fprintf(1,"Processing graph (use plot_graph=true for visualization)\n"); - [graph, node_sizes, node_colors] = processGraph(res,colors); +%% Generate rkNN graph +g = get_rknn(X,options); -end - - - -%% 09.09.2021 -if ~low_mem - - % store data matrices - res.X = X; - res.preprocessed_X = preprocessed_X; - res.lens_X = lens_X; - res.embed_X = embed_X; - res.filter_X = filter_X; - % distance matrices - res.dX = dX; - res.dX_lens = dX_lens; - if exist('dfX','var') - res.dfX = dfX; - end +%% Obtain cover and cluster bins +coverBins = get_cover_bins(g,options.resolution,options.gain); +pts_in_coverBins = cellfun(@find,num2cell(coverBins,2),'UniformOutput',false); - % membership bins - res.bigBin = pts_in_bigBin; - res.smallBin = pts_in_smallBin; - res.smallBinPruned = pts_in_smallBin_pruned; - -% % membership matrices -% res.bigBinMat = false(length(res.bigBin),size(res.lens_X,1)); -% res.smallBinMat = false(length(res.smallBin),size(res.lens_X,1)); -% res.smallBinPrunedMat = false(length(res.smallBinPruned),size(res.lens_X,1)); -% for ii = 1:size(res.smallBinMat,1) % only loop over biggest one for speed -% if ii < size(res.bigBinMat,1) -% res.bigBinMat(ii, res.bigBin{ii}) = true; -% end -% if ii < size(res.smallBinPruned,1) -% res.smallBinPrunedMat(ii, res.smallBinPruned{ii}) = true; -% end -% res.smallBinMat(ii, res.smallBin{ii}) = true; -% end +[pts_in_clusterBins, clusterBins] = get_cluster_bins(pts_in_coverBins,dX); -end +%% Construct mapper graph +[adjacency, clusterBins, pts_in_clusterBins] = get_mapper_graph(clusterBins); -%% Store graph in the struct -res.graph = graph; -res.node_sizes = node_sizes; -res.node_colors = node_colors; -res = rmfield(res,'adja_pruned'); % this is stored in sparse form in res.graph +res = struct; -save(save_to,'res') -fprintf(1,['Result saved to ',save_to,'\n']) +max_dim_to_store = min(size(X,2),3); % Store only up to 3 columns of data +res.filter_X = X(:,1:max_dim_to_store); +res.clusterBins = clusterBins; +res.pts_in_clusterBins = pts_in_clusterBins; +res.adjacency = adjacency; +res.labels = options.labels; +res.options = options; +h = plot_mapper_graph(res); end diff --git a/code/neumapper/pc_avel_hist.m b/code/neumapper/pc_avel_hist.m deleted file mode 100644 index 95a6cec..0000000 --- a/code/neumapper/pc_avel_hist.m +++ /dev/null @@ -1,4 +0,0 @@ -function pts_in_smallBin = pc_avel_hist(pts_in_bigBin,distMat, ... - sl_histo_bins) - pts_in_smallBin = pc_sl_hist(pts_in_bigBin, distMat, sl_histo_bins, 'average'); -end diff --git a/code/neumapper/pc_cl_hist.m b/code/neumapper/pc_cl_hist.m deleted file mode 100644 index 3602492..0000000 --- a/code/neumapper/pc_cl_hist.m +++ /dev/null @@ -1,4 +0,0 @@ -function pts_in_smallBin = pc_cl_hist(pts_in_bigBin,distMat, ... - sl_histo_bins) - pts_in_smallBin = pc_sl_hist(pts_in_bigBin, distMat, sl_histo_bins, 'complete'); -end diff --git a/code/neumapper/pc_sl_hist.m b/code/neumapper/pc_sl_hist.m deleted file mode 100644 index 33d548f..0000000 --- a/code/neumapper/pc_sl_hist.m +++ /dev/null @@ -1,88 +0,0 @@ -function [pts_in_smallBin, bigbin_idx_in_smallBin] = pc_sl_hist(... - pts_in_bigBin, distMat, sl_histo_bins, linkage_method) -% Function pc_sl_hist -% Partial clustering with single linkage and histograms - -% Notation: Mapper does two binning steps. We give the name "bigBins" to -% the bins produced in the first pass. Each bigBin is then clustered -% further through a partial clustering step. The resulting clusters are -% called "smallBins". - -% Inputs: -% (1) cell array of bigBins containing indices of the data points in -% each bigBin -% (2) full distance matrix of original space -% (3) number of histogram bins used when determining the cutoff - -% Output: cell array of smallBins containing indices of the data points in -% each smallBin. - -if nargin < 4 - linkage_method = 'single'; -end - -% Implementation notes: loop through each bigBin, cluster when possible - -num_bigBins = length(pts_in_bigBin); - -% The next variable stores, for each bigBin, the indices of the smallBins -% in that bigBin. -indices_smallBins_in_bigBin = cell(num_bigBins,1); - -% Initialize list of smallBins -smallBin_index = 0; -pts_in_smallBin= []; -bigbin_idx_in_smallBin = []; - - -for bin = 1:num_bigBins -% First we use an if statement to figure out how many smallBins will be -% produced from the current bigBin (i.e. how many clusters we will obtain) -% Then we loop over each smallBin to record the indices of the observations -% in the smallBin. - - len = length(pts_in_bigBin{bin}); - - if len == 0 - %fprintf(1,'Level set is empty\n'); - indices_smallBins_in_bigBin{bin} = -1; - continue; - elseif len == 1 - %fprintf(1,'Level set has only 1 pt\n'); - num_smallBins_in_bigBin = 1; - cluster_indices_within_bigBin = [1]; - % initialize a new smallBin and give it an index - indices_smallBins_in_bigBin{bin} = smallBin_index + 1; - elseif len > 1 - %fprintf(1,'Level set has %d pts\n', len); - % get restriction of distance matrix - bigBin_distMat = distMat(pts_in_bigBin{bin}, pts_in_bigBin{bin}); - - % perform clustering - [Z, cutoff] = find_cluster_cutoff(bigBin_distMat, sl_histo_bins, linkage_method); - cluster_indices_within_bigBin = cluster(Z, 'cutoff',cutoff, 'criterion','distance'); - - % above returns a list of clusters [1:number of clusters] - num_smallBins_in_bigBin = max(cluster_indices_within_bigBin); - % initialize new smallBins, give them indices relative to the last - % used index - indices_smallBins_in_bigBin{bin} = smallBin_index + ... - (1:num_smallBins_in_bigBin); - end - - for j = 1:num_smallBins_in_bigBin - % if the latter was not defined, i.e. we had len==0, then the continue - % statement passes to the next iteration of the enclosing loop - - % iterate counter for each new smallBin - smallBin_index = smallBin_index + 1; - pts_in_smallBin{smallBin_index} = pts_in_bigBin{bin}(cluster_indices_within_bigBin==j); - bigbin_idx_in_smallBin{smallBin_index} = bin; -% pts_in_smallBin changes size on each iteration, which can likely be -% optimized. But this is not immediate because we do not know how many -% smallBins will be created, a priori. - - end -end -end - diff --git a/code/neumapper/plot_mapper_graph.m b/code/neumapper/plot_mapper_graph.m new file mode 100644 index 0000000..6803384 --- /dev/null +++ b/code/neumapper/plot_mapper_graph.m @@ -0,0 +1,170 @@ +function h = plot_mapper_graph(res) +% Function plot_mapper_graph +% +% Inputs: +% res : struct containing several field. +% - filter_X : first few coordinates of data +% - adjacency : mapper graph adjacency matrix +% - pts_in_clusterBins: points in mapper graph nodes +% - labels : (num_obs,1) vector of data point labels. +% Labels are expected to be integers 1,2,... +% +% Outputs: +% h : Figure handle + +g = graph(res.adjacency); + +%% Set up colors for plotting +cmap_timing = zeros(size(res.filter_X,1),3); +color_vals = res.labels; +unique_colors = unique(color_vals, 'rows'); + +% optimize colormap +num_timing_colors = numel(unique_colors); +timing_colors = turbo(num_timing_colors+2); +timing_colors = timing_colors(2:end-1, :); % drop darker end colors + +% finish mapping colors +for n = 1:1:length(res.filter_X) %length(color_vals) + cmap_timing(n,:) = timing_colors(color_vals(n),:); +end + +fig = figure('Position', [0 0 1000 400]); +% plot embedding +subplot(1,2,1) +plot_embedding(res.filter_X,cmap_timing); + +% plot mapper graph +subplot(1,2,2) +[h, node_sizes, node_colors] = plot_mapper(g, res.pts_in_clusterBins, cmap_timing, 'force'); + + +end + + +%% Helper functions + +function plot_embedding(filter_X, cmap_timing) + + if size(filter_X,2) == 2 + + % 2d scatter plot + h = scatter(filter_X(:,1), filter_X(:,2),[], cmap_timing, 'filled'); + ax = get(h,'Parent'); % only keep tick labels at bounds and zeros + xtick = get(ax,'XTick'); + ytick = get(ax,'YTick'); + set(ax,'XTick',sort(unique([xtick(1), 0, xtick(end)]))); + set(ax,'YTick',sort(unique([ytick(1), 0, ytick(end)]))); + xlabel('Filter 1', 'interpreter', 'none'); + ylabel('Filter 2', 'interpreter', 'none'); + + elseif size(filter_X,2) == 3 + + % 3d scatter plot + h = scatter3(filter_X(:,1), filter_X(:,2), filter_X(:,3), [], cmap_timing, 'filled'); + ax = get(h,'Parent'); % only keep tick labels at bounds and zeros + xtick = get(ax,'XTick'); + ytick = get(ax,'YTick'); + ztick = get(ax,'ZTick'); + set(ax,'XTick',sort(unique([xtick(1), 0, xtick(end)]))); + set(ax,'YTick',sort(unique([ytick(1), 0, ytick(end)]))); + set(ax,'ZTick',sort(unique([ztick(1), 0, ztick(end)]))); + xlabel('Filter 1', 'interpreter', 'none'); + ylabel('Filter 2', 'interpreter', 'none'); + zlabel('Filter 3', 'interpreter', 'none'); + + elseif size(filter_X,2) > 3 + + % heatmap (TODO: rugplot?) + h = imagesc(filter_X); + xlabel('Filters', 'interpreter', 'none'); + ylabel('Time frames (TR)', 'interpreter', 'none'); + cmap = colormap('turbo'); + cbar = colorbar; + + else + + % 1d scatter plot (hack to match heatmaps, plot top to bottom) + h = scatter(filter_X(:,1), -[1:1:size(filter_X,1)], [], cmap_timing, 'filled'); + ax = get(h,'Parent'); % only keep tick labels at bounds and zeros + + % fix xtick lables + xtick = get(ax,'XTick'); + xtick = sort(unique([xtick(1), 0, xtick(end)])); + if numel(unique(filter_X(:,1))) < 10 + xtick = unique(filter_X(:,1)); + end + set(ax,'XTick',xtick); + + % simulate TR labels (plot from top to bottom) + set(ax, 'YLim',[-size(filter_X,1), 0]); + ytick = get(ax,'YTick'); + %ytick = sort(unique([ytick, -size(filter_X,1)])); + set(ax,'YTick', ytick); + set(ax,'YTickLabels',abs(ytick(1:1:end))); + ylabel('Time frames (TR)', 'interpreter', 'none'); + + end + + %set(gcf,'Color','none'); + %set(gca,'Color','none'); + axis square; + +end + +function plot_embedding_heatmap(filter_X, cmap_timing) + + % heatmap (TODO: rugplot?) + h = imagesc(filter_X); + xlabel('Filters', 'interpreter', 'none'); + ylabel('Time frames (TR)', 'interpreter', 'none'); + cmap = colormap('turbo'); + cbar = colorbar; + + %set(gcf,'Color','none'); + %set(gca,'Color','none'); + axis square; + +end + + +function [h, node_sizes, node_colors] = plot_mapper(g, smallBins, cmap_timing, useLayout) + +if ~exist('useLayout','var') + useLayout = 'force'; +end + +nodes = g.Nodes; +nn = size(nodes,1); + +node_colors = zeros(nn,3); + +%% create a scaling parameter for the node sizes +smallBin_sizes = cellfun('size',smallBins,2); +%max_size = max(smallBin_sizes); +%node_sizes = 5+log(1+smallBin_sizes); +node_sizes = 1+log(1+smallBin_sizes); + +%% Plot the graph and highlight nodes +for ii = 1:nn + node_colors(ii,:) = mean(cmap_timing(smallBins{ii},:),1); +end + +h = plot(g,'Layout', useLayout,'NodeLabel',{}); +if strcmp(useLayout,'force') || strcmp(useLayout,'force3') + layout(h,useLayout,'UseGravity',true,'WeightEffect','none'); +end + +h.MarkerSize = node_sizes; +h.NodeColor = node_colors; +h.EdgeColor = [0 0 0]; +h.LineWidth = 1; + +axis equal; +if strcmp(useLayout,'force3') + view(gca, [-30, 15.0]); +else + set(gca,'Visible','off'); +end + +end \ No newline at end of file diff --git a/code/neumapper/processGraph.m b/code/neumapper/processGraph.m deleted file mode 100644 index 316ed0e..0000000 --- a/code/neumapper/processGraph.m +++ /dev/null @@ -1,92 +0,0 @@ -function [g, node_sizes, node_colors] = processGraph(res,color_vals) -% Return a graph, and node sizes and colors (modified from replotGraph.m) -% res -- a struct containing the following variables from -% neumapper: -% - filter_X -% - smallBinPruned -% - graph, or adja_pruned if graph is not available -% color_vals -- an array containing categorical labels for each data -% point - - - -%% Extract necessary inputs from struct -filter_X = res.filter_X; -smallBins = res.smallBinPruned; - -if isfield(res,'graph') - g = res.graph; -elseif isfield(res,'adja_pruned') - adja = res.adja_pruned; - g = graph(adja); -else - error('Did not find graph information in input') -end - - - -%% Set up colors for plotting -% Output: -% cmap_timing -- an array coloring each data point according to the -% categorical labels provided in color_vals. Here we write "timing" because -% the labels often correspond to task labels, and the data points are -% coming from time series data in a continuous multitask experiment - -cmap_timing = zeros(size(filter_X,1),3); -%timing_colors = [0 0 1; 0.078 1 0.2275; 1 1 0; 0.9290 0.6940 0.1250; 1 0 0]; %blue, green, yellow, orange, red -timing_colors = [44/255 18/255 245/255; 117/255 250/255 75/255; 249/255 231/255 91/255; 240/255 156/255 57/255; 235/255 51/255 38/255]; %blue, green, yellow, orange, red - -unique_colors = unique(color_vals, 'rows'); -num_timing_colors = size(timing_colors,1); - -% changes for non-CME timing labels -if numel(unique_colors) ~= 5 % default behavior for CME - - % encode non-continuous values (e.g., 1,2,9 => 1,2,3) - if any(diff(unique_colors) > 1) - [rows_,color_enc_] = find(color_vals==transpose(unique_colors)); - color_vals(rows_) = color_enc_; - end - - % now get unique encoded values - unique_colors = unique(color_vals, 'rows'); - - % optimize colormap - num_timing_colors = numel(unique_colors); - timing_colors = turbo(num_timing_colors+2); - timing_colors = timing_colors(2:end-1, :); % drop darker end colors - -end - -% quick hack to accept continuous valued colors -if ~all(any(unique_colors == 1:num_timing_colors)) - color_vals = discretize(color_vals, num_timing_colors); -end - -% finish mapping colors -for n = 1:1:length(filter_X) %length(color_vals) - cmap_timing(n,:) = timing_colors(color_vals(n),:); -end - - -%% get node sizes, colors -nodes = g.Nodes; -nn = size(nodes,1); -node_colors = zeros(nn,3); - -%% create a scaling parameter for the node sizes -smallBin_sizes = cellfun('size',smallBins,2); -%node_sizes = 5+log(1+smallBin_sizes); -node_sizes = 1+log(1+smallBin_sizes); - -%% Compute node color as the mean color over members -for ii = 1:nn - node_colors(ii,:) = mean(cmap_timing(smallBins{ii},:),1); -end - - -end - - - - diff --git a/code/neumapper/replotGraph.m b/code/neumapper/replotGraph.m deleted file mode 100644 index 20ddbfb..0000000 --- a/code/neumapper/replotGraph.m +++ /dev/null @@ -1,329 +0,0 @@ -function [g, h, node_sizes, node_colors] = replotGraph(res,color_vals,labels_arr,titleText,displayEmbed,useLayout,save_plot) -% Function replotGraph -% Reproduce a mapper graph from stored struct -% Inputs: -% res -- a struct containing the following variables from -% neumapper: -% - filter_X -% - smallBinPruned -% - graph, or adja_pruned if graph is not available -% color_vals -- an array containing categorical labels for each data -% point -% titleText -- Figure caption -% displayEmbed -- Boolean flag. True displays the embedding of the data - -% Thanks to Oliver Xie for suggesting the logarithmic mapping for the node -% sizes - -if ~exist('titleText','var') - titleText = res.filename; -end - -if ~exist('displayEmbed','var') - displayEmbed = 0; -end - -if ~exist('useLayout','var') - useLayout = 'force'; -end - -% either 0/1,true/false, or filename for saving -if ~exist('save_plot','var') - save_plot = 0; -elseif save_plot & ~ischar(save_plot) & ~isstring(save_plot) - if isfield(res.options, 'save_to') - [save_path,save_name] = fileparts(res.options.save_to); - else - [save_path,save_name] = fileparts(res.filename); - end - save_plot = fullfile(save_path,strcat('plotGraph_',save_name,'.png')); -end - - -%% Extract necessary inputs from struct -filter_X = res.filter_X; -smallBins = res.smallBinPruned; - -if isfield(res,'graph') - g = res.graph; -elseif isfield(res,'adja_pruned') - adja = res.adja_pruned; - g = graph(adja); -else - error('Did not find graph information in input') -end - - - -%% Set up colors for plotting -% Output: -% cmap_timing -- an array coloring each data point according to the -% categorical labels provided in color_vals. Here we write "timing" because -% the labels often correspond to task labels, and the data points are -% coming from time series data in a continuous multitask experiment - -cmap_timing = zeros(size(filter_X,1),3); -% timing_colors = [0 0 1; 0.078 1 0.2275; 1 1 0; 0.9290 0.6940 0.1250; 1 0 0]; %blue, green, yellow, orange, red - -% As used by Dyneusr -% timing_colors = [44/255 18/255 245/255; 117/255 250/255 75/255; 249/255 231/255 91/255; 240/255 156/255 57/255; 235/255 51/255 38/255]; %blue, green, yellow, orange, red -timing_colors = [44/255 18/255 245/255; 117/255 250/255 75/255; 249/255 231/255 91/255; 240/255 156/255 57/255; 235/255 51/255 38/255]; %blue, green, yellow, orange, red - -unique_colors = unique(color_vals, 'rows'); -num_timing_colors = size(timing_colors,1); - -% changes for non-CME timing labels -if numel(unique_colors) ~= 5 % default behavior for CME - - % encode non-continuous values (e.g., 1,2,9 => 1,2,3) - if any(diff(unique_colors) > 1) - [rows_,color_enc_] = find(color_vals==transpose(unique_colors)); - color_vals(rows_) = color_enc_; - end - - % now get unique encoded values - unique_colors = unique(color_vals, 'rows'); - - % optimize colormap - num_timing_colors = numel(unique_colors); - timing_colors = turbo(num_timing_colors+2); - timing_colors = timing_colors(2:end-1, :); % drop darker end colors - - %disp([unique_colors, timing_colors]) -end - -% quick hack to accept continuous valued colors -if ~all(any(unique_colors == 1:num_timing_colors)) - color_vals = discretize(color_vals, num_timing_colors); -end - -% finish mapping colors -for n = 1:1:length(filter_X) %length(color_vals) - cmap_timing(n,:) = timing_colors(color_vals(n),:); -end - -% process labels, if available -legend_groups = 1:num_timing_colors; -legend_labels = num2cell(1:num_timing_colors); -if numel(unique(labels_arr)) == numel(unique(color_vals)) - legend_data = table(); - legend_data.groups = unique(color_vals,'rows','stable'); - legend_data.labels = unique(labels_arr,'rows','stable'); - legend_data.Row = string(legend_data.groups); - legend_data = legend_data(sort(legend_data.Row),:); - % get sorted (and aligned) groups, labels - legend_groups = legend_data.groups; - legend_labels = legend_data.labels; -end - - - -%% Plot images -if displayEmbed - - % TODO: handle special case when filter_X has more than 3 dimensions - if size(filter_X,2) > 3 - - fig = figure('Position', [0 0 1000 400]); - - % plot embedding - subplot(1,3,1) - plot_embedding_heatmap(filter_X,cmap_timing); - - % plot mapper graph - subplot(1,3,2) - [h, node_sizes, node_colors] = plot_mapper(g, smallBins, cmap_timing, useLayout); - - % plot colors only (need this so we can show the timing labels) - subplot(1,3,3) - plot_embedding(color_vals,cmap_timing); - - % show colorbar next to embedding - cmap = colormap(timing_colors); - cbar = colorbar; - cbar.TickLabelInterpreter = 'none'; - cbar.Ticks = linspace(0, 1, numel(legend_labels)); - cbar.TickLabels = legend_labels'; - - else - - fig = figure('Position', [0 0 1000 400]); - - % plot embedding - subplot(1,3,1) - plot_embedding(filter_X,cmap_timing); - - % plot mapper graph - subplot(1,3,2) - [h, node_sizes, node_colors] = plot_mapper(g, smallBins, cmap_timing, useLayout); - - % plot colors only (need this so we can show the timing labels) - subplot(1,3,3) - plot_embedding(color_vals,cmap_timing); - - % show colorbar next to embedding - cmap = colormap(timing_colors); - cbar = colorbar; - cbar.TickLabelInterpreter = 'none'; - cbar.Ticks = linspace(0, 1, numel(legend_labels)); - cbar.TickLabels = legend_labels'; - - end - - -else - - fig = figure('Position', [0 0 800 400], 'visible', 'off'); - [h, node_sizes, node_colors] = plot_mapper(g, smallBins, cmap_timing, useLayout); - - % show colorbar next to the graph - cmap = colormap(timing_colors); - cbar = colorbar; - cbar.TickLabelInterpreter = 'none'; - cbar.Ticks = linspace(0, 1, numel(legend_labels)); - cbar.TickLabels = legend_labels'; - -end - -sgtitle(titleText, 'Interpreter', 'none'); - - -% 9.9.2020 TODO make sure this works with parpool -if ischar(save_plot) | isstring(save_plot) - saveas(fig, save_plot); - close(fig); -end - -end - - -%% Helper functions - -function plot_embedding(filter_X, cmap_timing) - - if size(filter_X,2) == 2 - - % 2d scatter plot - h = scatter(filter_X(:,1), filter_X(:,2),[], cmap_timing, 'filled'); - ax = get(h,'Parent'); % only keep tick labels at bounds and zeros - xtick = get(ax,'XTick'); - ytick = get(ax,'YTick'); - set(ax,'XTick',sort(unique([xtick(1), 0, xtick(end)]))); - set(ax,'YTick',sort(unique([ytick(1), 0, ytick(end)]))); - xlabel('Filter 1', 'interpreter', 'none'); - ylabel('Filter 2', 'interpreter', 'none'); - - elseif size(filter_X,2) == 3 - - % 3d scatter plot - h = scatter3(filter_X(:,1), filter_X(:,2), filter_X(:,3), [], cmap_timing, 'filled'); - ax = get(h,'Parent'); % only keep tick labels at bounds and zeros - xtick = get(ax,'XTick'); - ytick = get(ax,'YTick'); - ztick = get(ax,'ZTick'); - set(ax,'XTick',sort(unique([xtick(1), 0, xtick(end)]))); - set(ax,'YTick',sort(unique([ytick(1), 0, ytick(end)]))); - set(ax,'ZTick',sort(unique([ztick(1), 0, ztick(end)]))); - xlabel('Filter 1', 'interpreter', 'none'); - ylabel('Filter 2', 'interpreter', 'none'); - zlabel('Filter 3', 'interpreter', 'none'); - - elseif size(filter_X,2) > 3 - - % heatmap (TODO: rugplot?) - h = imagesc(filter_X); - xlabel('Filters', 'interpreter', 'none'); - ylabel('Time frames (TR)', 'interpreter', 'none'); - cmap = colormap('turbo'); - cbar = colorbar; - - else - - % 1d scatter plot (hack to match heatmaps, plot top to bottom) - h = scatter(filter_X(:,1), -[1:1:size(filter_X,1)], [], cmap_timing, 'filled'); - ax = get(h,'Parent'); % only keep tick labels at bounds and zeros - - % fix xtick lables - xtick = get(ax,'XTick'); - xtick = sort(unique([xtick(1), 0, xtick(end)])); - if numel(unique(filter_X(:,1))) < 10 - xtick = unique(filter_X(:,1)); - end - set(ax,'XTick',xtick); - - % simulate TR labels (plot from top to bottom) - set(ax, 'YLim',[-size(filter_X,1), 0]); - ytick = get(ax,'YTick'); - %ytick = sort(unique([ytick, -size(filter_X,1)])); - set(ax,'YTick', ytick); - set(ax,'YTickLabels',abs(ytick(1:1:end))); - ylabel('Time frames (TR)', 'interpreter', 'none'); - - end - - %set(gcf,'Color','none'); - %set(gca,'Color','none'); - axis square; - -end - -function plot_embedding_heatmap(filter_X, cmap_timing) - - % heatmap (TODO: rugplot?) - h = imagesc(filter_X); - xlabel('Filters', 'interpreter', 'none'); - ylabel('Time frames (TR)', 'interpreter', 'none'); - cmap = colormap('turbo'); - cbar = colorbar; - - %set(gcf,'Color','none'); - %set(gca,'Color','none'); - axis square; - -end - - -function [h, node_sizes, node_colors] = plot_mapper(g, smallBins, cmap_timing, useLayout) - -if ~exist('useLayout','var') - useLayout = 'force'; -end - -nodes = g.Nodes; -nn = size(nodes,1); - -node_colors = zeros(nn,3); - -%% create a scaling parameter for the node sizes -smallBin_sizes = cellfun('size',smallBins,2); -%max_size = max(smallBin_sizes); -%node_sizes = 5+log(1+smallBin_sizes); -node_sizes = 1+log(1+smallBin_sizes); - -%% Plot the graph and highlight nodes -for ii = 1:nn - node_colors(ii,:) = mean(cmap_timing(smallBins{ii},:),1); -end - -h = plot(g,'Layout', useLayout,'NodeLabel',{}); -if strcmp(useLayout,'force') || strcmp(useLayout,'force3') - layout(h,useLayout,'UseGravity',true,'WeightEffect','none'); -end - -h.MarkerSize = node_sizes; -h.NodeColor = node_colors; -h.EdgeColor = [0 0 0]; -h.LineWidth = 1; - -axis equal; -if strcmp(useLayout,'force3') - view(gca, [-30, 15.0]); -else - set(gca,'Visible','off'); -end - -end - - - - diff --git a/code/tools/constructNPYheader.m b/code/tools/constructNPYheader.m deleted file mode 100755 index ca2840e..0000000 --- a/code/tools/constructNPYheader.m +++ /dev/null @@ -1,88 +0,0 @@ - - - -function header = constructNPYheader(dataType, shape, varargin) - - if ~isempty(varargin) - fortranOrder = varargin{1}; % must be true/false - littleEndian = varargin{2}; % must be true/false - else - fortranOrder = true; - littleEndian = true; - end - - dtypesMatlab = {'uint8','uint16','uint32','uint64','int8','int16','int32','int64','single','double', 'logical'}; - dtypesNPY = {'u1', 'u2', 'u4', 'u8', 'i1', 'i2', 'i4', 'i8', 'f4', 'f8', 'b1'}; - - magicString = uint8([147 78 85 77 80 89]); %x93NUMPY - - majorVersion = uint8(1); - minorVersion = uint8(0); - - % build the dict specifying data type, array order, endianness, and - % shape - dictString = '{''descr'': '''; - - if littleEndian - dictString = [dictString '<']; - else - dictString = [dictString '>']; - end - - dictString = [dictString dtypesNPY{strcmp(dtypesMatlab,dataType)} ''', ']; - - dictString = [dictString '''fortran_order'': ']; - - if fortranOrder - dictString = [dictString 'True, ']; - else - dictString = [dictString 'False, ']; - end - - dictString = [dictString '''shape'': (']; - -% if length(shape)==1 && shape==1 -% -% else -% for s = 1:length(shape) -% if s==length(shape) && shape(s)==1 -% -% else -% dictString = [dictString num2str(shape(s))]; -% if length(shape)>1 && s+1==length(shape) && shape(s+1)==1 -% dictString = [dictString ',']; -% elseif length(shape)>1 && s %s', tempFilename, inFilename, outFilename)); - - otherwise - fprintf(1, 'I don''t know how to concatenate files for your OS, but you can finish making the NPY youself by concatenating %s with %s.\n', tempFilename, inFilename); -end - diff --git a/code/tools/getoptions.m b/code/tools/getoptions.m deleted file mode 100755 index a6afa8f..0000000 --- a/code/tools/getoptions.m +++ /dev/null @@ -1,26 +0,0 @@ -function v = getoptions(options, name, v, mendatory) - -% getoptions - retrieve options parameter -% -% v = getoptions(options, 'entry', v0, mendatory); -% is equivalent to the code: -% if isfield(options, 'entry') -% v = options.entry; -% else -% v = v0; -% end -% -% Copyright (c) 2007 Gabriel Peyre - -if nargin<3 - error('Not enough arguments.'); -end -if nargin<4 - mendatory = 0; -end - -if isfield(options, name) - v = eval(['options.' name ';']); -elseif mendatory - error(['You have to provide options.' name '.']); -end \ No newline at end of file diff --git a/code/tools/px_maxmin.m b/code/tools/px_maxmin.m old mode 100755 new mode 100644 diff --git a/code/tools/readNPY.m b/code/tools/readNPY.m old mode 100755 new mode 100644 diff --git a/code/tools/readNPYheader.m b/code/tools/readNPYheader.m old mode 100755 new mode 100644 diff --git a/code/tools/savemystruct.m b/code/tools/savemystruct.m deleted file mode 100755 index 62da3c4..0000000 --- a/code/tools/savemystruct.m +++ /dev/null @@ -1,9 +0,0 @@ -function savemystruct(name,var,version) -% Function writemyfile -% Used to save files in parfor loop - if ~exist('version', 'var') - version = '-v7'; - end - save(name, '-struct', 'var', version); -end - diff --git a/code/tools/turbo.m/license.txt b/code/tools/turbo.m/license.txt deleted file mode 100755 index dc2ce2c..0000000 --- a/code/tools/turbo.m/license.txt +++ /dev/null @@ -1,25 +0,0 @@ -Copyright (c) 2020, Daniel Fortunato -All rights reserved. - -Redistribution and use in source and binary forms, with or without -modification, are permitted provided that the following conditions are met: - -* Redistributions of source code must retain the above copyright notice, this - list of conditions and the following disclaimer. - -* Redistributions in binary form must reproduce the above copyright notice, - this list of conditions and the following disclaimer in the documentation - and/or other materials provided with the distribution -* Neither the name of nor the names of its - contributors may be used to endorse or promote products derived from this - software without specific prior written permission. -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" -AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE -DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE -FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR -SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER -CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, -OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE -OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/code/tools/turbo.m/turbo.m b/code/tools/turbo.m/turbo.m deleted file mode 100755 index f7c98fe..0000000 --- a/code/tools/turbo.m/turbo.m +++ /dev/null @@ -1,278 +0,0 @@ -function map = turbo(m) -%TURBO Turbo colormap. -% TURBO(M) returns an M-by-3 matrix containing the turbo colormap, a -% variant of the jet colormap that is more perceptually uniform. -% -% See also JET, COLORMAP. - -if nargin < 1 - f = get(groot,'CurrentFigure'); - if isempty(f) - m = size(get(groot,'DefaultFigureColormap'),1); - else - m = size(f.Colormap,1); - end -end - -values = [ - 0.18995, 0.07176, 0.23217; - 0.19483, 0.08339, 0.26149; - 0.19956, 0.09498, 0.29024; - 0.20415, 0.10652, 0.31844; - 0.20860, 0.11802, 0.34607; - 0.21291, 0.12947, 0.37314; - 0.21708, 0.14087, 0.39964; - 0.22111, 0.15223, 0.42558; - 0.22500, 0.16354, 0.45096; - 0.22875, 0.17481, 0.47578; - 0.23236, 0.18603, 0.50004; - 0.23582, 0.19720, 0.52373; - 0.23915, 0.20833, 0.54686; - 0.24234, 0.21941, 0.56942; - 0.24539, 0.23044, 0.59142; - 0.24830, 0.24143, 0.61286; - 0.25107, 0.25237, 0.63374; - 0.25369, 0.26327, 0.65406; - 0.25618, 0.27412, 0.67381; - 0.25853, 0.28492, 0.69300; - 0.26074, 0.29568, 0.71162; - 0.26280, 0.30639, 0.72968; - 0.26473, 0.31706, 0.74718; - 0.26652, 0.32768, 0.76412; - 0.26816, 0.33825, 0.78050; - 0.26967, 0.34878, 0.79631; - 0.27103, 0.35926, 0.81156; - 0.27226, 0.36970, 0.82624; - 0.27334, 0.38008, 0.84037; - 0.27429, 0.39043, 0.85393; - 0.27509, 0.40072, 0.86692; - 0.27576, 0.41097, 0.87936; - 0.27628, 0.42118, 0.89123; - 0.27667, 0.43134, 0.90254; - 0.27691, 0.44145, 0.91328; - 0.27701, 0.45152, 0.92347; - 0.27698, 0.46153, 0.93309; - 0.27680, 0.47151, 0.94214; - 0.27648, 0.48144, 0.95064; - 0.27603, 0.49132, 0.95857; - 0.27543, 0.50115, 0.96594; - 0.27469, 0.51094, 0.97275; - 0.27381, 0.52069, 0.97899; - 0.27273, 0.53040, 0.98461; - 0.27106, 0.54015, 0.98930; - 0.26878, 0.54995, 0.99303; - 0.26592, 0.55979, 0.99583; - 0.26252, 0.56967, 0.99773; - 0.25862, 0.57958, 0.99876; - 0.25425, 0.58950, 0.99896; - 0.24946, 0.59943, 0.99835; - 0.24427, 0.60937, 0.99697; - 0.23874, 0.61931, 0.99485; - 0.23288, 0.62923, 0.99202; - 0.22676, 0.63913, 0.98851; - 0.22039, 0.64901, 0.98436; - 0.21382, 0.65886, 0.97959; - 0.20708, 0.66866, 0.97423; - 0.20021, 0.67842, 0.96833; - 0.19326, 0.68812, 0.96190; - 0.18625, 0.69775, 0.95498; - 0.17923, 0.70732, 0.94761; - 0.17223, 0.71680, 0.93981; - 0.16529, 0.72620, 0.93161; - 0.15844, 0.73551, 0.92305; - 0.15173, 0.74472, 0.91416; - 0.14519, 0.75381, 0.90496; - 0.13886, 0.76279, 0.89550; - 0.13278, 0.77165, 0.88580; - 0.12698, 0.78037, 0.87590; - 0.12151, 0.78896, 0.86581; - 0.11639, 0.79740, 0.85559; - 0.11167, 0.80569, 0.84525; - 0.10738, 0.81381, 0.83484; - 0.10357, 0.82177, 0.82437; - 0.10026, 0.82955, 0.81389; - 0.09750, 0.83714, 0.80342; - 0.09532, 0.84455, 0.79299; - 0.09377, 0.85175, 0.78264; - 0.09287, 0.85875, 0.77240; - 0.09267, 0.86554, 0.76230; - 0.09320, 0.87211, 0.75237; - 0.09451, 0.87844, 0.74265; - 0.09662, 0.88454, 0.73316; - 0.09958, 0.89040, 0.72393; - 0.10342, 0.89600, 0.71500; - 0.10815, 0.90142, 0.70599; - 0.11374, 0.90673, 0.69651; - 0.12014, 0.91193, 0.68660; - 0.12733, 0.91701, 0.67627; - 0.13526, 0.92197, 0.66556; - 0.14391, 0.92680, 0.65448; - 0.15323, 0.93151, 0.64308; - 0.16319, 0.93609, 0.63137; - 0.17377, 0.94053, 0.61938; - 0.18491, 0.94484, 0.60713; - 0.19659, 0.94901, 0.59466; - 0.20877, 0.95304, 0.58199; - 0.22142, 0.95692, 0.56914; - 0.23449, 0.96065, 0.55614; - 0.24797, 0.96423, 0.54303; - 0.26180, 0.96765, 0.52981; - 0.27597, 0.97092, 0.51653; - 0.29042, 0.97403, 0.50321; - 0.30513, 0.97697, 0.48987; - 0.32006, 0.97974, 0.47654; - 0.33517, 0.98234, 0.46325; - 0.35043, 0.98477, 0.45002; - 0.36581, 0.98702, 0.43688; - 0.38127, 0.98909, 0.42386; - 0.39678, 0.99098, 0.41098; - 0.41229, 0.99268, 0.39826; - 0.42778, 0.99419, 0.38575; - 0.44321, 0.99551, 0.37345; - 0.45854, 0.99663, 0.36140; - 0.47375, 0.99755, 0.34963; - 0.48879, 0.99828, 0.33816; - 0.50362, 0.99879, 0.32701; - 0.51822, 0.99910, 0.31622; - 0.53255, 0.99919, 0.30581; - 0.54658, 0.99907, 0.29581; - 0.56026, 0.99873, 0.28623; - 0.57357, 0.99817, 0.27712; - 0.58646, 0.99739, 0.26849; - 0.59891, 0.99638, 0.26038; - 0.61088, 0.99514, 0.25280; - 0.62233, 0.99366, 0.24579; - 0.63323, 0.99195, 0.23937; - 0.64362, 0.98999, 0.23356; - 0.65394, 0.98775, 0.22835; - 0.66428, 0.98524, 0.22370; - 0.67462, 0.98246, 0.21960; - 0.68494, 0.97941, 0.21602; - 0.69525, 0.97610, 0.21294; - 0.70553, 0.97255, 0.21032; - 0.71577, 0.96875, 0.20815; - 0.72596, 0.96470, 0.20640; - 0.73610, 0.96043, 0.20504; - 0.74617, 0.95593, 0.20406; - 0.75617, 0.95121, 0.20343; - 0.76608, 0.94627, 0.20311; - 0.77591, 0.94113, 0.20310; - 0.78563, 0.93579, 0.20336; - 0.79524, 0.93025, 0.20386; - 0.80473, 0.92452, 0.20459; - 0.81410, 0.91861, 0.20552; - 0.82333, 0.91253, 0.20663; - 0.83241, 0.90627, 0.20788; - 0.84133, 0.89986, 0.20926; - 0.85010, 0.89328, 0.21074; - 0.85868, 0.88655, 0.21230; - 0.86709, 0.87968, 0.21391; - 0.87530, 0.87267, 0.21555; - 0.88331, 0.86553, 0.21719; - 0.89112, 0.85826, 0.21880; - 0.89870, 0.85087, 0.22038; - 0.90605, 0.84337, 0.22188; - 0.91317, 0.83576, 0.22328; - 0.92004, 0.82806, 0.22456; - 0.92666, 0.82025, 0.22570; - 0.93301, 0.81236, 0.22667; - 0.93909, 0.80439, 0.22744; - 0.94489, 0.79634, 0.22800; - 0.95039, 0.78823, 0.22831; - 0.95560, 0.78005, 0.22836; - 0.96049, 0.77181, 0.22811; - 0.96507, 0.76352, 0.22754; - 0.96931, 0.75519, 0.22663; - 0.97323, 0.74682, 0.22536; - 0.97679, 0.73842, 0.22369; - 0.98000, 0.73000, 0.22161; - 0.98289, 0.72140, 0.21918; - 0.98549, 0.71250, 0.21650; - 0.98781, 0.70330, 0.21358; - 0.98986, 0.69382, 0.21043; - 0.99163, 0.68408, 0.20706; - 0.99314, 0.67408, 0.20348; - 0.99438, 0.66386, 0.19971; - 0.99535, 0.65341, 0.19577; - 0.99607, 0.64277, 0.19165; - 0.99654, 0.63193, 0.18738; - 0.99675, 0.62093, 0.18297; - 0.99672, 0.60977, 0.17842; - 0.99644, 0.59846, 0.17376; - 0.99593, 0.58703, 0.16899; - 0.99517, 0.57549, 0.16412; - 0.99419, 0.56386, 0.15918; - 0.99297, 0.55214, 0.15417; - 0.99153, 0.54036, 0.14910; - 0.98987, 0.52854, 0.14398; - 0.98799, 0.51667, 0.13883; - 0.98590, 0.50479, 0.13367; - 0.98360, 0.49291, 0.12849; - 0.98108, 0.48104, 0.12332; - 0.97837, 0.46920, 0.11817; - 0.97545, 0.45740, 0.11305; - 0.97234, 0.44565, 0.10797; - 0.96904, 0.43399, 0.10294; - 0.96555, 0.42241, 0.09798; - 0.96187, 0.41093, 0.09310; - 0.95801, 0.39958, 0.08831; - 0.95398, 0.38836, 0.08362; - 0.94977, 0.37729, 0.07905; - 0.94538, 0.36638, 0.07461; - 0.94084, 0.35566, 0.07031; - 0.93612, 0.34513, 0.06616; - 0.93125, 0.33482, 0.06218; - 0.92623, 0.32473, 0.05837; - 0.92105, 0.31489, 0.05475; - 0.91572, 0.30530, 0.05134; - 0.91024, 0.29599, 0.04814; - 0.90463, 0.28696, 0.04516; - 0.89888, 0.27824, 0.04243; - 0.89298, 0.26981, 0.03993; - 0.88691, 0.26152, 0.03753; - 0.88066, 0.25334, 0.03521; - 0.87422, 0.24526, 0.03297; - 0.86760, 0.23730, 0.03082; - 0.86079, 0.22945, 0.02875; - 0.85380, 0.22170, 0.02677; - 0.84662, 0.21407, 0.02487; - 0.83926, 0.20654, 0.02305; - 0.83172, 0.19912, 0.02131; - 0.82399, 0.19182, 0.01966; - 0.81608, 0.18462, 0.01809; - 0.80799, 0.17753, 0.01660; - 0.79971, 0.17055, 0.01520; - 0.79125, 0.16368, 0.01387; - 0.78260, 0.15693, 0.01264; - 0.77377, 0.15028, 0.01148; - 0.76476, 0.14374, 0.01041; - 0.75556, 0.13731, 0.00942; - 0.74617, 0.13098, 0.00851; - 0.73661, 0.12477, 0.00769; - 0.72686, 0.11867, 0.00695; - 0.71692, 0.11268, 0.00629; - 0.70680, 0.10680, 0.00571; - 0.69650, 0.10102, 0.00522; - 0.68602, 0.09536, 0.00481; - 0.67535, 0.08980, 0.00449; - 0.66449, 0.08436, 0.00424; - 0.65345, 0.07902, 0.00408; - 0.64223, 0.07380, 0.00401; - 0.63082, 0.06868, 0.00401; - 0.61923, 0.06367, 0.00410; - 0.60746, 0.05878, 0.00427; - 0.59550, 0.05399, 0.00453; - 0.58336, 0.04931, 0.00486; - 0.57103, 0.04474, 0.00529; - 0.55852, 0.04028, 0.00579; - 0.54583, 0.03593, 0.00638; - 0.53295, 0.03169, 0.00705; - 0.51989, 0.02756, 0.00780; - 0.50664, 0.02354, 0.00863; - 0.49321, 0.01963, 0.00955; - 0.47960, 0.01583, 0.01055]; - -P = size(values,1); -map = interp1(1:P, values, linspace(1,P,m), 'linear'); - -end \ No newline at end of file diff --git a/code/tools/writeNPY.m b/code/tools/writeNPY.m deleted file mode 100755 index 844dc35..0000000 --- a/code/tools/writeNPY.m +++ /dev/null @@ -1,25 +0,0 @@ - - -function writeNPY(var, filename) -% function writeNPY(var, filename) -% -% Only writes little endian, fortran (column-major) ordering; only writes -% with NPY version number 1.0. -% -% Always outputs a shape according to matlab's convention, e.g. (10, 1) -% rather than (10,). - - -shape = size(var); -dataType = class(var); - -header = constructNPYheader(dataType, shape); - -fid = fopen(filename, 'w'); -fwrite(fid, header, 'uint8'); -fwrite(fid, var, dataType); -fclose(fid); - - -end - diff --git a/code/tools/writemyfile.m b/code/tools/writemyfile.m deleted file mode 100755 index 85c98fe..0000000 --- a/code/tools/writemyfile.m +++ /dev/null @@ -1,7 +0,0 @@ -function writemyfile(name,res) -% Function writemyfile -% Used to save files in parfor loop - save(name,'res'); - -end - diff --git a/code/tools/writemyfilevar.m b/code/tools/writemyfilevar.m deleted file mode 100755 index d47c7bf..0000000 --- a/code/tools/writemyfilevar.m +++ /dev/null @@ -1,7 +0,0 @@ -function writemyfilevar(name,var) -% Function writemyfile -% Used to save files in parfor loop - save(name,'var'); - -end -

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UJEU1=7H0WnW3Ra4GS->@23kch0ssI2 diff --git a/code/dimReducMethods/d2p.m b/code/dimReducMethods/d2p.m deleted file mode 100644 index 65eb5f0..0000000 --- a/code/dimReducMethods/d2p.m +++ /dev/null @@ -1,100 +0,0 @@ -function [P, beta] = d2p(D, u, tol) -%D2P Identifies appropriate sigma's to get kk NNs up to some tolerance -% -% [P, beta] = d2p(D, kk, tol) -% -% Identifies the required precision (= 1 / variance^2) to obtain a Gaussian -% kernel with a certain uncertainty for every datapoint. The desired -% uncertainty can be specified through the perplexity u (default = 15). The -% desired perplexity is obtained up to some tolerance that can be specified -% by tol (default = 1e-4). -% The function returns the final Gaussian kernel in P, as well as the -% employed precisions per instance in beta. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('u', 'var') || isempty(u) - u = 15; - end - if ~exist('tol', 'var') || isempty(tol) - tol = 1e-4; - end - - % Initialize some variables - n = size(D, 1); % number of instances - P = zeros(n, n); % empty probability matrix - beta = ones(n, 1); % empty precision vector - logU = log(u); % log of perplexity (= entropy) - - % Run over all datapoints - for i=1:n - - if ~rem(i, 500) - disp(['Computed P-values ' num2str(i) ' of ' num2str(n) ' datapoints...']); - end - - % Set minimum and maximum values for precision - betamin = -Inf; - betamax = Inf; - - % Compute the Gaussian kernel and entropy for the current precision - [H, thisP] = Hbeta(D(i, [1:i - 1, i + 1:end]), beta(i)); - - % Evaluate whether the perplexity is within tolerance - Hdiff = H - logU; - tries = 0; - while abs(Hdiff) > tol && tries < 50 - - % If not, increase or decrease precision - if Hdiff > 0 - betamin = beta(i); - if isinf(betamax) - beta(i) = beta(i) * 2; - else - beta(i) = (beta(i) + betamax) / 2; - end - else - betamax = beta(i); - if isinf(betamin) - beta(i) = beta(i) / 2; - else - beta(i) = (beta(i) + betamin) / 2; - end - end - - % Recompute the values - [H, thisP] = Hbeta(D(i, [1:i - 1, i + 1:end]), beta(i)); - Hdiff = H - logU; - tries = tries + 1; - end - - % Set the final row of P - P(i, [1:i - 1, i + 1:end]) = thisP; - end - disp(['Mean value of sigma: ' num2str(mean(sqrt(1 ./ beta)))]); - disp(['Minimum value of sigma: ' num2str(min(sqrt(1 ./ beta)))]); - disp(['Maximum value of sigma: ' num2str(max(sqrt(1 ./ beta)))]); -end - - - -% Function that computes the Gaussian kernel values given a vector of -% squared Euclidean distances, and the precision of the Gaussian kernel. -% The function also computes the perplexity of the distribution. -function [H, P] = Hbeta(D, beta) - P = exp(-D * beta); - sumP = sum(P); - H = log(sumP) + beta * sum(D .* P) / sumP; - % why not: H = exp(-sum(P(P > 1e-5) .* log(P(P > 1e-5)))); ??? - P = P / sumP; -end - diff --git a/code/dimReducMethods/data1 b/code/dimReducMethods/data1 deleted file mode 100644 index de80351..0000000 --- a/code/dimReducMethods/data1 +++ /dev/null @@ -1,1017 +0,0 @@ - 3.7025325e-01 1.1833366e-01 -4.3875320e-01 2.6894495e-01 8.0332229e-02 8.2523199e-02 1.3916199e-01 -1.6608020e-01 8.2113978e-02 -7.8212252e-01 3.1420710e-04 2.1818882e-01 1.3460242e-01 3.9656377e-01 3.3829265e-01 8.5868835e-02 -5.3384892e-02 -2.3692737e-01 -1.0408676e-01 1.2598140e-01 1.5835390e-01 5.7458231e-02 2.8330824e-01 1.5435413e-01 3.1706370e-01 1.4948550e-01 -8.0888631e-02 6.4769145e-02 1.6835330e-01 6.4535669e-02 -4.6970105e-02 1.0460247e-01 -1.8313376e-01 4.9336581e-02 2.8157012e-01 -3.2734144e-02 -4.7074487e-01 -2.2174182e-01 -4.3919107e-01 1.9532971e-01 1.4614812e-01 3.4614159e-01 4.7604989e-01 1.2510653e-01 -2.3965990e-01 -1.2053754e-01 -6.5054875e-02 4.8882920e-01 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-1,48 +0,0 @@ -function mappedX = diffusion_maps(X, no_dims, alpha, sigma) -%DIFFUSION_MAPS Runs the diffusion map algorithm -% -% mappedX = diffusion_maps(X, no_dims, alpha, sigma) -% -% The functions runs the diffusion map algorithm on dataset X to reduce it -% to dimensionality no_dims. The variable sigma is the variance of the Gaussian -% used in the affinity computation (default = 1). The variable alpha -% determines the operator that is applied on the graph (default = 1). -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Give memory warning - if size(X, 1) > 3000 - warning(['Due to the large number of instances (' num2str(size(X, 1)) '), diffusion maps may run out of memory.']); - end - - % Normalize data - X = double(X); - X = X - min(X(:)); - X = X / max(X(:)); - - % Compute Gaussian kernel matrix - disp('Compute Markov forward transition probability matrix ...'); - sumX = sum(X .^ 2, 2); - K = exp(-bsxfun(@plus, sumX, bsxfun(@plus, sumX', -2 * (X * X'))) ./ (2 .* sigma ^ 2)); - - % Compute Markov probability matrix - p = sum(K, 1)'; - K = K ./ ((p * p') .^ alpha); - p = sqrt(sum(K, 1))'; - K = K ./ (p * p'); - - % Perform economy-size SVD - disp('Perform eigendecomposition...'); - [U, S, V] = svd(K, 0); - U = bsxfun(@rdivide, U, U(:,1)); - mappedX = U(:,2:no_dims + 1); - \ No newline at end of file diff --git a/code/dimReducMethods/dijk.m b/code/dimReducMethods/dijk.m deleted file mode 100644 index 21c553c..0000000 --- a/code/dimReducMethods/dijk.m +++ /dev/null @@ -1,121 +0,0 @@ -function D = dijk(A,s,t) -%DIJK Shortest paths from nodes 's' to nodes 't' using Dijkstra algorithm. -% D = dijk(A,s,t) -% A = n x n node-node weighted adjacency matrix of arc lengths -% (Note: A(i,j) = 0 => Arc (i,j) does not exist; -% A(i,j) = NaN => Arc (i,j) exists with 0 weight) -% s = FROM node indices -% = [] (default), paths from all nodes -% t = TO node indices -% = [] (default), paths to all nodes -% D = |s| x |t| matrix of shortest path distances from 's' to 't' -% = [D(i,j)], where D(i,j) = distance from node 'i' to node 'j' -% -% (If A is a triangular matrix, then computationally intensive node -% selection step not needed since graph is acyclic (triangularity is a -% sufficient, but not a necessary, condition for a graph to be acyclic) -% and A can have non-negative elements) -% -% (If |s| >> |t|, then DIJK is faster if DIJK(A',t,s) used, where D is now -% transposed and P now represents successor indices) -% -% (Based on Fig. 4.6 in Ahuja, Magnanti, and Orlin, Network Flows, -% Prentice-Hall, 1993, p. 109.) - -% Copyright (c) 1998-2000 by Michael G. Kay -% Matlog Version 1.3 29-Aug-2000 -% -% Modified by JBT, Dec 2000, to delete paths -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - -% Input Error Checking ****************************************************** -error(nargchk(1,3,nargin)); - -[n,cA] = size(A); - -if nargin < 2 | isempty(s), s = (1:n)'; else s = s(:); end -if nargin < 3 | isempty(t), t = (1:n)'; else t = t(:); end - -if ~any(any(tril(A) ~= 0)) % A is upper triangular - isAcyclic = 1; -elseif ~any(any(triu(A) ~= 0)) % A is lower triangular - isAcyclic = 2; -else % Graph may not be acyclic - isAcyclic = 0; -end - -if n ~= cA - error('A must be a square matrix'); -elseif ~isAcyclic & any(any(A < 0)) - error('A must be non-negative'); -elseif any(s < 1 | s > n) - error(['''s'' must be an integer between 1 and ',num2str(n)]); -elseif any(t < 1 | t > n) - error(['''t'' must be an integer between 1 and ',num2str(n)]); -end -% End (Input Error Checking) ************************************************ - -A = A'; % Use transpose to speed-up FIND for sparse A - -D = zeros(length(s),length(t)); -P = zeros(length(s),n); - -for i = 1:length(s) - j = s(i); - - Di = Inf*ones(n,1); Di(j) = 0; - - isLab = logical(zeros(length(t),1)); - if isAcyclic == 1 - nLab = j - 1; - elseif isAcyclic == 2 - nLab = n - j; - else - nLab = 0; - UnLab = 1:n; - isUnLab = logical(ones(n,1)); - end - - while nLab < n & ~all(isLab) - if isAcyclic - Dj = Di(j); - else % Node selection - [Dj,jj] = min(Di(isUnLab)); - j = UnLab(jj); - UnLab(jj) = []; - isUnLab(j) = 0; - end - - nLab = nLab + 1; - if length(t) < n, isLab = isLab | (j == t); end - - [jA,kA,Aj] = find(A(:,j)); - Aj(isnan(Aj)) = 0; - - if isempty(Aj), Dk = Inf; else Dk = Dj + Aj; end - - P(i,jA(Dk < Di(jA))) = j; - Di(jA) = min(Di(jA),Dk); - - if isAcyclic == 1 % Increment node index for upper triangular A - j = j + 1; - elseif isAcyclic == 2 % Decrement node index for lower triangular A - j = j - 1; - end - - %disp( num2str( nLab )); - end - D(i,:) = Di(t)'; -end - diff --git a/code/dimReducMethods/dijkstra.cpp b/code/dimReducMethods/dijkstra.cpp deleted file mode 100644 index acd159b..0000000 --- a/code/dimReducMethods/dijkstra.cpp +++ /dev/null @@ -1,1054 +0,0 @@ -/** - * dijkstra.cpp - * - * [D, P] = DIJKSTRA(G, S) - * - * This function computes the shortest distance tree(s) from one (or more) - * source node(s) in a graph. - * - * G is a sparse matrix where element (i,j) contains the cost of going - * from node i to node j in the graph. That is, G contains the edge - * weights or distances between nodes. - * - * Note: Matlab's convention is that the absence of an element in a sparse - * matrix means edge weight = 0. However, in this function, the lack of an - * entry in the sparse matrix is understood as a lack of edge (or edge - * weight = Inf). - * - * S is a vector with a list of source nodes. A shortest path tree will be - * computed for - * - * D, P are matrices where each row corresponds to a source node in S. D - * is the shortest distance from each node to the source node. - * - * P is the predecessor of each node in the shortest path tree. - * - * Because this function is implemented as a MEX function in C++, - * takes a sparse matrix at the input, and uses a Fibonacci heap - * implementation [1], it is well suited for huge sparse graphs. - * - * [1] - * http://www.ahhf45.com/info/Data_Structures_and_Algorithms/resources/technical_artile/fibonacci_heap/fibonacci.htm - * - * Author: Mark Steyvers, Stanford University, 19 Dec 2000. - * - * Modified by Ramon Casero , University of Oxford, - * 23 Mar 2010 to also provide the predecessor list at the output. - * - * This file is distributed as a derivative work of a third-party function - * with project Gerardus. - * - * http://code.google.com/p/gerardus/ - * - * - * To compile dijkstra.cpp with mex from Matlab's GUI: - * - * 32 bit - * >> mex dijkstra.cpp - * - * 64 bit - * >> mex -largeArrayDims dijkstra.cpp - * - **/ - -#include -#include "mex.h" - -extern void _main(); - -#include -// #include -#include -#include -// #include -#include -#include -#include - -#include "fibheap.h" - -#define _FIBHEAP_CPP - -//*************************************************************************** -// This Fibonacci heap implementation is Copyright (c) 1996 by John Boyer. -// See the header file for free usage information. -//*************************************************************************** - -//*************************************************************************** -// The classes in this package are designed to allow the package user -// to quickly and easily develop applications that require a heap data -// structure. Using amortized analysis, the asymptotically fastest heap -// data structure is the Fibonacci heap. The constants are a little -// high so the real speed gain will not be seen until larger data sets -// are required, but in most cases, if the data set is small, then the -// run-time will be neglible anyway. -// -// To use this heap class you need do only two things. First, subclass -// the FibHeapNode class to create the class of objects that you'd -// like to store in a heap. Second, create an instance of the FibHeap -// class, which can then be used to Insert(), ExtractMin(), etc., -// instances of your FibHeapNode subclass. Notice that you don't need -// to create a subclass of the FibHeap class. -// -// The application-specific data object that you'd like to store in a heap -// will have a key value. In the class that you derive from FibHeapNode, -// you will need to define the key structure then provide assignment (=), -// equality (==) and less-than operators and a destructor. These functions -// are declared virtual so that the code in the FibHeap class can compare, -// assign and destroy your objects by calling on your code. -// -// The overloaded operators in your defined class MUST call functions in -// the Fibonacci heap node class first. For assignment, the function -// FHN_Assign() should be called before code that deals with the copy of -// the key value. For comparison operators, the function FHN_Cmp() should -// appear first. If it returns 0, then keys can be compared as normal. -// The following indicates what the three most common operators must do -// based on the return value of FHN_Cmp() -// -// For ==, if zero returned, then compare keys -// if non-zero X returned, then return 0 -// For <, if zero returned, then compare keys -// if non-zero X returned, then return X<0?1:0 -// For >, if zero returned, then compare keys -// if non-zero X returned, then return X>0?1:0 -//*************************************************************************** - -#include -#include -#include - -#include "fibheap.h" - -//*************************************************************************** -//========================================================= -// FibHeapNode Constructor -//========================================================= -//*************************************************************************** - -FibHeapNode::FibHeapNode() -{ - Left = Right = Parent = Child = NULL; - Degree = Mark = NegInfinityFlag = 0; -} - -//========================================================= -// FibHeapNode Destructor -// -// Body is empty, but declaration is required in order to -// force virtual. This will ensure that FibHeap class -// calls derived class destructors. -//========================================================= - -FibHeapNode::~FibHeapNode() -{ -} - -//========================================================= -// FHN_Assign() -// -// To be used as first step of an assignment operator in a -// derived class. The derived class will handle assignment -// of key value, and this function handles copy of the -// NegInfinityFlag (which overrides the key value if it is -// set). -//========================================================= - -void FibHeapNode::FHN_Assign(FibHeapNode& RHS) -{ - NegInfinityFlag = RHS.NegInfinityFlag; -} - -//========================================================= -// FHN_Cmp() -// -// To be used as the first step of ALL comparators in a -// derived class. -// -// Compares the relative state of the two neg. infinity -// flags. Note that 'this' is the left hand side. If -// LHS neg. infinity is set, then it will be less than (-1) -// the RHS unless RHS neg. infinity flag is also set. -// Only if function returns 0 should the key comparison -// defined in the derived class be performed, e.g. -// -// For ==, if zero returned, then compare keys -// if non-zero X returned, then return 0 -// For <, if zero returned, then compare keys -// if non-zero X returned, then return X<0?1:0 -// For >, if zero returned, then compare keys -// if non-zero X returned, then return X>0?1:0 -//========================================================= - -int FibHeapNode::FHN_Cmp(FibHeapNode& RHS) -{ - if (NegInfinityFlag) - return RHS.NegInfinityFlag ? 0 : -1; - return RHS.NegInfinityFlag ? 1 : 0; -} - -//======================================================================== -// We do, on occasion, compare and assign objects of type FibHeapNode, but -// only when the NegInfinityFlag is set. See for example FibHeap::Delete(). -// -// Also, these functions exemplify what a derived class should do. -//======================================================================== - -void FibHeapNode::operator =(FibHeapNode& RHS) -{ - FHN_Assign(RHS); - // Key assignment goes here in derived classes -} - -int FibHeapNode::operator ==(FibHeapNode& RHS) -{ - if (FHN_Cmp(RHS)) return 0; - // Key compare goes here in derived classes - return 1; -} - -int FibHeapNode::operator <(FibHeapNode& RHS) -{ -int X; - - if ((X=FHN_Cmp(RHS)) != 0) - return X < 0 ? 1 : 0; - // Key compare goes here in derived classes - return 0; -} - -//========================================================= -// Print() -//========================================================= - -void FibHeapNode::Print() -{ - if (NegInfinityFlag) - std::cout << "-inf."; -} - -//*************************************************************************** -//=========================================================================== -// FibHeap Constructor -//=========================================================================== -//*************************************************************************** - -FibHeap::FibHeap() -{ - MinRoot = NULL; - NumNodes = NumTrees = NumMarkedNodes = 0; - ClearHeapOwnership(); -} - -//=========================================================================== -// FibHeap Destructor -//=========================================================================== - -FibHeap::~FibHeap() -{ -FibHeapNode *Temp; - - if (GetHeapOwnership()) - { - while (MinRoot != NULL) - { - Temp = ExtractMin(); - delete Temp; - } - } -} - -//=========================================================================== -// Insert() - O(1) actual; O(2) amortized -// -// I am using O(2) here to indicate that although Insert() is -// constant time, its amortized rating is more costly because some -// of the work of inserting is done by other operations such as -// ExtractMin(), which is where tree-balancing occurs. -// -// The child pointer is deliberately not set to NULL because Insert() -// is also used internally to help put whole trees onto the root list. -//=========================================================================== - -void FibHeap::Insert(FibHeapNode *NewNode) -{ - if (NewNode == NULL) return; - -// If the heap is currently empty, then new node becomes singleton -// circular root list - - if (MinRoot == NULL) - MinRoot = NewNode->Left = NewNode->Right = NewNode; - - else - { -// Pointers from NewNode set to insert between MinRoot and MinRoot->Right - - NewNode->Right = MinRoot->Right; - NewNode->Left = MinRoot; - -// Set Pointers to NewNode - - NewNode->Left->Right = NewNode; - NewNode->Right->Left = NewNode; - -// The new node becomes new MinRoot if it is less than current MinRoot - - if (*NewNode < *MinRoot) - MinRoot = NewNode; - } - -// We have one more node in the heap, and it is a tree on the root list - - NumNodes++; - - NumTrees++; - NewNode->Parent = NULL; -} - -//=========================================================================== -// Union() - O(1) actual; O(1) amortized -//=========================================================================== - -void FibHeap::Union(FibHeap *OtherHeap) -{ -FibHeapNode *Min1, *Min2, *Next1, *Next2; - - if (OtherHeap == NULL || OtherHeap->MinRoot == NULL) return; - -// We join the two circular lists by cutting each list between its -// min node and the node after the min. This code just pulls those -// nodes into temporary variables so we don't get lost as changes -// are made. - - Min1 = MinRoot; - Min2 = OtherHeap->MinRoot; - Next1 = Min1->Right; - Next2 = Min2->Right; - -// To join the two circles, we join the minimum nodes to the next -// nodes on the opposite chains. Conceptually, it looks like the way -// two bubbles join to form one larger bubble. They meet at one point -// of contact, then expand out to make the bigger circle. - - Min1->Right = Next2; - Next2->Left = Min1; - Min2->Right = Next1; - Next1->Left = Min2; - -// Choose the new minimum for the heap - - if (*Min2 < *Min1) - MinRoot = Min2; - -// Set the amortized analysis statistics and size of the new heap - - NumNodes += OtherHeap->NumNodes; - NumMarkedNodes += OtherHeap->NumMarkedNodes; - NumTrees += OtherHeap->NumTrees; - -// Complete the union by setting the other heap to emptiness -// then destroying it - - OtherHeap->MinRoot = NULL; - OtherHeap->NumNodes = - OtherHeap->NumTrees = - OtherHeap->NumMarkedNodes = 0; - - delete OtherHeap; -} - -//=========================================================================== -// Minimum - O(1) actual; O(1) amortized -//=========================================================================== - -FibHeapNode *FibHeap::Minimum() -{ - return MinRoot; -} - -//=========================================================================== -// ExtractMin() - O(n) worst-case actual; O(lg n) amortized -//=========================================================================== - -FibHeapNode *FibHeap::ExtractMin() -{ -FibHeapNode *Result; -FibHeap *ChildHeap = NULL; - -// Remove minimum node and set MinRoot to next node - - if ((Result = Minimum()) == NULL) - return NULL; - - MinRoot = Result->Right; - Result->Right->Left = Result->Left; - Result->Left->Right = Result->Right; - Result->Left = Result->Right = NULL; - - NumNodes --; - if (Result->Mark) - { - NumMarkedNodes --; - Result->Mark = 0; - } - Result->Degree = 0; - -// Attach child list of Minimum node to the root list of the heap -// If there is no child list, then do no work - - if (Result->Child == NULL) - { - if (MinRoot == Result) - MinRoot = NULL; - } - -// If MinRoot==Result then there was only one root tree, so the -// root list is simply the child list of that node (which is -// NULL if this is the last node in the list) - - else if (MinRoot == Result) - MinRoot = Result->Child; - -// If MinRoot is different, then the child list is pushed into a -// new temporary heap, which is then merged by Union() onto the -// root list of this heap. - - else - { - ChildHeap = new FibHeap(); - ChildHeap->MinRoot = Result->Child; - } - -// Complete the disassociation of the Result node from the heap - - if (Result->Child != NULL) - Result->Child->Parent = NULL; - Result->Child = Result->Parent = NULL; - -// If there was a child list, then we now merge it with the -// rest of the root list - - if (ChildHeap) - Union(ChildHeap); - -// Consolidate heap to find new minimum and do reorganize work - - if (MinRoot != NULL) - _Consolidate(); - -// Return the minimum node, which is now disassociated with the heap -// It has Left, Right, Parent, Child, Mark and Degree cleared. - - return Result; -} - -//=========================================================================== -// DecreaseKey() - O(lg n) actual; O(1) amortized -// -// The O(lg n) actual cost stems from the fact that the depth, and -// therefore the number of ancestor parents, is bounded by O(lg n). -//=========================================================================== - -int FibHeap::DecreaseKey(FibHeapNode *theNode, FibHeapNode& NewKey) -{ -FibHeapNode *theParent; - - if (theNode==NULL || *theNode < NewKey) - return NOTOK; - - *theNode = NewKey; - - theParent = theNode->Parent; - if (theParent != NULL && *theNode < *theParent) - { - _Cut(theNode, theParent); - _CascadingCut(theParent); - } - - if (*theNode < *MinRoot) - MinRoot = theNode; - - return OK; -} - -//=========================================================================== -// Delete() - O(lg n) amortized; ExtractMin() dominates -// -// Notice that if we don't own the heap nodes, then we clear the -// NegInfinityFlag on the deleted node. Presumably, the programmer -// will be reusing the node. -//=========================================================================== - -int FibHeap::Delete(FibHeapNode *theNode) -{ -FibHeapNode Temp; -int Result; - - if (theNode == NULL) return NOTOK; - - Temp.NegInfinityFlag = 1; - Result = DecreaseKey(theNode, Temp); - - if (Result == OK) - if (ExtractMin() == NULL) - Result = NOTOK; - - if (Result == OK) - { - if (GetHeapOwnership()) - delete theNode; - else theNode->NegInfinityFlag = 0; - } - - return Result; -} - -//=========================================================================== - -void FibHeap::_Exchange(FibHeapNode*& N1, FibHeapNode*& N2) -{ -FibHeapNode *Temp; - - Temp = N1; - N1 = N2; - N2 = Temp; -} - -//=========================================================================== -// Consolidate() -// -// Internal function that reorganizes heap as part of an ExtractMin(). -// We must find new minimum in heap, which could be anywhere along the -// root list. The search could be O(n) since all nodes could be on -// the root list. So, we reorganize the tree into more of a binomial forest -// structure, and then find the new minimum on the consolidated O(lg n) sized -// root list, and in the process set each Parent pointer to NULL, and count -// the number of resulting subtrees. -// -// Note that after a list of n inserts, there will be n nodes on the root -// list, so the first ExtractMin() will be O(n) regardless of whether or -// not we consolidate. However, the consolidation causes subsequent -// ExtractMin() operations to be O(lg n). Furthermore, the extra cost of -// the first ExtractMin() is covered by the higher amortized cost of -// Insert(), which is the real governing factor in how costly the first -// ExtractMin() will be. -//=========================================================================== - -void FibHeap::_Consolidate() -{ -FibHeapNode *x, *y, *w; -FibHeapNode *A[1+8*sizeof(long)]; // 1+lg(n) -int I=0, Dn = 1+8*sizeof(long); -short d; - -// Initialize the consolidation detection array - - for (I=0; I < Dn; I++) - A[I] = NULL; - -// We need to loop through all elements on root list. -// When a collision of degree is found, the two trees -// are consolidated in favor of the one with the lesser -// element key value. We first need to break the circle -// so that we can have a stopping condition (we can't go -// around until we reach the tree we started with -// because all root trees are subject to becoming a -// child during the consolidation). - - MinRoot->Left->Right = NULL; - MinRoot->Left = NULL; - w = MinRoot; - - do { -//cout << "Top of Consolidate's loop\n"; -//Print(w); - - x = w; - d = x->Degree; - w = w->Right; - -// We need another loop here because the consolidated result -// may collide with another large tree on the root list. - - while (A[d] != NULL) - { - y = A[d]; - if (*y < *x) - _Exchange(x, y); - if (w == y) w = y->Right; - _Link(y, x); - A[d] = NULL; - d++; -//cout << "After a round of Linking\n"; -//Print(x); - } - A[d] = x; - - } while (w != NULL); - -// Now we rebuild the root list, find the new minimum, -// set all root list nodes' parent pointers to NULL and -// count the number of subtrees. - - MinRoot = NULL; - NumTrees = 0; - for (I = 0; I < Dn; I++) - if (A[I] != NULL) - _AddToRootList(A[I]); -} - -//=========================================================================== -// The node y is removed from the root list and becomes a subtree of node x. -//=========================================================================== - -void FibHeap::_Link(FibHeapNode *y, FibHeapNode *x) -{ -// Remove node y from root list - - if (y->Right != NULL) - y->Right->Left = y->Left; - if (y->Left != NULL) - y->Left->Right = y->Right; - NumTrees--; - -// Make node y a singleton circular list with a parent of x - - y->Left = y->Right = y; - y->Parent = x; - -// If node x has no children, then list y is its new child list - - if (x->Child == NULL) - x->Child = y; - -// Otherwise, node y must be added to node x's child list - - else - { - y->Left = x->Child; - y->Right = x->Child->Right; - x->Child->Right = y; - y->Right->Left = y; - } - -// Increase the degree of node x because it's now a bigger tree - - x->Degree ++; - -// Node y has just been made a child, so clear its mark - - if (y->Mark) NumMarkedNodes--; - y->Mark = 0; -} - -//=========================================================================== -//=========================================================================== - -void FibHeap::_AddToRootList(FibHeapNode *x) -{ - if (x->Mark) NumMarkedNodes --; - x->Mark = 0; - - NumNodes--; - Insert(x); -} - -//=========================================================================== -// Remove node x from the child list of its parent node y -//=========================================================================== - -void FibHeap::_Cut(FibHeapNode *x, FibHeapNode *y) -{ - if (y->Child == x) - y->Child = x->Right; - if (y->Child == x) - y->Child = NULL; - - y->Degree --; - - x->Left->Right = x->Right; - x->Right->Left = x->Left; - - _AddToRootList(x); -} - -//=========================================================================== -// Cuts each node in parent list, putting successive ancestor nodes on the -// root list until we either arrive at the root list or until we find an -// ancestor that is unmarked. When a mark is set (which only happens during -// a cascading cut), it means that one child subtree has been lost; if a -// second subtree is lost later during another cascading cut, then we move -// the node to the root list so that it can be re-balanced on the next -// consolidate. -//=========================================================================== - -void FibHeap::_CascadingCut(FibHeapNode *y) -{ -FibHeapNode *z = y->Parent; - - while (z != NULL) - { - if (y->Mark == 0) - { - y->Mark = 1; - NumMarkedNodes++; - z = NULL; - } - else - { - _Cut(y, z); - y = z; - z = y->Parent; - } - } -} - - -class HeapNode : public FibHeapNode -{ - double N; - long int IndexV; - -public: - - HeapNode() : FibHeapNode() { N = 0; }; - - virtual void operator =(FibHeapNode& RHS); - virtual int operator ==(FibHeapNode& RHS); - virtual int operator <(FibHeapNode& RHS); - - virtual void operator =(double NewKeyVal ); - virtual void Print(); - - double GetKeyValue() { return N; }; /* !!!! */ - void SetKeyValue(double n) { N = n; }; - - long int GetIndexValue() { return IndexV; }; - void SetIndexValue( long int v) { IndexV = v; }; - -}; - -void HeapNode::Print() -{ - FibHeapNode::Print(); - mexPrintf( "%f (%d)" , N , IndexV ); -} - -void HeapNode::operator =(double NewKeyVal) -{ - HeapNode Temp; - Temp.N = N = NewKeyVal; - FHN_Assign(Temp); -} - -void HeapNode::operator =(FibHeapNode& RHS) -{ - FHN_Assign(RHS); - N = ((HeapNode&) RHS).N; -} - -int HeapNode::operator ==(FibHeapNode& RHS) -{ - if (FHN_Cmp(RHS)) return 0; - return N == ((HeapNode&) RHS).N ? 1 : 0; -} - -int HeapNode::operator <(FibHeapNode& RHS) -{ -int X; - - if ((X=FHN_Cmp(RHS)) != 0) - return X < 0 ? 1 : 0; - - return N < ((HeapNode&) RHS).N ? 1 : 0; -}; - -int IntCmp(const void *pA, const void *pB) -{ -int A, B; - - A = *((const int *) pA); - B = *((const int *) pB); - if (A < B) return -1; - if (A == B) return 0; - return 1; -} - -void dodijk_sparse( - long int M, - long int N, - long int S, - long int *P, // parents - double *D, // distances - double *sr, - mwSize *irs, - mwSize *jcs, - HeapNode *A, - FibHeap *theHeap ) -{ - int finished; - long int i,startind,endind,whichneighbor,ndone,index,switchwith,closest,closesti; - long int *INDICES; - double closestD,arclength; - double INF,SMALL,olddist; - HeapNode *Min; - HeapNode Temp; - - INF = mxGetInf(); - SMALL = mxGetEps(); - - /* initialize */ - for (i=0; iInsert( &A[i] ); - A[ i ].SetIndexValue( (long int) i ); - P[i] = 0; - } - - - // Insert 0 then extract it. This will cause the - // Fibonacci heap to get balanced. - - theHeap->Insert(&Temp); - theHeap->ExtractMin(); - - /*theHeap->Print(); - for (i=0; iExtractMin(); - closest = Min->GetIndexValue(); - closestD = Min->GetKeyValue(); - - if ((closest<0) || (closest>=M)) mexErrMsgTxt( "Minimum Index out of bound..." ); - - //theHeap->Print(); -// mexPrintf( "EXTRACTED MINIMUM NDone=%d S=%d closest=%d closestD=%f\n" , ndone , S , closest , closestD );//TT - //mexErrMsgTxt( "Exiting..." ); - - D[ closest ] = closestD; - - if (closestD == INF) finished=1; else - { - /* add the closest to the determined list */ - ndone++; - - /* relax all nodes adjacent to closest */ - startind = jcs[ closest ]; - endind = jcs[ closest+1 ] - 1; - - if (startind!=endind+1) - for (i=startind; i<=endind; i++) - { - whichneighbor = irs[ i ]; - arclength = sr[ i ]; - olddist = D[ whichneighbor ]; - -// mexPrintf( "INSPECT NEIGHBOR #%d olddist=%f newdist=%f\n" , whichneighbor , olddist , closestD+arclength );//TT - - if ( olddist > ( closestD + arclength )) - { - D[ whichneighbor ] = closestD + arclength; - P[whichneighbor] = closest; - - Temp = A[ whichneighbor ]; - Temp.SetKeyValue( closestD + arclength ); - theHeap->DecreaseKey( &A[ whichneighbor ], Temp ); - -// mexPrintf( "UPDATING NODE #%d olddist=%f newdist=%f newpred=%d\n", -// whichneighbor, olddist, closestD+arclength, closest );//TT - - } - } - - } - - } - // source node has no parent - P[S] = -1; - -} - - -//======================================================================== -// Print() -// -// Used internally for debugging purposes. The function prints the key -// value for each node along the root list, then it calls itself on each -// child list. -//======================================================================== - -void FibHeap::Print(FibHeapNode *Tree, FibHeapNode *theParent) -{ -FibHeapNode* Temp = NULL; - - - if (Tree == NULL) { - Tree = MinRoot; - } - - Temp = Tree; - do { - if (Temp->Left == NULL) - mexPrintf( "(Left is NULL)" ); - Temp->Print(); - if (Temp->Parent != theParent) - mexPrintf("(Parent is incorrect)" ); - if (Temp->Right == NULL) - mexPrintf( "(Right is NULL)" ); - else if (Temp->Right->Left != Temp) - mexPrintf( "(Error in left link left) ->" ); - else mexPrintf( " <-> " ); - - Temp = Temp->Right; - -// if (kbhit() && getch() == 27) -// { -// std::cout << "Hit a key to resume or ESC to break\n"; -// if (getch() == 27) -// break; -// } - } while (Temp != NULL && Temp != Tree); - mexPrintf( "\n" ); - - Temp = Tree; - do { - mexPrintf( "Children of " ); - Temp->Print(); - mexPrintf( ": " ); - if (Temp->Child == NULL) - mexPrintf( "NONE\n" ); - else Print(Temp->Child, Temp); - Temp = Temp->Right; - } while (Temp!=NULL && Temp != Tree); - - if (theParent == NULL) - { - char ch; - - mexPrintf( "\n\n\n" ); - std::cin >> ch; - } -} - -//=========================================================================== - -void mexFunction( - int nlhs, - mxArray *plhs[], - int nrhs, - const mxArray *prhs[] - ) -{ - double *sr,*D,*P,*SS,*Dsmall; - long int *Psmall; - mwIndex *irs,*jcs; - mwSize M,N,S,MS,NS,i,j,in; - - HeapNode *A = NULL; - FibHeap *theHeap = NULL; - - if (nrhs != 2) - { - mexErrMsgTxt( "Two input arguments required." ); - } - else if (nlhs > 2) - { - mexErrMsgTxt( "Too many output arguments." ); - } - - M = mxGetM( prhs[0] ); - N = mxGetN( prhs[0] ); - - if (M != N) mexErrMsgTxt( "Input matrix needs to be square." ); - - SS = mxGetPr(prhs[1]); - MS = mxGetM( prhs[1] ); - NS = mxGetN( prhs[1] ); - - if ((MS==0) || (NS==0) || ((MS>1) && (NS>1))) mexErrMsgTxt( "Source nodes are specified in one dimensional matrix only" ); - if (NS>MS) MS=NS; - - // distance values output - plhs[0] = mxCreateDoubleMatrix( MS,M, mxREAL); - D = mxGetPr(plhs[0]); - - // predecessors output - plhs[1] = mxCreateDoubleMatrix( MS,M, mxREAL); - P = mxGetPr(plhs[1]); - - Dsmall = (double *) mxCalloc( M , sizeof( double )); - Psmall = (long int *) mxCalloc(M , sizeof(long int)); - - if (Dsmall == NULL || Psmall == NULL) { - mexErrMsgTxt("Memory allocation failed"); - } - - if (mxIsSparse( prhs[ 0 ] ) == 1) - { - /* dealing with sparse array */ - sr = mxGetPr(prhs[0]); - irs = mxGetIr(prhs[0]); - jcs = mxGetJc(prhs[0]); - - // Setup for the Fibonacci heap - - for (i=0; iClearHeapOwnership(); - - S = (long int) *( SS + i ); - S--; - - if ((S < 0) || (S > M-1)) mexErrMsgTxt( "Source node(s) out of bound" ); - - /* ------------------------------------------------------------------------------------------------- - run the dijkstra code - 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z{C>vzYgS1w$aID|QZr+t(jD=IqfU2@@N$@J*x8NGU7T({HnXOEt)~{(%1|)Sfh$(t z@a*7!10D?hX{XyD(~Zx-qvo zxw+CZ6gXF&rnC&NO&D&JSsg3ny@7Ww*9X(=X|D7*olVz!b~LRw<~iMkI#WXp#%tGm zJov~9?kg{;K3o_Pdd>z7Y+0JD8iq_@L~w7*liA zoMT(e?+Ktc-e@SSnA|sd826?s5B}4*( 1 - invC = ((1 / sigma2) * eye(D)) - ((1 / sigma2) * W * invM * W'); - detC = det(sigma2 * eye(D)) * det(eye(no_dims) + W' * ((sigma2 .^ -1) * eye(D)) * W); - Q = (-n / 2) * (D * log(2 * pi) + log(detC) + trace(invC * S)); - end - - % Stop condition to detect convergence - if abs(oldQ - Q) < 1e-3 - converged = 1; - end - end - - % Compute mapped data - disp(' '); - mapping.M = (inW \ W')'; - mapping.sigma2 = sigma2; - mappedX = X' * mapping.M; - \ No newline at end of file diff --git a/code/dimReducMethods/fa.m b/code/dimReducMethods/fa.m deleted file mode 100644 index 0693a64..0000000 --- a/code/dimReducMethods/fa.m +++ /dev/null @@ -1,69 +0,0 @@ -function [mappedX, mapping] = fa(X, no_dims) -%FA Perform factor analysis (FA) on dataset X -% -% mappedX = fa(X, no_dims) -% -% Perform factor analysis on dataset X in order to reduce its -% dimensionality to no_dims dimensions. The reduced data representation is -% returned in mappedX. - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - - % Make sure data is zero-mean - mapping.mean = mean(X, 1); - X = X - repmat(mapping.mean, [size(X, 1) 1]); - - % Initialize some variables - X = X'; - [D, n] = size(X); - epsilon = 1e-5; - iter = 0; - max_iter = 200; - - % Initialize FA model - Sig = eye(D); % initial variances - A = rand(D, no_dims); % initial linear mapping - - % Main loop - while iter < max_iter - - % Update number of iterations - iter = iter + 1; - if rem(iter, 5) == 0 - fprintf('.'); - end - - % Perform E-step - invC = inv(A * A' + Sig); % compute inverse of covariance matrix - M = A' * invC * X; - SC = n * (eye(no_dims) - A' * invC * A) + M * M'; - - % Perform M-step - A = (X * M') / SC; - Sig = (diag(diag(X * X' - A * M * X')) / n) + epsilon; - - % Compute log-likelihood of FA model - newll = 0.5 * (log(det(invC)) - sum(sum((invC * X) .* X)) / n); - - % Check for convergence - if iter ~=1 && abs(newll - ll) < epsilon - break; - end - ll = newll; - end - - % Apply linear mapping - mapping.M = A; - mappedX = X' * mapping.M; - disp(' '); diff --git a/code/dimReducMethods/fastmvu.m b/code/dimReducMethods/fastmvu.m deleted file mode 100644 index f4a4bba..0000000 --- a/code/dimReducMethods/fastmvu.m +++ /dev/null @@ -1,119 +0,0 @@ -function [mappedX, mapping] = fastmvu(X, no_dims, k, finetune, eig_impl) -%FAST_MVU Runs the Fast Maximum Variance Unfolding algorithm -% -% [mappedX, mapping] = fastmvu(X, no_dims, k, finetune) -% -% Computes a low dimensional embedding of data points using the Fast -% Maximum Variance Unfolding algorithm. The data is specified in an NxD -% data matrix X. The lowdimensional representation is returned in mappedX. -% Information on the mapping is returned in the mapping struct. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('finetune', 'var') - finetune = true; - end - if ~exist('eig_impl', 'var') - eig_impl = 'Matlab'; - end - - % Initialize some parameters - maxiter = 10000; % maximum number of iterations - eta = 1e-5 ; % regularization parameter - initial_dims = 2 * no_dims; % dimensionality of first guess - - % Compute sparse distance matrix D on dataset X - disp('Constructing neighborhood graph...'); - D = find_nn(X, k); - D(D ~= 0) = 1; - - % Select largest connected component - blocks = components(D)'; - count = zeros(1, max(blocks)); - for i=1:max(blocks) - count(i) = length(find(blocks == i)); - end - [count, block_no] = max(count); - conn_comp = find(blocks == block_no); - D = D(conn_comp,:); - D = D(:,conn_comp); - mapping.conn_comp = conn_comp; - mapping.D = D; - - % Perform eigendecomposition of the graph Laplacian - disp('Perform eigendecomposition of graph Laplacian...'); - DD = diag(sum(D, 2)); % degree matrix - L = DD - D; % graph Laplacian - L(isnan(L)) = 0; - L(isinf(L)) = 0; - if strcmp(eig_impl, 'JDQR') - options.Disp = 0; - options.LSolver = 'bicgstab'; - [laplX, lambda] = jdqr(L, initial_dims + 1, 'SR', options); % only need bottom (initial_dims + 1) eigenvectors - else - options.disp = 0; - options.isreal = 1; - options.issym = 1; - [laplX, lambda] = eigs(L, initial_dims + 1, 'SR', options); % only need bottom (initial_dims + 1) eigenvectors - end - [lambda, ind] = sort(diag(lambda), 'ascend'); - laplX = real(laplX(:,ind(2:initial_dims + 1))); - clear DD L - - % Maximize sum of pairwise distances while retaining distances inside - % neighborhood graph distances. I.e. perform SDP optimization, starting - % with eigendecomposition of the Laplacian. The constraints of the - % optimization are formed by the upper triangle of D. - disp('Perform semi-definite programming...'); - disp('CSDP OUTPUT ============================================================================='); - try - [LL, mappedX, L, newV, idx] = sdecca2(laplX', triu(D), eta, 0); - catch - error('Error while performing SDP. Maybe the binaries of CSDP are not suitable for your platform.'); - end - disp('========================================================================================='); - - % Perform initial conjugate gradient search (in initial-dimensional space) - if finetune - disp('Finetune initial solution using conjugate gradient descent...'); - mappedX = hillclimber2c(D, mappedX, 'maxiter', maxiter, 'eta', eta); - end - - % Perform PCA to remove noise and further reduce dimensionality - disp('Perform PCA to obtain final solution...'); - [mappedX, mapping2] = compute_mapping(mappedX', 'PCA', no_dims); - - % Finetune final solution - if finetune - mappedX = mappedX'; - disp('Finetune final solution using conjugate gradient descent...'); - mappedX = hillclimber2c(D, mappedX, 'maxiter', maxiter, 'eta', 0); - mappedX = mappedX'; - end - - % Save data for the out-of-sample extension - mapping.k = k; - mapping.L = L; - mapping.X = X; - mapping.newV = newV; - mapping.idx = idx; - mapping.vec = laplX; - mapping.pca_map = mapping2; - mapping.pca_map.name = 'PCA'; - mapping.finetune = finetune; - \ No newline at end of file diff --git a/code/dimReducMethods/fibheap.h b/code/dimReducMethods/fibheap.h deleted file mode 100644 index 8f5b910..0000000 --- a/code/dimReducMethods/fibheap.h +++ /dev/null @@ -1,106 +0,0 @@ -#ifndef _FIBHEAP_H -#define _FIBHEAP_H - -//*************************************************************************** -// The Fibonacci heap implementation contained in FIBHEAP.H and FIBHEAP.CPP -// is Copyright (c) 1996 by John Boyer -// -// Once this Fibonacci heap implementation (the software) has been published -// by Dr. Dobb's Journal, permission to use and distribute the software is -// granted provided that this copyright notice remains in the source and -// and the author (John Boyer) is acknowledged in works that use this program. -// -// Every effort has been made to ensure that this implementation is free of -// errors. Nonetheless, the author (John Boyer) assumes no liability regarding -// your use of this software. -// -// The author would also be very glad to hear from anyone who uses the -// software or has any feedback about it. -// Email: jboyer@gulf.csc.uvic.ca -//*************************************************************************** - -#define OK 0 -#define NOTOK -1 - -//====================================================== -// Fibonacci Heap Node Class -//====================================================== - -class FibHeap; - -class FibHeapNode -{ -friend class FibHeap; - - FibHeapNode *Left, *Right, *Parent, *Child; - short Degree, Mark, NegInfinityFlag; - -protected: - - inline int FHN_Cmp(FibHeapNode& RHS); - inline void FHN_Assign(FibHeapNode& RHS); - -public: - - inline FibHeapNode(); - virtual ~FibHeapNode(); - - virtual void operator =(FibHeapNode& RHS); - virtual int operator ==(FibHeapNode& RHS); - virtual int operator <(FibHeapNode& RHS); - - virtual void Print(); -}; - -//======================================================================== -// Fibonacci Heap Class -//======================================================================== - -class FibHeap -{ - FibHeapNode *MinRoot; - long NumNodes, NumTrees, NumMarkedNodes; - - int HeapOwnershipFlag; - -public: - - FibHeap(); - virtual ~FibHeap(); - -// The Standard Heap Operations - - void Insert(FibHeapNode *NewNode); - void Union(FibHeap *OtherHeap); - - inline FibHeapNode *Minimum(); - FibHeapNode *ExtractMin(); - - int DecreaseKey(FibHeapNode *theNode, FibHeapNode& NewKey); - int Delete(FibHeapNode *theNode); - -// Extra utility functions - - int GetHeapOwnership() { return HeapOwnershipFlag; }; - void SetHeapOwnership() { HeapOwnershipFlag = 1; }; - void ClearHeapOwnership() { HeapOwnershipFlag = 0; }; - - long GetNumNodes() { return NumNodes; }; - long GetNumTrees() { return NumTrees; }; - long GetNumMarkedNodes() { return NumMarkedNodes; }; - - void Print(FibHeapNode *Tree = NULL, FibHeapNode *theParent=NULL); - -private: - -// Internal functions that help to implement the Standard Operations - - inline void _Exchange(FibHeapNode*&, FibHeapNode*&); - void _Consolidate(); - void _Link(FibHeapNode *, FibHeapNode *); - void _AddToRootList(FibHeapNode *); - void _Cut(FibHeapNode *, FibHeapNode *); - void _CascadingCut(FibHeapNode *); -}; - -#endif diff --git a/code/dimReducMethods/find_nn.c b/code/dimReducMethods/find_nn.c deleted file mode 100755 index 3e8e86f..0000000 --- a/code/dimReducMethods/find_nn.c +++ /dev/null @@ -1,111 +0,0 @@ -#include "mex.h" -#include - - -void mexFunction( - int nlhs, mxArray *plhs[], - int nrhs, const mxArray *prhs[] - ) -{ - - /* Declare variables. */ - int *irs, *jcs, *k_ind, i, j, k, l, m, n, p, cc, ck, nzmax, min_ind, *ind; - double *d, *k_d, *pr, *sr, dist, tmp, min_d; - mxArray *rhs[1], *lhs[2]; - - /* Check for proper number of input and output arguments. */ - if (nrhs < 1) { - mexErrMsgTxt("At least one input argument required."); - } - if (nrhs > 2) { - mexErrMsgTxt("No more than two input arguments allowed."); - } - if (nlhs > 1) { - mexErrMsgTxt("Too many output arguments."); - } - if (!(mxIsDouble(prhs[0]))) { - mexErrMsgTxt("Input argument must be of type double."); - } - - /* Get all input data. */ - m = mxGetM(prhs[0]); // height - n = mxGetN(prhs[0]); // width - pr = mxGetPr(prhs[0]); // pointer to data array (double) - if (nrhs > 1) { - k = (int)mxGetScalar(prhs[1]); // number of neighbors - } - else { - k = 12; // number of neighbors - } - - /* Allocate space for sparse matrix (don't allow complex values). */ - nzmax = m * k; - plhs[0] = mxCreateSparse(m, n, nzmax, 0); - sr = mxGetPr(plhs[0]); // pointer to sparse values - irs = mxGetIr(plhs[0]); // pointer to sparse row indices - jcs = mxGetJc(plhs[0]); // pointer to sparse column indices - cc = 0; // current row position in sparse matrix - ck = 0; // current column position in sparse matrix - - /* Allocate space for matrix containing the distances between one datapoint and all other datapoints. */ - d = malloc(m * sizeof(double)); // stores distances with n datapoints - k_d = malloc(k * sizeof(double)); // stores distance values to k nearest neighbors - k_ind = malloc(k * sizeof(int)); // stores indices of k nearest neighbors - for (i = 0; i < m; i++) { - for (j = 0; j < m; j++) { - /* Compute Euclidean distance between datapoint i and j. */ - dist = 0; - for (l = 0; l < n; l++) { - tmp = pr[i * n + l] - pr[j * n + l]; - dist += (tmp * tmp); - } - d[j] = sqrt(dist); - } - - /* Find the k nearest neighbors. */ -/* for (l = 0; l < k; l++) { - min_ind = 0; - min_d = 0xffffff; - for (p = 0; p < m; p++) { - if(d[p] < min_d) { - min_d = d[p]; - min_ind = p; - } - } - k_d[l] = min_d; - k_ind[l] = min_ind; - d[min_ind] = 0xffffff; - } */ - - /* Find the k nearest neighbors */ - rhs[0] = (mxArray*)d; - mexCallMATLAB(2, lhs, 1, rhs, 'sort'); - d = lhs[0]; - ind = lhs[1]; - for (l = 0; l < k; l++) { - k_d[l] = d[l]; - k_ind[l] = (int)ind[l]; - } - - /* Store the k nearest neighbors in the sparse dissimilarity matrix. */ - for (l = 0; l < k; l++) { - if(cc < nzmax) { - sr[cc] = k_d[l]; // store sparse value - irs[cc] = k_ind[l]; // store row index - cc++; - } - } - jcs[i] = ck; // store column index - ck += k; - } - jcs[m] = ck; - - /* Clean up memory. */ - free(d); - free(k_d); - free(k_ind); - - return; -} - - diff --git a/code/dimReducMethods/find_nn.m b/code/dimReducMethods/find_nn.m deleted file mode 100644 index 4df50c0..0000000 --- a/code/dimReducMethods/find_nn.m +++ /dev/null @@ -1,64 +0,0 @@ -function [D, ni] = find_nn(X, k) -%FIND_NN Finds k nearest neigbors for all datapoints in the dataset -% -% [D, ni] = find_nn(X, k) -% -% Finds the k nearest neighbors for all datapoints in the dataset X. -% In X, rows correspond to the observations and columns to the -% dimensions. The value of k is the number of neighbors that is -% stored. The function returns a sparse distance matrix D, in which -% only the distances to the k nearest neighbors are stored. For -% equal datapoints, the distance is set to a tolerance value. -% The method is relatively slow, but has a memory requirement of O(nk). -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('k', 'var') || isempty(k) - k = 12; - end - - % Perform adaptive neighborhood selection if desired - if ischar(k) - [D, max_k] = find_nn_adaptive(X); - ni = zeros(size(X, 1), max_k); - for i=1:size(X, 1) - tmp = find(D(i,:) ~= 0); - tmp(tmp == i) = []; - tmp = [tmp(2:end) zeros(1, max_k - length(tmp) + 1)]; - ni(i,:) = tmp; - end - - % Perform normal neighborhood selection - else - - % Compute distances in batches - n = size(X, 1); - sum_X = sum(X .^ 2, 2); - batch_size = round(2e7 ./ n); - D = zeros(n, k); - ni = zeros(n, k); - for i=1:batch_size:n - batch_ind = i:min(i + batch_size - 1, n); - DD = bsxfun(@plus, sum_X', bsxfun(@plus, sum_X(batch_ind), ... - -2 * (X(batch_ind,:) * X'))); - [DD, ind] = sort(abs(DD), 2, 'ascend'); - D(batch_ind,:) = sqrt(DD(:,2:k + 1)); - ni(batch_ind,:) = ind(:,2:k + 1); - end - D(D == 0) = 1e-9; - Dout = sparse(n, n); - idx = repmat(1:n, [1 k])'; - Dout(sub2ind([n, n], idx, ni(:))) = D; - Dout(sub2ind([n, n], ni(:), idx)) = D; - D = Dout; - end - \ No newline at end of file diff --git a/code/dimReducMethods/find_nn_adaptive.m b/code/dimReducMethods/find_nn_adaptive.m deleted file mode 100644 index 013b8e0..0000000 --- a/code/dimReducMethods/find_nn_adaptive.m +++ /dev/null @@ -1,102 +0,0 @@ -function [D, max_k_val, no_dims] = find_nn_adaptive(X) -%FIND_NN Constructs nearest neighbor graph using adaptive nbhd selection -% -% [D, max_k_val, no_dims] = find_nn_adaptive(X) -% -% Constructs nearest neighbor graph on the data in dataset X using adaptive -% neighborhood selection. In X, rows correspond to the observations and -% columns to the dimensions. -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % First, estimate intrinsic dimensionality using the MLE estimator - no_dims = round(intrinsic_dim(X, 'MLE')); - - % Initialize some variables - n = size(X, 1); - min_k = no_dims + 1; - max_k = n; - max_k_val = 0; - - % Perform some precomputations for speed - X = X'; - D = sparse([], [], [], n, n, n * 12); % Pre-allocate for speed! - XX = sum(X .* X); - onez = ones(1,n); - %tmp_L1_Dist = mandist(X); %returns a n x n datapoint distance matrix - - % For all datapoints - for i=1:n - % current data point - p = X(:,i); - - % Compute Euclidean distance to all other datapoints - d2 = sum(p.^2).*onez + XX - 2*p'*X; - - %[MANISH] implement a L1 distance - %d2 = tmp_L1_Dist(i,:); - - % Sort distances - [d2, ind] = sort(d2); - - % Estimate local tangent space by updating the number of neighbors k - stop = 0; - k = min_k; - while ~stop && k + 1 < max_k - - % Update k - k = k + 1; - - % Estimate local tangent space (for current value of k) - tmpX = X(:,ind(2:k + 1)) - repmat(p, 1, k); - lambda = svd(tmpX); - [lambda, ind2] = sort(lambda, 'descend'); - if length(lambda) < no_dims - break; - end - - % Estimate T_{1} - T = (1 / k) ^ (1 / no_dims) * sqrt(d2(k + 1)); - - % Check whether stop condition is violated - if lambda(no_dims) >= T - stop = true; - end - end - - % Compute tangent space at k - 1 since k failed stop condition - [U, lambda, M] = svd(tmpX(:,1:k-1)); - [lambda, ind2] = sort(diag(lambda), 'descend'); - U = U(:,ind2(1:no_dims))'; - - % Select neighbors that correspond to the local tangent space - stop = 0; - while ~stop && k + 1 < max_k - % Update k - k = k + 1; - - % Projection of (x_{k} - x_{i}) onto tangent space - onto = sum( (U * (X(:,ind(k + 1)) - p)).^2 ); - - % Check whether stop condition is violated - if d2(k + 1) - onto > T^2 - k = k - 1; - stop = true; - end - end - - % Update neighborhood graph - d2(1) = 1e-7; - D(i, ind(1:k + 1)) = sqrt(d2(1:k + 1)); - if max_k_val < k - max_k_val = k; - end - end diff --git a/code/dimReducMethods/gda.m b/code/dimReducMethods/gda.m deleted file mode 100644 index df4dfbf..0000000 --- a/code/dimReducMethods/gda.m +++ /dev/null @@ -1,117 +0,0 @@ -function mappedX = gda(X, Y, no_dims, varargin) -%GDA Perform Generalized Discriminant Analysis -% -% mappedX = gda(X, Y, no_dims) -% mappedX = gda(X, Y, no_dims, kernel) -% mappedX = gda(X, Y, no_dims, kernel, param1) -% mappedX = gda(X, Y, no_dims, kernel, param1, param2) -% -% Perform Generalized Discriminant Analysis. GDA or Kernel LDA is the -% nonlinear generalization of LDA by means of the kernel trick. X is the -% data on which to perform GDA, Y are the corresponding labels. -% The value of kernel determines the used kernel. Possible values are 'linear', -% 'gauss', 'poly', 'subsets', or 'princ_angles' (default = 'gauss'). For -% more info on setting the parameters of the kernel function, type HELP -% GRAM. -% The function returns the locations of the embedded trainingdata in -% mappedX. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Process inputs - if ~exist('no_dims', 'var') - no_dims = 2; - end - kernel = 'gauss'; - param1 = 1; - param2 = 0; - if length(varargin) > 0 & strcmp(class(varargin{1}), 'char'), kernel = varargin{1}; end - if length(varargin) > 1 & strcmp(class(varargin{2}), 'double'), param1 = varargin{2}; end - if length(varargin) > 2 & strcmp(class(varargin{3}), 'double'), param2 = varargin{3}; end - - % Make sure labels are nice - [foo, bar, Y] = unique(Y, 'rows'); - - % Get dimensions - [n, dim] = size(X); - nclass = max(Y); - - % Sort data according to labels - [foo, ind] = sort(Y); - Y = Y(ind); - X = X(ind,:); - - % Compute kernel matrix - disp('Computing kernel matrix...'); - K = gram(X, X, kernel, param1, param2); - - % Compute centering matrix - ell = size(X, 1); - D = sum(K) / ell; - E = sum(D) / ell; - J = ones(ell, 1) * D; - K = K - J - J' + E * ones(ell, ell); - - % Perform eigenvector decomposition of kernel matrix (Kc = P * gamma * P') - disp('Performing eigendecomposition of kernel matrix...'); - K(isnan(K)) = 0; - K(isinf(K)) = 0; - [P, gamma] = eig(K); - - if size(P, 2) < n - error('Singularities in kernel matrix prevent solution.'); - end - - % Sort eigenvalues and vectors in descending order - [gamma, ind] = sort(diag(gamma), 'descend'); - P = P(:,ind); - - % Remove eigenvectors with relatively small value - minEigv = max(gamma) / 1e5; - ind = find(gamma > minEigv); - P = P(:,ind); - gamma = gamma(ind); - rankK = length(ind); - - % Recompute kernel matrix - K = P * diag(gamma) * P'; - - % Construct diagonal block matrix W - W = []; - for i=1:nclass - num_data_class = length(find(Y == i)); - W = blkdiag(W, ones(num_data_class) / num_data_class); - end - - % Determine target dimensionality of data - old_no_dims = no_dims; - no_dims = min([no_dims rankK nclass]); - if old_no_dims > no_dims - warning(['Target dimensionality reduced to ' num2str(no_dims) '.']); - end - - % Perform eigendecomposition of matrix (P' * W * P) - disp('Performing GDA eigenanalysis...'); - [Beta, lambda] = eig(P' * W * P); - lambda = diag(lambda); - - % Sort eigenvalues and eigenvectors in descending order - [lambda, ind] = sort(lambda, 'descend'); - Beta = Beta(:,ind(1:no_dims)); - - % Compute final embedding mappedX - mappedX = P * diag(1 ./ gamma) * Beta; - - % Normalize embedding - for i=1:no_dims - mappedX(:,i) = mappedX(:,i) / sqrt(mappedX(:,i)' * K * mappedX(:,i)); - end diff --git a/code/dimReducMethods/gplvm.m b/code/dimReducMethods/gplvm.m deleted file mode 100644 index ca30504..0000000 --- a/code/dimReducMethods/gplvm.m +++ /dev/null @@ -1,41 +0,0 @@ -function Y = gplvm(X, no_dims, sigma) -%GPLVM Gaussian Process Latent Variable Model -% -% Y = gplvm(X, no_dims, sigma) -% -% Simple implementation of the Gaussian Process Latent Variable Model using -% a Gaussian kernel with bandwidth alpha. The function reduces the -% dimenisonality of the dataset X to no_dims dimensions. The resulting -% low-dimensional dataset is returned in Y. -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('sigma', 'var') || isempty(sigma) - sigma = 1; - end - - % Initialize some variables - n = size(X, 1); - - % Initialize solution using PCA - disp('Preprocessing data using PCA...'); - X = bsxfun(@minus, X, mean(X, 1)); - [M, lambda] = eig(X' * X); - [lambda, ind] = sort(diag(lambda), 'descend'); - M = M(:,ind(1:no_dims)); - Y = X * M; - clear M lambda ind - - % Check gradient - disp('Learn GPLVM model...'); - Y = minimize(Y(:), 'gplvm_grad', -500, X, sigma); - Y = reshape(Y, [n no_dims]); - \ No newline at end of file diff --git a/code/dimReducMethods/gplvm_grad.m b/code/dimReducMethods/gplvm_grad.m deleted file mode 100644 index 1b6f575..0000000 --- a/code/dimReducMethods/gplvm_grad.m +++ /dev/null @@ -1,41 +0,0 @@ -function [C, dC] = gplvm_grad(x, X, sigma) -%GPLVM_GRAD Gradient of the Gaussian Process Latent Variable model -% -% [C, dC] = gplvm_grad(x, no_dims, sigma) -% -% Computes the gradient of the Gaussian Process Latent Variable model. - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Decode solution - [n, d] = size(X); - no_dims = numel(x) ./ n; - Y = reshape(x, [n no_dims]); - - % Compute kernel matrix (in latent space) - sum_Y = sum(Y .^ 2, 2); - K = exp(bsxfun(@minus, bsxfun(@minus, 2 * (Y * Y'), sum_Y'), sum_Y) / (2 * sigma ^ 2)); - - % Compute gradient with respect to kernel -% invK = inv(K); -% dLdK = invK * X * X' * invK - d * invK; - tmp = (K \ X) * X'; - dLdK = (tmp - d * eye(n)) / K; - - % Compute gradient with respect to coordinates - dC = zeros(n, no_dims); - dLdK = K .* dLdK; - for i=1:n - dC(i,:) = sum(bsxfun(@times, dLdK(:,i), bsxfun(@minus, Y(i,:), Y)), 1); - end - dC = (-1 / sigma ^ 2) * dC(:); - - % Compute log-likelihood - C = -((d * n) / 2) * log(2 * pi) - (d / 2) * log(det(K) + realmin) - .5 * trace(tmp); diff --git a/code/dimReducMethods/gram.m b/code/dimReducMethods/gram.m deleted file mode 100644 index b1cb156..0000000 --- a/code/dimReducMethods/gram.m +++ /dev/null @@ -1,59 +0,0 @@ -function G = gram(X1, X2, kernel, param1, param2) -%GRAM Computes the Gram-matrix of data points X using a kernel function -% -% G = gram(X1, X2, kernel, param1, param2) -% -% Computes the Gram-matrix of data points X1 and X2 using the specified kernel -% function. If no kernel is specified, no kernel function is applied. The -% function GRAM is than equal to X1*X2'. The use of the function is different -% depending on the specified kernel function (because different kernel -% functions require different parameters. The possibilities are listed -% below. -% Linear kernel: G = gram(X1, X2, 'linear') -% which is parameterless -% Gaussian kernel: G = gram(X1, X2, 'gauss', s) -% where s is the variance of the used Gaussian function (default = 1). -% Polynomial kernel: G = gram(X1, X2, 'poly', R, d) -% where R is the addition value and d the power number (default = 0 and 3) -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - % Check inputs - if size(X1, 2) ~= size(X2, 2) - error('Dimensionality of both datasets should be equal'); - end - - % If no kernel function is specified - if nargin == 2 || strcmp(kernel, 'none') - kernel = 'linear'; - end - - switch kernel - - % Linear kernel - case 'linear' - G = X1 * X2'; - - % Gaussian kernel - case 'gauss' - if ~exist('param1', 'var'), param1 = 1; end - G = L2_distance(X1', X2'); - G = exp(-(G.^2 / (2 * param1.^2))); - - % Polynomial kernel - case 'poly' - if ~exist('param1', 'var'), param1 = 1; param2 = 3; end - G = ((X1 * X2') + param1) .^ param2; - - otherwise - error('Unknown kernel function.'); - end - \ No newline at end of file diff --git a/code/dimReducMethods/hill_obj.m b/code/dimReducMethods/hill_obj.m deleted file mode 100644 index 1af6029..0000000 --- a/code/dimReducMethods/hill_obj.m +++ /dev/null @@ -1,27 +0,0 @@ -function [f,df]=hill_obj(x,dims,ii,dd,pars); -% -% computes the objective function and gradient of the non-convex formulation of MVU. -% -% copyright by Kilian Q. Weinberger, 2006 -% -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - X=reshape(x,dims); - [df,f]=computegr(X,ii(:,1),ii(:,2),dd); - df=df(:).*8; - - if(pars.eta>0) % incorporate the trace term - df=df-pars.eta.*x; - f=f-pars.eta.*sum(sum(x.^2)); - end; - diff --git a/code/dimReducMethods/hillclimber2c.m b/code/dimReducMethods/hillclimber2c.m deleted file mode 100644 index d47ab7a..0000000 --- a/code/dimReducMethods/hillclimber2c.m +++ /dev/null @@ -1,39 +0,0 @@ -function [x,obj] = hillclimber2c(DD, x, varargin) -%HILLCLIMBER Performs hillclimbing using initial solution -% -% function [x, obj] = hillclimber(DD, x, varargin) -% -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - n = length(DD); - - % Set parameters for the hillclimber - pars.maxiter = 10000; - pars.stepsize = 1e-05; - pars.ETA = 1e0-5; - pars.truex = []; - pars.verbose = 1; - pars.acc = 1.01; - pars.printevery = 100; - pars.othresh = 1e-10; - pars.eta = 0; - - % Initialize variables - ii = find(DD); - dd = full(DD(ii)); - [i2,i1] = ind2sub(size(DD), ii); - dims = size(x); - - % Perform hill-climbing - [x, obj, i] = minimize(x(:), 'hill_obj', -pars.maxiter, dims, [i1 i2], dd, pars); - x = reshape(x, dims); \ No newline at end of file diff --git a/code/dimReducMethods/hlle.m b/code/dimReducMethods/hlle.m deleted file mode 100644 index c33c325..0000000 --- a/code/dimReducMethods/hlle.m +++ /dev/null @@ -1,129 +0,0 @@ -function mappedX = hlle(X, no_dims, k, eig_impl) -%HLLE Runs the Hessian LLE algorithm -% -% mappedX = hlle(X, no_dims, k, eig_impl) -% -% Runs the Hessian LLE algorithm on dataset X to reduce its dimensionality -% to no_dims. The variable k specifies the number of nearest negihbors that -% is used. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('eig_impl', 'var') - eig_impl = 'Matlab'; - end - - % Compute nearest neighbors - if ischar(k) - warning('Adaptive neighborhood selection often leads to problems in Hessian LLE.'); - end - disp('Finding nearest neighbors...'); - [D, nind] = find_nn(X, k); - max_k = size(nind, 2); - - % Size of original data - n = size(X, 1); - - % Extra term count for quadratic form - dp = no_dims * (no_dims + 1) / 2; - W = sparse([], [], [], dp * n, n, dp * n * max_k); - - % For all datapoints - disp('Building Hessian estimator for neighboring points...'); - for i=1:n - % Center datapoints by substracting their mean - tmp_ind = nind(i,:); - tmp_ind = tmp_ind(tmp_ind ~= 0); - kt = length(tmp_ind); - thisx = X(tmp_ind,:); - thisx = (thisx - repmat(mean(thisx, 1), kt, 1))'; - - % Compute local coordinates (using SVD) - [U, D, Vpr] = svd(thisx); - if size(Vpr, 2) < no_dims - no_dims = size(Vpr, 2); - dp = no_dims * (no_dims + 1) / 2; - warning(['Target dimensionality reduced to ' num2str(no_dims) '...']); - end - V = Vpr(:,1:no_dims); - % Basically, the above is applying PCA to the neighborhood of Xi. The PCA mapping that is found - % (and that is contained in V) is an approximation for the tangent space at Xi. - - % Build Hessian estimator - clear Yi; clear Pii; - ct = 0; - for mm=1:no_dims - startp = V(:,mm); - for nn=1:length(mm:no_dims) - indles = mm:no_dims; - Yi(:,ct+nn) = startp .* (V(:,indles(nn))); - end - ct = ct + length(mm:no_dims); - end - Yi = [repmat(1, kt, 1) V Yi]; - - % Gram-Schmidt orthogonalization (works different from Matlab QR function) - [Yt, Orig] = mgs(Yi); - Pii = Yt(:,no_dims + 2:end)'; - - % Double check weights sum to 1 - for j=1:dp - if sum(Pii(j,:)) > 0.0001 - tpp = Pii(j,:) ./ sum(Pii(j,:)); - else - tpp = Pii(j,:); - end - - % Fill weight matrix - W((i - 1) * dp + j, tmp_ind) = tpp; - end - end - - % The weight matrix W is now entirely filled, perform eigenanalysis of W - disp('Computing HLLE embedding (eigenanalysis)...'); - - % Make sparse matrix that is inproduct of W - G = W' * W; - G(isnan(G)) = 0; - G = sparse(G); - - % Clear some memory - clear X thisx W D nind U D Vpr; - - % Perform eigendecomposition - tol = 0; - if strcmp(eig_impl, 'JDQR') - options.Disp = 0; - options.LSolver = 'bicgstab'; - [mappedX, eigenvals] = jdqr(G, no_dims + 1, tol, options); - else - options.disp = 0; - options.issym = 1; - options.isreal = 1; - [mappedX, eigenvals] = eigs(G, no_dims + 1, tol, options); - end - - % Sort eigenvalues and eigenvectors - [eigenvals, ind] = sort(diag(eigenvals), 'ascend'); - if size(mappedX, 2) < no_dims + 1, no_dims = size(mappedX, 2) - 1; end - mappedX = mappedX(:,ind(2:no_dims + 1)); - - % Extract nonzero coordinates - mappedX = mappedX(:,1:no_dims)' * sqrt(n); - mappedX = mappedX'; - diff --git a/code/dimReducMethods/infermfa.m b/code/dimReducMethods/infermfa.m deleted file mode 100644 index 0781996..0000000 --- a/code/dimReducMethods/infermfa.m +++ /dev/null @@ -1,50 +0,0 @@ -function [R, Z] = infermfa(X, LX, MX, PX) -%INFERMFA Infer MoFA using information from EM algorithm in MPPCA -% -% [R, Z] = infermfa(X, LX, MX, PX) -% -% Computes local data representations and responsibilities of the datapoints -% to the clusters specified by LX, MX, and PX. Basically, this method performs -% an additional E-step of the EM-algorithm executed in MPPCA. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Initialize some variables - [D N] = size(X); - [D no_dims no_analyzers] = size(LX); - const = -D / 2 * log(2 * pi); - R = zeros(no_analyzers, N); - Z = zeros(no_dims, N, no_analyzers); - - % Estimate the cluster centers based on input (= E-step) - pii = 1 ./ PX; - for kk=1:no_analyzers - l = LX(:,:,kk); - ltpi = (repmat(pii, [1 no_dims]) .* l)'; - ltpil = ltpi * l; - iltpil = eye(no_dims) + ltpil; - cc = chol(iltpil); - cci = inv(cc); - covz = cci * cci'; - delta = X - MX(:,kk * ones(1, N)); - meanz = ((eye(no_dims) - ltpil * covz) * ltpi) * delta; - - Z(:,:,kk) = meanz; - R(kk,:) = -.5 * (pii' * (delta .* delta) - sum(meanz .* (iltpil * meanz), 1)) - ... - sum(log(diag(cc))); - end - - % Compute responsibilities of clusters to points - R = R + const + .5 * sum(log(pii)); - R = exp(R - repmat(max(R, [], 1), [no_analyzers 1])); - R = R ./ repmat(sum(R, 1), [no_analyzers 1]); - diff --git a/code/dimReducMethods/isomap.m b/code/dimReducMethods/isomap.m deleted file mode 100644 index 91af226..0000000 --- a/code/dimReducMethods/isomap.m +++ /dev/null @@ -1,79 +0,0 @@ -function [mappedX, mapping] = isomap(X, no_dims, k) -%ISOMAP Runs the Isomap algorithm -% -% [mappedX, mapping] = isomap(X, no_dims, k); -% -% The functions runs the Isomap algorithm on dataset X to reduce the -% dimensionality of the dataset to no_dims. The number of neighbors used in -% the compuations is set by k (default = 12). This implementation does not -% use the Landmark-Isomap algorithm. -% -% If the neighborhood graph that is constructed is not completely -% connected, only the largest connected component is embedded. The indices -% of this component are returned in mapping.conn_comp. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - - % Construct neighborhood graph - disp('Constructing neighborhood graph...'); - D = real(find_nn(X, k)); - - % Select largest connected component - blocks = components(D)'; - count = zeros(1, max(blocks)); - for i=1:max(blocks) - count(i) = length(find(blocks == i)); - end - [count, block_no] = max(count); - conn_comp = find(blocks == block_no); - D = D(conn_comp, conn_comp); - mapping.D = D; - n = size(D, 1); - - % Compute shortest paths - disp('Computing shortest paths...'); - D = dijkstra(D, 1:n); - mapping.DD = D; - - % Performing MDS using eigenvector implementation - disp('Constructing low-dimensional embedding...'); - D = D .^ 2; - M = -.5 .* (bsxfun(@minus, bsxfun(@minus, D, sum(D, 1)' ./ n), sum(D, 1) ./ n) + sum(D(:)) ./ (n .^ 2)); - M(isnan(M)) = 0; - M(isinf(M)) = 0; - [vec, val] = eig(M); - if size(vec, 2) < no_dims - no_dims = size(vec, 2); - warning(['Target dimensionality reduced to ' num2str(no_dims) '...']); - end - - % Computing final embedding - [val, ind] = sort(real(diag(val)), 'descend'); - vec = vec(:,ind(1:no_dims)); - val = val(1:no_dims); - mappedX = real(bsxfun(@times, vec, sqrt(val)')); - - % Store data for out-of-sample extension - mapping.conn_comp = conn_comp; - mapping.k = k; - mapping.X = X(conn_comp,:); - mapping.vec = vec; - mapping.val = val; - mapping.no_dims = no_dims; - \ No newline at end of file diff --git a/code/dimReducMethods/jdqr.m b/code/dimReducMethods/jdqr.m deleted file mode 100644 index cc984c1..0000000 --- a/code/dimReducMethods/jdqr.m +++ /dev/null @@ -1,2439 +0,0 @@ -function varargout=jdqr(varargin) -%JDQR computes a partial Schur decomposition of a square matrix or operator. -% Lambda = JDQR(A) returns the absolute largest eigenvalues in a K vector -% Lambda. Here K=min(5,N) (unless K has been specified), where N=size(A,1). -% JDQR(A) (without output argument) displays the K eigenvalues. -% -% [X,Lambda] = JDQR(A) returns the eigenvectors in the N by K matrix X and -% the eigenvalues in the K by K diagonal matrix Lambda. Lambda contains the -% Jordan structure if there are multiple eigenvalues. -% -% [X,Lambda,HISTORY] = JDQR(A) returns also the convergence history -% (that is, norms of the subsequential residuals). -% -% [X,Lambda,Q,S] = JDQR(A) returns also a partial Schur decomposition: -% S is an K by K upper triangular matrix and Q is an N by K orthonormal matrix -% such that A*Q = Q*S. The diagonal elements of S are eigenvalues of A. -% -% [X,Lambda,Q,S,HISTORY] = JDQR(A) returns also the convergence history. -% -% [X,Lambda,HISTORY] = JDQR('Afun') -% [X,Lambda,HISTORY] = JDQR('Afun',N) -% The first input argument is either a square matrix (which can be -% full or sparse, symmetric or nonsymmetric, real or complex), or a -% string containing the name of an M-file which applies a linear -% operator to a given column vector. In the latter case, the M-file must -% return the the order N of the problem with N = Afun([],'dimension') or -% N must be specified in the list of input arguments. -% For example, EIGS('fft',...) is much faster than EIGS(F,...) -% where F is the explicit FFT matrix. -% -% The remaining input arguments are optional and can be given in -% practically any order: -% ... = JDQR(A,K,SIGMA,OPTIONS) -% ... = JDQR('Afun',K,SIGMA,OPTIONS) -% where -% -% K An integer, the number of eigenvalues desired. -% SIGMA A scalar shift or a two letter string. -% OPTIONS A structure containing additional parameters. -% -% With one output argument, S is a vector containing K eigenvalues. -% With two output arguments, S is a K-by-K upper triangular matrix -% and Q is a matrix with K columns so that A*Q = Q*S and Q'*Q=I. -% With three output arguments, HISTORY contains the convergence history. -% -% If K is not specified, then K = MIN(N,5) eigenvalues are computed. -% -% If SIGMA is not specified, then the K-th eigenvalues largest in magnitude -% are computed. If SIGMA is zero, then the K-th eigenvalues smallest in -% magnitude are computed. If SIGMA is a real or complex scalar then the -% K-th eigenvalues nearest SIGMA are computed. If SIGMA is one of the -% following strings, then it specifies the desired eigenvalues. -% -% SIGMA Location wanted eigenvalues -% -% 'LM' Largest Magnitude (the default) -% 'SM' Smallest Magnitude (same as sigma = 0) -% 'LR' Largest Real part -% 'SR' Smallest Real part -% 'BE' Both Ends. Computes k/2 eigenvalues -% from each end of the spectrum (one more -% from the high end if k is odd.) -% -% -% The OPTIONS structure specifies certain parameters in the algorithm. -% -% Field name Parameter Default -% -% OPTIONS.Tol Convergence tolerance: 1e-8 -% norm(A*Q-Q*S,1) <= tol * norm(A,1) -% OPTIONS.jmin minimum dimension search subspace k+5 -% OPTIONS.jmax maximum dimension search subspace jmin+5 -% OPTIONS.MaxIt Maximum number of iterations. 100 -% OPTIONS.v0 Starting space ones+0.1*rand -% OPTIONS.Schur Gives schur decomposition 'no' -% also in case of 2 or 3 output -% arguments (X=Q, Lambda=R). -% -% OPTIONS.TestSpace For using harmonic Ritz values 'Standard' -% If 'TestSpace'='Harmonic' then -% sigma=0 is the default value for SIGMA -% -% OPTIONS.Disp Shows size of intermediate residuals 1 -% and displays the appr. eigenvalues. -% -% OPTIONS.LSolver Linear solver 'GMRES' -% OPTIONS.LS_Tol Residual reduction linear solver 1,0.7,0.7^2,.. -% OPTIONS.LS_MaxIt Maximum number it. linear solver 5 -% OPTIONS.LS_ell ell for BiCGstab(ell) 4 -% -% OPTIONS.Precond Preconditioner LU=[[],[]]. -% -% For instance -% -% OPTIONS=STRUCT('Tol',1.0e-10,'LSolver','BiCGstab','LS_ell',2,'Precond',M); -% -% changes the convergence tolerance to 1.0e-10, takes BiCGstab(2) as linear -% solver and the preconditioner defined in M.m if M is the string 'M', -% or M = L*U if M is an n by 2*n matrix: M = [L,U]. -% -% The preconditoner can be specified in the OPTIONS structure, -% but also in the argument list: -% ... = JDQR(A,K,SIGMA,M,OPTIONS) -% ... = JDQR(A,K,SIGMA,L,U,OPTIONS) -% ... = JDQR('Afun',K,SIGMA,'M',OPTIONS) -% ... = JDQR('Afun',K,SIGMA,'L','U',OPTIONS) -% as an N by N matrix M (then M is the preconditioner), or an N by 2*N -% matrix M (then L*U is the preconditioner, where M = [L,U]), -% or as N by N matrices L and U (then L*U is the preconditioner), -% or as one or two strings containing the name of M-files ('M', or -% 'L' and 'U') which apply a linear operator to a given column vector. -% -% JDQR (without input arguments) lists the options and the defaults. - - -% Gerard Sleijpen. -% Copyright (c) 98 -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - -global Qschur Rschur PinvQ Pinv_u Pu nm_operations - -if nargin==0, possibilities, return, end - -%%% Read/set parameters -[n,nselect,sigma,SCHUR,... - jmin,jmax,tol,maxit,V,INTERIOR,SHOW,PAIRS,JDV0,t_tol,... - lsolver,LSpar] = ReadOptions(varargin{1:nargin}); -LSpar0=LSpar; JDV=0; tol0=tol; LOCK0=~ischar(sigma); -if nargout>3, SCHUR=0; end -tau=0; if INTERIOR>=1 & LOCK0, tau=sigma(1); end -n_tar=size(sigma,1); nt=1; FIG=gcf; - -%%% Initiate global variables -Qschur = zeros(n,0); Rschur = []; -PinvQ = zeros(n,0); Pinv_u = zeros(n,1); Pu = []; -nm_operations = 0; history = []; - -%%% Return if eigenvalueproblem is trivial -if n<2 - if n==1, Qschur=1; Rschur=MV(1); end - if nargout == 0, eigenvalue=Rschur, else - [varargout{1:nargout}]=output(history,Qschur,Rschur); end, -return, end - -String = ['\r#it=%i #MV=%i dim(V)=%i |r_%i|=%6.1e ']; -StrinP = '--- Checking for conjugate pair ---\n'; -time = clock; - -%%% Initialize V, W: -%%% V,W orthonormal, A*V=W*R+Qschur*E, R upper triangular -[V,W,R,E,M]=SetInitialSpaces(V,nselect,tau,jmin,tol); -j=size(V,2); k=size(Rschur,1); -nit=0; nlit=0; SOLVED=0; - -switch INTERIOR - -case 0 - -%%% The JD loop (Standard) -%%% V orthogonal, V orthogonal to Qschur -%%% V*V=eye(j), Qschur'*V=0, -%%% W=A*V, M=V'*W -%%% -W=W*R; if tau ~=0; W=W+tau*V; end, M=M'*R; temptarget=sigma(nt,:); -while (k=nselect, break, end, r_KNOWN=0; - - - %%% Expand preconditioned Schur matrix PinvQ - SOLVED=UpdateMinv(u,SOLVED); - - if j==1, - [V,W,R,E,M]=SetInitialSpaces(zeros(n,0),nselect,tau,jmin,tol); - k=size(Rschur,1); if k>=nselect, break, end - W=W*R; if tau ~=0; W=W+tau*V; end; M=M'*R; j=size(V,2); - else, - J=[2:j]; j=j-1; UR=UR(:,J); - M=S(J,J); V=V*UR; W=W*UR; - end - - if PAIRS & abs(imag(theta))>tol, v=imag(u/sign(max(u))); - if norm(v)>tol, v=RepGS(Qschur,v,0); EXPAND=(norm(v)>sqrt(tol)); end - end - - if EXPAND, temptarget=conj(theta); if SHOW, fprintf(StrinP), end - else, nlit=0; nt=min(nt+1,n_tar); temptarget=sigma(nt,:); end - - end % nr=jmax - j=jmin; J=[1:j]; UR=UR(:,J); - M=S(J,J); V=V*UR; W=W*UR; - end % if j>=jmax - - if r_KNOWN - %%% Solve correction equation - v=Solve_pce(theta,u,r,lsolver,LSpar,nlit); SOLVED=1; - nlit=nlit+1; nit=nit+1; r_KNOWN=0; EXPAND=1; - end % if r_KNOWN - - if EXPAND - %%% Expand the subspaces of the interaction matrix - v=RepGS([Qschur,V],v); - if size(v,2)>0 - w=MV(v); - M=[M,V'*w;v'*W,v'*w]; - V=[V,v]; W=[W,w]; j=j+1; EXPAND=0; tol=tol0; - else - tol=2*tol; - end - end % if EXPAND - -end % while (nit=jmax,jmin); - y=UR(:,1); theta=T(1,1)'*S(1,1); - u=V*y; w=W*(R*y); r=w-theta*u; nr=norm(r); r_KNOWN=1; - if nr=nselect, break, end, r_KNOWN=0; JDV=0; - - %%% Expand preconditioned Schur matrix PinvQ - SOLVED=UpdateMinv(u,SOLVED); - - if j==1, - [V,W,R,E,M]=... - SetInitialSpaces(zeros(n,0),nselect,tau,jmin,tol); - k=size(Rschur,1); if k>=nselect, break, end, j=size(V,2); - else - J=[2:j]; j=j-1; UR=UR(:,J); UL=UL(:,J); - R=S(J,J); M=T(J,J); V=V*UR; W=W*UL; - [r,a]=RepGS(u,r,0); E=[E*UR;(T(1,1)'-a/S(1,1))*S(1,J)]; - - s=(S(1,J)/S(1,1))/R; W=W+r*s; M=M+s'*(r'*V); - if (nr*norm(s))^2>eps, [W,R0]=qr(W,0); R=R0*R; M=R0'\M; end - - end - - if PAIRS & abs(imag(theta))>tol, v=imag(u/sign(max(u))); - if norm(v)>tol, v=RepGS(Qschur,v,0); EXPAND=(norm(v)>sqrt(tol)); end - end - - if EXPAND, if SHOW, fprintf(StrinP), end - temptarget=[conj(theta)-tau;0]; - else, nlit=0; temptarget=0; - if nt=jmax - j=jmin; J=[1:j]; UR=UR(:,J); UL=UL(:,J); - R=S(J,J); M=T(J,J); V=V*UR; W=W*UL; E=E*UR; - end % if j>=jmax - - if r_KNOWN - %%% Solve correction equation - if JDV, disp('Stagnation'), - LSpar(end-1)=(LSpar(end-1)+15)*2; - % lsolver='bicgstab'; LSpar=[1.e-2,300,4]; - else - LSpar=LSpar0; JDV=0; lsolver=lsolver0; - end - if nr>0.001 & FIXT, theta=tau; else, FIXT=0; end - v=Solve_pce(theta,u,r,lsolver,LSpar,nlit); - nlit=nlit+1; nit=nit+1; r_KNOWN=0; EXPAND=1; SOLVED=1; JDV=0; - end - - if EXPAND - %%% Expand the subspaces of the interaction matrix - [v,zeta]=RepGS([Qschur,V],v); - if JDV0 & abs(zeta(end,1))/norm(zeta)<0.06, JDV=JDV+1; end - if size(v,2)>0 - w=MV(v); if tau ~=0, w=w-tau*v; end - [w,e]=RepGS(Qschur,w,0); [w,y]=RepGS(W,w); - R=[[R;zeros(1,j)],y]; M=[M,W'*v;w'*V,w'*v]; E=[E,e]; - V=[V,v]; W=[W,w]; j=j+1; EXPAND=0; tol=tol0; - else - tol=2*tol; - end - end - -end % while (nit=jmax,jmin); - y=UR(:,1); u=V*y; w=AV*y; theta=u'*w; - r=w-theta*u; [r,y]=RepGS(Qschur,r,0); nr=norm(r); r_KNOWN=1; - if nr=nselect, break, end, r_KNOWN=0; - - %%% Expand preconditioned Schur matrix PinvQ - SOLVED=UpdateMinv(u,SOLVED); - - if j==1 - [V,W,R,E,M]=SetInitialSpaces(zeros(n,0),nselect,tau,jmin,tol); - k=size(Rschur,1); if k>=nselect, break, end - AV=W*R; j=size(V,2); - else - J=[2:j]; j=j-1; UR=UR(:,J); UL=UL(:,J); - AV=AV*UR; R=S(J,J); M=T(J,J); V=V*UR; W=W*UL; - end - - if PAIRS & abs(imag(theta))>tol, v=imag(u/sign(max(u))); - if norm(v)>tol, v=RepGS(Qschur,v,0); EXPAND=(norm(v)>sqrt(tol)); end - end - - if EXPAND,if SHOW, fprintf(StrinP), end - temptarget=[conj(theta)-tau;0]; - else, nlit=0; temptarget=0; - if nt=jmax - j=jmin; J=[1:j]; UR=UR(:,J); UL=UL(:,J); - AV=AV*UR; R=S(J,J); M=T(J,J); V=V*UR; W=W*UL; - end % if j>=jmax - - if r_KNOWN - %%% Solve correction equation - v=Solve_pce(theta,u,r,lsolver,LSpar,nlit); SOLVED=1; - nlit=nlit+1; nit=nit+1; r_KNOWN=0; EXPAND=1; - end - - if EXPAND - %%% Expand the subspaces of the interaction matrix - v=RepGS([Qschur,V],v); - if size(v,2)>0 - w=MV(v); if tau ~=0, w=w-tau*v;end - AV=[AV,w]; R=[R,W'*w]; - w=RepGS([Qschur,W],w); - R=[R;w'*AV]; M=[M,W'*v;w'*V,w'*v]; - V=[V,v]; W=[W,w]; j=j+1; EXPAND=0; tol=tol0; - else - tol=2*tol; - end - end - -end % while (nit=nselect, break, end, r_KNOWN=0; - - %%% Expand preconditioned Schur matrix PinvQ - SOLVED=UpdateMinv(u,SOLVED); - - if j==1 - [V,W,R,E,M]=SetInitialSpaces(zeros(n,0),nselect,tau,jmin,tol); - k=size(Rschur,1); if k>=nselect, break, end - V=V/R; j=size(V,2); M=M/R; E=E/R; - else - J=[2:j]; j=j-1; UR=UR(:,J); M=S(J,J); - V=V*UR; W=W*UR; [r,a]=RepGS(u,r,0); - s=u'*V; V=V-u*s; W=W-r*s; M=M-s'*(r'*V)-(W'*u)*s; - E=[E*UR-y*s;(tau-theta-a)*s]; - - if (nr*norm(s))^2>eps, [W,R]=qr(W,0); V=V/R; M=(R'\M)/R; E=E/R; end - - end - - if PAIRS & abs(imag(theta))>tol, v=imag(u/sign(max(u))); - if norm(v)>tol, v=RepGS(Qschur,v,0); EXPAND=(norm(v)>sqrt(tol)); end - end - - if EXPAND, if SHOW, fprintf(StrinP), end - temptarget=[1/(conj(theta)-tau);inf]; - else, nlit=0; temptarget='LM'; - if nt=jmax - j=jmin; J=[1:j]; UR=UR(:,J); - M=S(J,J); V=V*UR; W=W*UR; E=E*UR; - end % if j>=jmax - - if r_KNOWN - %%% Solve correction equation - v=Solve_pce(theta,u,r,lsolver,LSpar,nlit); SOLVED=1; - nlit=nlit+1; nit=nit+1; r_KNOWN=0; EXPAND=1; - end - - if EXPAND - %%% Expand the subspaces of the interaction matrix - v=RepGS(Qschur,v,0); - if size(v,2)>0 - w=MV(v); if tau ~=0, w=w-tau*v; end - [w,e]=RepGS(Qschur,w,0); [w,y]=RepGS(W,w); - nrw=y(j+1,1); y=y(1:j,:); - v=v-V*y; v=v/nrw; e=e-E*y; e=e/nrw; - M=[M,W'*v;w'*V,w'*v]; - V=[V,v]; W=[W,w]; j=j+1; E=[E,e]; - - if 1/cond(M)<10*tol - [V,W,R,E,M]=SetInitialSpaces(V,nselect,tau,jmin,tol,W,E); - k=size(Rschur,1); if k>=nselect, break, end - V=V/R; M=M/R; j=size(V,2);temptarget='LM'; E=E/R; - end - - EXPAND=0; tol=tol0; - else - tol=2*tol; - end - end - -end % while (nit0, [z,Lambda]=Jordan(Rschur); X=Qschur*z; end - -%-------------- display results ---------------------------- -if SHOW == 2, MovieTheta, figure(FIG), end -if SHOW & size(history,1)>0 - - switch INTERIOR - case 0 - testspace='V, V orthonormal'; - case 1 - testspace='A*V-sigma*V, V and W orthonormal'; - case 1.1 - testspace='A*V-sigma*V, V and W orthonormal, AV'; - case 1.2 - testspace='A*V-sigma*V, W orthogonal'; - otherwise - testspace='Experimental'; - end - - StringT=sprintf('The test subspace W is computed as W = %s.',testspace); - StringX=sprintf('JDQZ with jmin=%g, jmax=%g, residual tolerance %g.',... - jmin,jmax,tol); - StringY=sprintf('Correction equation solved with %s.',lsolver); - date=fix(clock); - String=sprintf('\n%2i-%2i-%2i, %2i:%2i:%2i',date(3:-1:1),date(4:6)); - - StringL='log_{10} || r_{#it} ||_2'; - for pl=1:SHOW - subplot(SHOW,1,pl), t=history(:,pl+1); - plot(t,log10(history(:,1)),'*-',t,log10(tol)+0*t,':') - legend(StringL), title(StringT) - StringL='log_{10} || r_{#MV} ||_2'; StringT=StringX; - end - if SHOW==2, xlabel([StringY,String]) - else, xlabel([StringX,String]), ylabel(StringY), end - drawnow -end - -if SHOW - str1=num2str(abs(k-nselect)); str='s'; - if k>nselect, - if k==nselect+1, str1='one'; str=''; end - fprintf('\n\nDetected %s additional eigenpair%s.',str1,str) - end - if k0, ShowLambda(diag(Rschur)); else, fprintf('\n'); end - - Str='time_needed'; DispResult(Str,eval(Str)) - if (k>0) - if ~SCHUR - Str='norm(MV(X)-X*Lambda)'; DispResult(Str,eval(Str)) - end - Str='norm(MV(Qschur)-Qschur*Rschur)'; DispResult(Str,eval(Str)) - I=eye(k); Str='norm(Qschur''*Qschur-I)'; DispResult(Str,eval(Str)) - end - fprintf('\n\n') - -end - -if nargout == 0, if ~SHOW, eigenvalues=diag(Rschur), end, return, end -[varargout{1:nargout}]=output(history,X,Lambda); - -return - -%=========================================================================== -%======= PREPROCESSING ===================================================== -%=========================================================================== - -%======= INITIALIZE SUBSPACE =============================================== -function [V,W,R,E,M]=SetInitialSpaces(V,nselect,tau,jmin,tol,W,E); -%[V,W,R,E,M]=SetInitialSpaces(VV,nselect,tau,jmin,tol); -% Output: V(:,1:SIZE(VV,2))=ORTH(VV), -% V'*V=W'*W=EYE(JMIN), M=W'*V; -% such that A*V-tau*V=W*R+Qschur*E, -% with R upper triangular, and E=Qschur'*(A*V-tau*V). -% -%[V,W,R,E,M]=SetInitialSpaces(VV,nselect,tau,jmin,tol,AV,EE); -% Input such that -% A*VV-tau*VV=AV+Qschur*EE, EE=Qschur'*(A*VV-tau*VV); -% -% Output: V(:,1:SIZE(VV,2))=ORTH(VV), -% V'*V=W'*W=EYE(JMIN), M=W'*V; -% such that A*V-tau*V=W*R+Qschur*E, -% with R upper triangular, and E=Qschur'*(A*V-tau*V). - -global Qschur Rschur - -[n,j]=size(V); k=size(Qschur,2); - -if j>1, - [V,R]=qr(V,0); - if nargin <6, - W=MV(V); R=eye(j); if tau~=0, W=W-tau*V; end - if k>0, E=Qschur'*W; W=W-Qschur*E; else, E=zeros(0,j); end - end - [V,W,R,E,M]=CheckForNullSpace(V,nselect,tau,tol,W,E,R); - l=size(Qschur,2); j=size(V,2); - if l>=nselect, if size(V,2)==0; R=1; M=1; return, end, end - if l>k, UpdateMinv(Qschur(:,k+1:l),0); end, k=l; -end -if j==0, nr=0; - while nr==0 - V = ones(n,1)+0.1*rand(n,1); V=RepGS(Qschur,V); nr=norm(V); - end, j=1; -end -if j==1 - [V,H,E]=Arnoldi(V,tau,jmin,nselect,tol); - l=size(Qschur,2); j=max(size(H,2),1); - if l>=nselect, W=V; R=eye(j); M=R; return, end - if l>k, UpdateMinv(Qschur(:,k+1:l),0); end - [Q,R]=qr(full(H),0); - W=V*Q; V(:,j+1)=[]; M=Q(1:j,:)'; - %% W=V*Q; V=V(:,1:j)/R; E=E/R; R=eye(j); M=Q(1:j,:)'/R; - %% W=V*H; V(:,j+1)=[];R=R'*R; M=H(1:j,:)'; -end - -return -%%%======== ARNOLDI (for initializing spaces) =============================== -function [V,H,E]=Arnoldi(v,tau,jmin,nselect,tol) -% -%[V,AV,H,nMV,tau]=ARNOLDI(A,V0,TAU,JMIN,NSELECT,TOL) -% ARNOLDI computes the Arnoldi factorization of dimenison JMIN+1: -% (A-tau)*V(:,1:JMIN)=V*H where V is n by JMIN+1 orthonormal with -% first column a multiple of V0, and H is JMIN+1 by JMIN Hessenberg. -% -% If an eigenvalue if H(1:j,1:j) is an eigenvalue of A -% within the required tolerance TOL then the Schurform -% A*Qschur=Qschur*Rschur is expanded and the Arnoldi factorization -% (A-tau)*V(:,1:j)=V(:,1:j+1)*H(1:j+1,1:j) is deflated. -% Returns if size(Qschur,2) = NSELECT or size(V,2) = JMIN+1 - -% (A-tau)*V(:,1:JMIN)=V*H+Qschur*E, Qschur'*V=0 - -% Coded November 5, 1998, G. Sleijpen - -global Qschur Rschur - -k=size(Qschur,2); [n,j]=size(v); - -if ischar(tau), tau=0; end - -H=zeros(1,0); V=zeros(n,0); E=[]; -j=0; nr=norm(v); - -while j=tol - v=v/nr; V=[V,v]; j=j+1; - Av=MV(v); - end - if j==0 - H=zeros(1,0); j=1; - nr=0; while nr==0, v=RepGS(Qschur,rand(n,1)); nr=norm(v); end - v=v/nr; V=v; Av=MV(v); - end - if tau~=0; Av=Av-tau*v; end, [v,e] = RepGS(Qschur,Av,0); - if k==0, E=zeros(0,j); else, E = [E,e(1:k,1)]; end - [v,y] = RepGS(V,v,0); H = [H,y(1:j,1)]; - nr = norm(v); H = [H;zeros(1,j-1),nr]; - [Q,U,H1] = DeflateHess(full(H),tol); - j=size(U,2); l=size(Q,2); - if l>0 %--- expand Schur form ------ - Qschur=[Qschur,V*Q]; - Rschur=[Rschur,E*Q; zeros(l,k),H1(1:l,1:l)+tau*eye(l)]; k=k+l; - E=[E*U;H1(1:l,l+1:l+j)]; - if j>0, V=V*U; H=H1(l+1:l+j+1,l+1:l+j); - else, V=zeros(n,0); H=zeros(1,0); end - end -end % while - -if nr>=tol - v=v/nr; V=[V,v]; -end - -return -%---------------------------------------------------------------------- -function [Q,U,H]=DeflateHess(H,tol) -% H_in*[Q,U]=[Q,U]*H_out such that H_out(K,K) upper triangular -% where K=1:SIZE(Q,2) and ABS(Q(end,2)*H_in(j+1,j))=nselect, return, end - - CHECK=1; l=k; - - [S,T,Z,Q]=qz(R,M); Z=Z'; - while CHECK - I=SortEigPairVar(S,T,2); [Q,Z,S,T]=SwapQZ(Q,Z,S,T,I(1)); - s=abs(S(1,1)); t=min(abs(T(1,1)),1); CHECK=(s*sqrt(1-t*t)=tol, - W=W+r*s; M=M+s'*(r'*V); - if nrs^2>eps, [W,R0]=qr(W,0); R=R0*R; M=R0'\M; end - end - - S=R; T=M; - - CHECK=(k0); - end - end - -return - - -%=========================================================================== -%======= POSTPROCESSING ==================================================== -%=========================================================================== -function Refine(V,gamma); - -if gamma==0, return, end - -global Qschur Rschur - - J=1:size(Rschur,1); - - if gamma==1, - [V,R]=qr(V(:,J),0); W=MV(V); M=V'*W; - [U,Rschur]=schur(M); - [U,Rschur]=rsf2csf(U,Rschur); Qschur=V*U; - return - elseif gamma==2 - [V,R]=qr(V,0); W=MV(V); M=V'*W; - [U,S]=schur(M); [U,S]=rsf2csf(U,S); - R=R*U; F=R'*R-S'*S; - [X,Lambda]=Jordan(S); - % Xinv=inv(X); D=sqrt(diag(Xinv*Xinv')); X=X*diag(D); - [d,I]=sort(abs(diag(X'*F*X))); - [U,S]=SwapSchur(U,S,I(J)); - Qschur=V*U(:,J); Rschur=S(J,J); - end - -return - -%=========================================================================== -function CheckSortSchur(sigma) -global Qschur Rschur - -k=size(Rschur,1); if k==0, return, end - -I=SortEig(diag(Rschur),sigma); - -if ~min((1:k)'==I) - [U,Rschur]=SwapSchur(eye(k),Rschur,I); - Qschur=Qschur*U; -end - -return - -%%%=========== COMPUTE SORTED JORDAN FORM ================================== -function [X,Jordan]=Jordan(S) -% [X,J]=JORDAN(S) -% For S k by k upper triangular matrix with ordered diagonal elements, -% JORDAN computes the Jordan decomposition. -% X is a k by k matrix of vectors spanning invariant spaces. -% If J(i,i)=J(i+1,i+1) then X(:,i)'*X(:,i+1)=0. -% J is a k by k matrix, J is Jordan such that S*X=X*J. -% diag(J)=diag(S) are the eigenvalues - -% coded by Gerard Sleijpen, Januari 14, 1998 - -k=size(S,1); X=zeros(k); -if k==0, Jordan=[]; return, end - -%%% accepted separation between eigenvalues: -delta=2*sqrt(eps)*norm(S,inf); delta=max(delta,10*eps); - -T=eye(k); s=diag(S); Jordan=diag(s); -for i=1:k - I=[1:i]; e=zeros(i,1); e(i,1)=1; - C=S(I,I)-s(i,1)*T(I,I); C(i,i)=1; - j=i-1; q=[]; jj=0; - while j>0 - if abs(C(j,j)) 2, varargout{nargout}=history; end -if nargout > 3, varargout{3} = Qschur; varargout{4} = Rschur; end -if nargout < 4 & size(X,2)<2 - varargout{1}=Qschur; varargout{2}=Rschur; return -else - varargout{1}=X; varargout{2}=Lambda; -end - -return - -%=========================================================================== -%===== UPDATE PRECONDITIONED SCHUR VECTORS ================================= -%=========================================================================== -function solved=UpdateMinv(u,solved) - -global Qschur PinvQ Pinv_u Pu L_precond - - if ~isempty(L_precond) - if ~solved, Pinv_u=SolvePrecond(u); end - Pu=[[Pu;u'*PinvQ],Qschur'*Pinv_u]; - PinvQ=[PinvQ,Pinv_u]; - solved=0; - end - -return -%=========================================================================== -%===== SOLVE CORRECTION EQUATION =========================================== -%=========================================================================== -function t=Solve_pce(theta,u,r,lsolver,par,nit) - -global Qschur PinvQ Pinv_u Pu L_precond - - switch lsolver - case 'exact' - t = exact(theta,[Qschur,u],r); - - case 'iluexact' - t = iluexact(theta,[Qschur,u],r); - - case {'gmres','bicgstab','olsen'} - if isempty(L_precond) %%% no preconditioning - - t = feval(lsolver,theta,... - [Qschur,u],[Qschur,u],1,r,spar(par,nit)); - - else %%% solve left preconditioned system - - %%% compute vectors and matrices for skew projection - Pinv_u=SolvePrecond(u); - mu=[Pu,Qschur'*Pinv_u;u'*PinvQ,u'*Pinv_u]; - - %%% precondion and project r - r=SolvePrecond(r); - r=SkewProj([Qschur,u],[PinvQ,Pinv_u],mu,r); - - %%% solve preconditioned system - t = feval(lsolver,theta,... - [Qschur,u],[PinvQ,Pinv_u],mu,r,spar(par,nit)); - end - - case {'cg','minres','symmlq'} - if isempty(L_precond) %%% no preconditioning - - t = feval(lsolver,theta,... - [Qschur,u],[Qschur,u],1,r,spar(par,nit)); - - else %%% solve two-sided expl. precond. system - - %%% compute vectors and matrices for skew projection - Pinv_u=SolvePrecond(u,'L'); - mu=[Pu,Qschur'*Pinv_u;u'*PinvQ,u'*Pinv_u]; - - %%% precondion and project r - r=SolvePrecond(r,'L'); - r=SkewProj([Qschur,u],[PinvQ,Pinv_u],mu,r); - - %%% solve preconditioned system - t = feval(lsolver,theta,... - [Qschur,u],[PinvQ,Pinv_u],mu,r,spar(par,nit)); - - %%% "unprecondition" solution - t=SkewProj([PinvQ,Pinv_u],[Qschur,u],mu,t); - t=SolvePrecond(t,'U'); - end - - end - -return -%======================================================================= -%======= LINEAR SOLVERS ================================================ -%======================================================================= -function x = exact(theta,Q,r) - -global A_operator - - [n,k]=size(Q); [n,l]=size(r); - - if ischar(A_operator) - [x,xtol]=bicgstab(theta,Q,Q,1,r,[5.0e-14/norm(r),200,4]); - return - end - - x = [A_operator-theta*speye(n,n),Q;Q',zeros(k,k)]\[r;zeros(k,l)]; - x = x(1:n,1:l); - -return -%---------------------------------------------------------------------- -function x = iluexact(theta,Q,r) - -global L_precond U_precond - - [n,k]=size(Q); [n,l]=size(r); - - y = L_precond\[r,Q]; - x = [U_precond,y(:,l+1:k+1);Q',zeros(k,k)]\[y(:,1:l);zeros(k,l)]; - x = x(1:n,1:l); - -return -%---------------------------------------------------------------------- -function r = olsen(theta,Q,Z,M,r,par) -return -% -%======= Iterative methods ============================================= -% -function x = bicgstab(theta,Q,Z,M,r,par) -% BiCGstab(ell) -% [x,rnrm] = bicgstab(theta,Q,Z,M,r,par) -% Computes iteratively an approximation to the solution -% of the linear system Q'*x = 0 and Atilde*x=r -% where Atilde=(I-Z*M^(-1)*Q')*(U\L\(A-theta)). -% -% This function is specialized for use in JDQZ. -% integer nmv: number of matrix multiplications -% rnrm: relative residual norm -% -% par=[tol,mxmv,ell] where -% integer m: max number of iteration steps -% real tol: residual reduction -% -% nmv: number of MV with Atilde -% rnrm: obtained residual reduction -% -% -- References: ETNA - -% Gerard Sleijpen (sleijpen@math.uu.nl) -% Copyright (c) 1998, Gerard Sleijpen - -% -- Initialization -- -% - -tol=par(1); max_it=par(2); l=par(3); n=size(r,1); -rnrm=1; nmv=0; - -if max_it==0 | tol>=1, x=r; return, end - -rnrm=norm(r); snrm=rnrm; tol=tol*rnrm; - -sigma=1; omega=1; -x=zeros(n,1); u=zeros(n,1); tr=r; -% hist=rnrm; -% -- Iteration loop -while (rnrm > tol) & (nmv <= max_it) - - sigma=-omega*sigma; - for j = 1:l, - rho=tr'*r(:,j); bet=rho/sigma; - u=r-bet*u; - %%%%%% u(:,j+1)=Atilde*u(:,j) - u(:,j+1)=mvp(theta,Q,Z,M,u(:,j)); - sigma=tr'*u(:,j+1); alp=rho/sigma; - x=x+alp*u(:,1); - r=r-alp*u(:,2:j+1); - %%%%%% r(:,j+1)=Atilde*r(:,j) - r(:,j+1)=mvp(theta,Q,Z,M,r(:,j)); - end - - gamma=r(:,2:l+1)\r(:,1); omega=gamma(l,1); - x=x+r*[gamma;0]; u=u*[1;-gamma]; r=r*[1;-gamma]; - - rnrm = norm(r); nmv = nmv+2*l; - % hist=[hist,rnrm]; -end - % figure(3), - % plot([0:length(hist)-1]*2*l,log10(hist/snrm),'-*'), - % drawnow, - -rnrm = rnrm/snrm; - -return -%---------------------------------------------------------------------- -function v = gmres(theta,Q,Z,M,v,par) -% GMRES -% [x,rnrm] = gmres(theta,Q,Z,M,b,par) -% Computes iteratively an approximation to the solution -% of the linear system Q'*x = 0 and Atilde*x=b -% where Atilde=(I-Z*M^(-1)*Q')*(U\L\(A-theta)). -% -% par=[tol,m] where -% integer m: degree of the minimal residual polynomial -% real tol: residual reduction -% -% nmv: number of MV with Atilde -% rnrm: obtained residual reduction -% -% -- References: Saad - -% Gerard Sleijpen (sleijpen@math.uu.nl) -% Copyright (c) 1998, Gerard Sleijpen - -% -- Initialization - -tol=par(1); n = size(v,1); max_it=min(par(2),n); -rnrm = 1; nmv=0; - -if max_it==0 | tol>=1, return, end - -H = zeros(max_it +1,max_it); Rot=[ones(1,max_it);zeros(1,max_it)]; - -rnrm = norm(v); v = v/rnrm; V = [v]; -tol = tol * rnrm; snrm = rnrm; -y = [ rnrm ; zeros(max_it,1) ]; -j=0; % hist=rnrm; -while (nmv < max_it) & (rnrm > tol), - j=j+1; nmv=nmv+1; - v=mvp(theta,Q,Z,M,v); - % [v, H(1:j+1,j)] = RepGS(V,v); - [v,h] = RepGS(V,v); H(1:size(h,1),j)=h; - V = [V, v]; - for i = 1:j-1, - a = Rot(:,i); - H(i:i+1,j) = [a'; -a(2) a(1)]*H(i:i+1,j); - end - J=[j, j+1]; - a=H(J,j); - if a(2) ~= 0 - cs = norm(a); - a = a/cs; Rot(:,j) = a; - H(J,j) = [cs; 0]; - y(J) = [a'; -a(2) a(1)]*y(J); - end - rnrm = abs(y(j+1)); - % hist=[hist,rnrm]; -end - % figure(3) - % plot([0:length(hist)-1],log10(hist/snrm),'-*') - % drawnow, pause - -J=[1:j]; -v = V(:,J)*(H(J,J)\y(J)); -rnrm = rnrm/snrm; - -return -%====================================================================== -%========== BASIC OPERATIONS ========================================== -%====================================================================== -function v=MV(v) - -global A_operator nm_operations - -if ischar(A_operator) - v = feval(A_operator,v); -else - v = A_operator*v; -end - -nm_operations = nm_operations+1; - -return -%---------------------------------------------------------------------- -function v=mvp(theta,Q,Z,M,v) -% v=Atilde*v - - v = MV(v) - theta*v; - v = SolvePrecond(v); - v = SkewProj(Q,Z,M,v); - -return -%---------------------------------------------------------------------- -function u=SolvePrecond(u,flag); - -global L_precond U_precond - -if isempty(L_precond), return, end - -if nargin<2 - - if ischar(L_precond) - if ischar(U_precond) - u=feval(L_precond,u,U_precond); - elseif isempty(U_precond) - u=feval(L_precond,u); - else - u=feval(L_precond,u,'L'); u=feval(L_precond,u,'U'); - end - else - u=U_precond\(L_precond\u); - end - -else - - switch flag - case 'U' - if ischar(L_precond), u=feval(L_precond,u,'U'); else, u=U_precond\u; end - - case 'L' - if ischar(L_precond), u=feval(L_precond,u,'L'); else, u=L_precond\u; end - - end -end - -return -%---------------------------------------------------------------------- -function r=SkewProj(Q,Z,M,r); - - if ~isempty(Q), - r=r-Z*(M\(Q'*r)); - end - -return -%---------------------------------------------------------------------- -function ppar=spar(par,nit) -% Changes par=[tol(:),max_it,ell] to -% ppap=[TOL,max_it,ell] where -% if lenght(tol)==1 -% TOL=tol -% else -% red=tol(end)/told(end-1); tole=tol(end); -% tol=[tol,red*tole,red^2*tole,red^3*tole,...] -% TOL=tol(nit); -% end - -k=size(par,2)-2; -ppar=par(1,k:k+2); - -if k>1 - if nit>k - ppar(1,1)=par(1,k)*((par(1,k)/par(1,k-1))^(nit-k)); - else - ppar(1,1)=par(1,max(nit,1)); - end -end - -ppar(1,1)=max(ppar(1,1),1.0e-8); - -return -% -%======= Iterative methods for symmetric systems ======================= -% -function x = cg(theta,Q,Z,M,r,par) -% CG -% [x,rnrm] = cg(theta,Q,Z,M,b,par) -% Computes iteratively an approximation to the solution -% of the linear system Q'*x = 0 and Atilde*x=b -% where Atilde=(I-Z*M^(-1)*Q')*(U\L\(A-theta)). -% -% par=[tol,m] where -% integer m: degree of the minimal residual polynomial -% real tol: residual reduction -% -% nmv: number of MV with Atilde -% rnrm: obtained residual reduction -% -% -- References: Hestenes and Stiefel - -% Gerard Sleijpen (sleijpen@math.uu.nl) -% Copyright (c) 1998, Gerard Sleijpen - -% -- Initialization - - -tol=par(1); max_it=par(2); n = size(r,1); -rnrm = 1; nmv=0; - - b=r; - -if max_it ==0 | tol>=1, x=r; return, end - -x= zeros(n,1); u=zeros(n,1); - -rho = norm(r); snrm = rho; rho = rho*rho; -tol = tol*tol*rho; -sigma=1; - -while ( rho > tol & nmv < max_it ) - - beta=rho/sigma; - u=r-beta*u; - y=smvp(theta,Q,Z,M,u); nmv=nmv+1; - sigma=y'*r; alpha=rho/sigma; - x=x+alpha*u; - r=r-alpha*y; sigma=-rho; rho=r'*r; - -end % while - -rnrm=sqrt(rho)/snrm; - -return -%---------------------------------------------------------------------- -function x = minres(theta,Q,Z,M,r,par) -% MINRES -% [x,rnrm] = minres(theta,Q,Z,M,b,par) -% Computes iteratively an approximation to the solution -% of the linear system Q'*x = 0 and Atilde*x=b -% where Atilde=(I-Z*M^(-1)*Q')*(U\L\(A-theta)). -% -% par=[tol,m] where -% integer m: degree of the minimal residual polynomial -% real tol: residual reduction -% -% nmv: number of MV with Atilde -% rnrm: obtained residual reduction -% -% -- References: Paige and Saunders - -% Gerard Sleijpen (sleijpen@math.uu.nl) -% Copyright (c) 1998, Gerard Sleijpen - -% -- Initialization - - -tol=par(1); max_it=par(2); n = size(r,1); -rnrm = 1; nmv=0; - -if max_it ==0 | tol>=1, x=r; return, end - -x=zeros(n,1); rho = norm(r); v = r/rho; snrm=rho; -beta = 0; v_old = zeros(n,1); -beta_t = 0; c = -1; s = 0; -w = zeros(n,1); www = v; - -tol=tol*rho; - -while ( nmv < max_it & abs(rho) > tol ) - - wv =smvp(theta,Q,Z,M,v)-beta*v_old; nmv=nmv+1; - alpha = v'*wv; wv = wv-alpha*v; - beta = norm(wv); v_old = v; v = wv/beta; - - l1 = s*alpha - c*beta_t; l2 = s*beta; - - alpha_t = -s*beta_t - c*alpha; beta_t = c*beta; - l0 = sqrt(alpha_t*alpha_t+beta*beta); - c = alpha_t/l0; s = beta/l0; - - ww = www - l1*w; www = v - l2*w; w = ww/l0; - - x = x + (rho*c)*w; rho = s*rho; - -end % while - -rnrm=abs(rho)/snrm; - -return - -%---------------------------------------------------------------------- -function x = symmlq(theta,Q,Z,M,r,par) -% SYMMLQ -% [x,rnrm] = symmlq(theta,Q,Z,M,b,par) -% Computes iteratively an approximation to the solution -% of the linear system Q'*x = 0 and Atilde*x=b -% where Atilde=(I-Z*M^(-1)*Q')*(U\L\(A-theta)). -% -% par=[tol,m] where -% integer m: degree of the minimal residual polynomial -% real tol: residual reduction -% -% nmv: number of MV with Atilde -% rnrm: obtained residual reduction -% -% -- References: Paige and Saunders - -% Gerard Sleijpen (sleijpen@math.uu.nl) -% Copyright (c) 1998, Gerard Sleijpen - -% -- Initialization - - -tol=par(1); max_it=par(2); n = size(r,1); -rnrm = 1; nmv=0; - -if max_it ==0 | tol>=1, x=r; return, end - -x=zeros(n,1); rho = norm(r); v = r/rho; snrm=rho; -beta = 0; beta_t = 0; c = -1; s = 0; -v_old = zeros(n,1); w = v; gtt = rho; g = 0; - -tol=tol*rho; - -while ( nmv < max_it & rho > tol ) - - wv = smvp(theta,Q,Z,M,v) - beta*v_old; nmv=nmv+1; - alpha = v'*wv; wv = wv - alpha*v; - beta = norm(wv); v_old = v; v = wv/beta; - - l1 = s*alpha - c*beta_t; l2 = s*beta; - - alpha_t = -s*beta_t - c*alpha; beta_t = c*beta; - l0 = sqrt(alpha_t*alpha_t+beta*beta); - c = alpha_t/l0; s = beta/l0; - - gt = gtt - l1*g; gtt = -l2*g; g = gt/l0; - - rho = sqrt(gt*gt+gtt*gtt); - - x = x + (g*c)*w + (g*s)*v; - w = s*w - c*v; - -end % while - -rnrm=rho/snrm; - -return - -%---------------------------------------------------------------------- -function v=smvp(theta,Q,Z,M,v) -% v=Atilde*v - - v = SkewProj(Z,Q,M,v); - v = SolvePrecond(v,'U'); - v = MV(v) - theta*v; - v = SolvePrecond(v,'L'); - v = SkewProj(Q,Z,M,v); - -return -%======================================================================= -%========== Orthogonalisation ========================================== -%======================================================================= -function [v,y]=RepGS(V,v,gamma) -% [v,y]=REP_GS(V,w) -% If V orthonormal then [V,v] orthonormal and w=[V,v]*y; -% If size(V,2)=size(V,1) then w=V*y; -% -% The orthonormalisation uses repeated Gram-Schmidt -% with the Daniel-Gragg-Kaufman-Stewart (DGKS) criterion. -% -% [v,y]=REP_GS(V,w,GAMMA) -% GAMMA=1 (default) same as [v,y]=REP_GS(V,w) -% GAMMA=0, V'*v=zeros(size(V,2)) and w = V*y+v (v is not normalized). - - -% coded by Gerard Sleijpen, August 28, 1998 - -if nargin < 3, gamma=1; end - -[n,d]=size(V); - -if size(v,2)==0, y=zeros(d,0); return, end - -nr_o=norm(v); nr=eps*nr_o; y=zeros(d,1); -if d==0 - if gamma, v=v/nr_o; y=nr_o; else, y=zeros(0,1); end, return -end - -y=V'*v; v=v-V*y; nr_n=norm(v); ort=0; - -while (nr_n<0.5*nr_o & nr_n > nr) - s=V'*v; v=v-V*s; y=y+s; - nr_o=nr_n; nr_n=norm(v); ort=ort+1; -end - -if nr_n <= nr, if ort>2, disp(' dependence! '), end - if gamma % and size allows, expand with a random vector - if d0, [Q,S]=rsf2csf(Q,S); end - -%%%------ find order eigenvalues --------------- - I = SortEig(diag(S),sigma); - -%%%------ reorder schur form ---------------- - [Q,S] = SwapSchur(Q,S,I(1:kk)); - -return -%---------------------------------------------------------------------- -function I=SortEig(t,sigma); -%I=SortEig(T,SIGMA) sorts the indices of T. -% -% T is a vector of scalars, -% SIGMA is a string or a vector of scalars. -% I is a permutation of (1:LENGTH(T))' such that: -% if SIGMA is a vector of scalars then -% for K=1,2,...,LENGTH(T) with KK = MIN(K,SIZE(SIGMA,1)) -% ABS( T(I(K))-SIGMA(KK) ) <= ABS( T(I(J))-SIGMA(KK) ) -% SIGMA(kk)=INF: ABS( T(I(K)) ) >= ABS( T(I(J)) ) -% for all J >= K - -if ischar(sigma) - switch sigma - case 'LM' - [s,I]=sort(-abs(t)); - case 'SM' - [s,I]=sort(abs(t)); - case 'LR'; - [s,I]=sort(-real(t)); - case 'SR'; - [s,I]=sort(real(t)); - case 'BE'; - [s,I]=sort(real(t)); I=twistdim(I,1); - end -else - - [s,I]=sort(abs(t-sigma(1,1))); - ll=min(size(sigma,1),size(t,1)-1); - for j=2:ll - if sigma(j,1)==inf - [s,J]=sort(abs(t(I(j:end)))); J=flipdim(J,1); - else - [s,J]=sort(abs(t(I(j:end))-sigma(j,1))); - end - I=[I(1:j-1);I(J+j-1)]; - end - -end - -return -%---------------------------------------------------------------------- -function t=twistdim(t,k) - - d=size(t,k); J=1:d; J0=zeros(1,2*d); - J0(1,2*J)=J; J0(1,2*J-1)=flipdim(J,2); I=J0(1,J); - if k==1, t=t(I,:); else, t=t(:,I); end - -return -%---------------------------------------------------------------------- -function [Q,S]=SwapSchur(Q,S,I) -% [Q,S]=SwapSchur(QQ,SS,P) -% QQ and SS are square matrices of size K by K -% P is the first part of a permutation of (1:K)'. -% -% If M = QQ*SS*QQ' and QQ'*QQ = EYE(K), SS upper triangular -% then M*Q = Q*S with Q'*Q = EYE(K), S upper triangular -% and D(1:LENGTH(P))=DD(P) where D=diag(S), DD=diag(SS) -% -% Computations uses Givens rotations. - - kk=min(length(I),size(S,1)-1); - j=1; while (j<=kk & j==I(j)), j=j+1; end; - while j<=kk - i=I(j); - for k=i-1:-1:j - q = [S(k,k)-S(k+1,k+1),S(k,k+1)]; - if q(1) ~= 0 - q = q/norm(q); - G = [[q(2);-q(1)],q']; - J = [k,k+1]; - Q(:,J) = Q(:,J)*G; - S(:,J) = S(:,J)*G; - S(J,:) = G'*S(J,:); - end - S(k+1,k) = 0; - end - I=I+(I=0, -% scale B by a scalar G such that NORM(G*B)=1 and G*B(2)>=0, -% then D(A,B)=ABS((F*A)*RROT(G*B)) where RROT(alpha,beta)=(beta,-alpha) - - -% coded by Gerard Sleijpen, version Januari 14, 1998 - -n=sign(t); n=n+(n==0); t=abs(t./n); s=s./n; - -if ischar(sigma) - switch sigma - case {'LM','SM'} - case {'LR','SR','BE'} - s=real(s); - end - [s,I]=sort((-t./sqrt(s.*conj(s)+t.*t))); - switch sigma - case {'LM','LR'} - I=flipdim(I,1); - case {'SM','SR'} - case 'BE' - I=twistdim(I,1); - end -else - - n=sqrt(sigma.*conj(sigma)+1); ll=size(sigma,1); - tau=[ones(ll,1)./n,-sigma./n]; tau=tau.'; - - n=sqrt(s.*conj(s)+t.*t); s=[s./n,t./n]; - - [t,I]=sort(abs(s*tau(:,1))); - ll = min(ll,size(I,1)-1); - for j=2:ll - [t,J]=sort(abs(s(I(j:end),:)*tau(:,j))); - I=[I(1:j-1);I(J+j-1)]; - end - -end - -return - -%---------------------------------------------------------------------- -function [Q,Z,S,T]=SwapQZ(Q,Z,S,T,I) -% [Q,Z,S,T]=SwapQZ(QQ,ZZ,SS,TT,P) -% QQ and ZZ are K by K unitary, SS and TT are K by K uper triangular. -% P is the first part of a permutation of (1:K)'. -% -% Then Q and Z are K by K unitary, S and T are K by K upper triangular, -% such that, for A = ZZ*SS*QQ' and B = ZZ*T*QQ', we have -% A*Q = Z*S, B*Q = Z*T and LAMBDA(1:LENGTH(P))=LLAMBDA(P) where -% LAMBDA=DIAG(S)./DIAGg(T) and LLAMBDA=DIAG(SS)./DIAG(TT). -% -% Computation uses Givens rotations. -% - -% coded by Gerard Sleijpen, version October 12, 1998 - - - kk=min(length(I),size(S,1)-1); - j=1; while (j<=kk & j==I(j)), j=j+1; end - while j<=kk - i=I(j); - for k = i-1:-1:j, - %%% i>j, move ith eigenvalue to position j - J = [k,k+1]; - q = T(k+1,k+1)*S(k,J) - S(k+1,k+1)*T(k,J); - if q(1) ~= 0 - q = q/norm(q); - G = [[q(2);-q(1)],q']; - Q(:,J) = Q(:,J)*G; - S(:,J) = S(:,J)*G; T(:,J) = T(:,J)*G; - end - if abs(S(k+1,k)) 0) - if n==-1 - n=s; eval('v=feval(A_operator,zeros(n,0));','n=-1;') - if n>-1, J=[J,jj]; end - end - else - if isempty(sigma), sigma=s; - elseif ischar(sigma) & isempty(L_precond) - ok=1; eval('v=feval(sigma0,zeros(n,1));','ok=0') - if ok, L_precond=sigma0; sigma=s; end - end, J=[J,jj]; - end -end -varg(J)=[]; - -if n==-1, - msg1=sprintf(' Cannot find the dimension of ''%s''. \n',A_operator); - msg2=sprintf(' Put the dimension n in the parameter list: \n like'); - msg3=sprintf('\t\n\n\t jdqr(''%s'',n,..), \n\n',A_operator); - msg4=sprintf(' or let\n\n\t n = %s(',A_operator); - msg5=sprintf('[],''dimension'')\n\n give n.'); - msg=[msg1,msg2,msg3,msg4,msg5]; - errordlg(msg,'MATRIX') -end - -nselect=[]; -if n<2, return, end - -if length(varg) == 1 - nselect=min(n,varg); -elseif length(varg)>1 - if isempty(sigma), sigma=varg(end); varg(end)=[]; end - nselect=min(n,min(varg)); -end - -fopts = []; if ~isempty(options), fopts=fields(options); end - -if isempty(L_precond) - if strmatch('Precond',fopts) - L_precond = options.Precond; - elseif strmatch('L_Precond',fopts) - L_precond = options.L_Precond; - end -end - -if isempty(U_precond) & strmatch('U_Precond',fopts) - U_precond = options.U_Precond; -end - -if isempty(L_precond), ls_tol = [0.7,0.49]; end -if ~isempty(L_precond) & ischar(L_precond) - if exist(L_precond) ~=2 - msg=sprintf(' Can not find the M-file ''%s.m'' ',L_precond); n=-1; - elseif ~isempty(U_precond) & ~ischar(U_precond) & n>0 - msg=sprintf(' L and U should both be strings or matrices'); n=-1; - elseif strcmp(L_precond,U_precond) - eval('v=feval(L_precond,zeros(n,1),''L'');','n=-1;') - eval('v=feval(L_precond,zeros(n,1),''U'');','n=-1;') - if n<0 - msg='L and U use the same M-file'; - msg1=sprintf(' %s.m \n',L_precond); - msg2='Therefore L and U are called'; - msg3=sprintf(' as\n\n\tw=%s(v,''L'')',L_precond); - msg4=sprintf(' \n\tw=%s(v,''U'')\n\n',L_precond); - msg5=sprintf('Check the dimensions and/or\n'); - msg6=sprintf('put this "switch" in %s.m.',L_precond); - msg=[msg,msg1,msg2,msg3,msg4,msg5,msg6]; - else - U_precond=0; - end - elseif ischar(A_operator) & strcmp(A_operator,L_precond) - U_precond='preconditioner'; - eval('v=feval(L_precond,zeros(n,1),U_precond);','n=-1;') - if n<0 - msg='Preconditioner and matrix use the same M-file'; - msg1=sprintf(' %s. \n',L_precond); - msg2='Therefore the preconditioner is called'; - msg3=sprintf(' as\n\n\tw=%s(v,''preconditioner'')\n\n',L_precond); - msg4='Put this "switch" in the M-file.'; - msg=[msg,msg1,msg2,msg3,msg4]; - end - else - eval('v=feval(L_precond,zeros(n,1));','n=-1') - if n<0 - msg=sprintf('''%s'' should produce %i-vectors',L_precond,n); - end - end -end - -Ud=1; -if ~isempty(L_precond) & ~ischar(L_precond) & n>0 - if ~isempty(U_precond) & ischar(U_precond) - msg=sprintf(' L and U should both be strings or matrices'); n=-1; - elseif ~isempty(U_precond) - if ~min([n,n]==size(L_precond) & [n,n]==size(U_precond)) - msg=sprintf('Both L and U should be %iX%i.',n,n); n=-1; - end - elseif min([n,n]==size(L_precond)) - U_precond=speye(n); Ud=0; - elseif min([n,2*n]==size(L_precond)) - U_precond=L_precond(:,n+1:2*n); L_precond=L_precond(:,1:n); - else - msg=sprintf('The preconditioning matrix\n'); - msg2=sprintf('should be %iX%i or %ix%i ([L,U]).\n',n,n,n,2*n); - msg=[msg,msg2]; n=-1; - end -end -if n<0, errordlg(msg,'PRECONDITIONER'), return, end - -ls_tol0=ls_tol; -if strmatch('Tol',fopts), tol = options.Tol; end - -if isempty(nselect), nselect=min(n,5); end - -if strmatch('jmin',fopts), jmin=min(n,options.jmin); end -if strmatch('jmax',fopts) - jmax=min(n,options.jmax); - if jmin<0, jmin=max(1,jmax-p1); end -else - if jmin<0, jmin=min(n,nselect+p0); end - jmax=min(n,jmin+p1); -end - -if strmatch('MaxIt',fopts), maxit = abs(options.MaxIt); end - -if strmatch('v0',fopts); - V = options.v0; - [m,d]=size(V); - if m~=n | d==0 - if m>n, V = V(1:n,:); end - nrV=norm(V); if nrV>0, V=V/nrV; end - d=max(d,1); - V = [V; ones(n-m,d) +0.1*rand(n-m,d)]; - end -else - V = ones(n,1) +0.1*rand(n,1); d=1; -end - -if strmatch('TestSpace',fopts), INTERIOR = boolean(options.TestSpace,... - [INTERIOR,0,1,1.1,1.2],strvcat('standard','harmonic')); -end - -if isempty(sigma) - if INTERIOR, sigma=0; else, sigma = 'LM'; end -elseif ischar(sigma) - switch sigma - case {'LM','LR','SR','BE'} - case {'SM'} - sigma=0; - otherwise - if INTERIOR, sigma=0; else, sigma='LM'; end - end -end - -if strmatch('Schur',fopts), SCHUR = boolean(options.Schur,SCHUR); end -if strmatch('Disp',fopts), SHOW = boolean(options.Disp,[SHOW,2]); end -if strmatch('Pairs',fopts), PAIRS = boolean(options.Pairs,PAIRS); end -if strmatch('AvoidStag',fopts),JDV = boolean(options.AvoidStag,JDV); end -if strmatch('Track',fopts) - OLD = boolean(options.Track,[OLD,0,OLD,inf],strvcat('no','yes')); end -OLD=max(abs(OLD),10*tol); - -if strmatch('LSolver',fopts), lsolver = lower(options.LSolver); end - -switch lsolver - case {'exact'} - L_precond=[]; - if ischar(A_operator) - msg=sprintf('The operator must be a matrix for ''exact''.'); - msg=[msg,sprintf('\nDo you want to solve the correction equation')]; - msg=[msg,sprintf('\naccurately with an iterative solver (BiCGstab)?')]; - button=questdlg(msg,'Solving exactly','Yes','No','Yes'); - if strcmp(button,'No'), n=-1; return, end - end - case {'iluexact'} - if ischar(L_precond) - msg=sprintf('The preconditioner must be matrices for ''iluexact''.'); - errordlg(msg,'Solving with ''iluexact''') - n=-1; return - end - case {'olsen'} - case {'cg','minres','symmlq'} - ls_tol=1.0e-12; - case 'gmres' - ls_maxit=5; - case 'bicgstab' - ls_tol=1.0e-10; - otherwise - error(['Unknown method ''' lsolver '''.']); -end - -if strmatch('LS_MaxIt',fopts), ls_maxit=abs(options.LS_MaxIt); end -if strmatch('LS_Tol',fopts), ls_tol=abs(options.LS_Tol); end -if strmatch('LS_ell',fopts), ell=round(abs(options.LS_ell)); end - -par=[ls_tol,ls_maxit,ell]; - -if SHOW - - fprintf('\n'),fprintf('PROBLEM\n') - if ischar(A_operator) - fprintf(' A: ''%s''\n',A_operator); - elseif issparse(A_operator) - fprintf(' A: [%ix%i sparse]\n',n,n); - else - fprintf(' A: [%ix%i double]\n',n,n); - end - fprintf(' dimension: %i\n',n); - fprintf(' nselect: %i\n\n',nselect); - - fprintf('TARGET\n') - if ischar(sigma) - fprintf(' sigma: ''%s''',sigma) - else - Str=ShowLambda(sigma); - fprintf(' sigma: %s',Str) - end - fprintf('\n\n') - - fprintf('OPTIONS\n'); - fprintf(' Schur: %i\n',SCHUR); - fprintf(' Tol: %g\n',tol); - fprintf(' Disp: %i\n',SHOW); - fprintf(' jmin: %i\n',jmin); - fprintf(' jmax: %i\n',jmax); - fprintf(' MaxIt: %i\n',maxit); - fprintf(' v0: [%ix%i double]\n',size(V)); - fprintf(' TestSpace: %g\n',INTERIOR); - fprintf(' Pairs: %i\n',PAIRS); - fprintf(' AvoidStag: %i\n',JDV); - fprintf(' Track: %g\n',OLD); - - fprintf(' LSolver: ''%s''\n',lsolver); - - - switch lsolver - case {'exact','iluexact','olsen'} - case {'cg','minres','symmlq','gmres','bicgstab'} - if length(ls_tol)>1 - fprintf(' LS_Tol: ['); fprintf(' %g',ls_tol); fprintf(' ]\n'); - else - fprintf(' LS_Tol: %g\n',ls_tol); - end - fprintf(' LS_MaxIt: %i\n',ls_maxit); - end - if strcmp(lsolver,'bicgstab') - fprintf(' LS_ell: %i\n',ell); - end - - if isempty(L_precond) - fprintf(' Precond: []\n'); - else - StrL='Precond'; StrU='U precond'; Us='double'; Ls=Us; ok=0; - if issparse(L_precond), Ls='sparse'; end - if ~isempty(U_precond) & Ud, StrL='L precond'; ok=1; - if issparse(U_precond), Us='sparse'; end - end - if ischar(L_precond) - fprintf('%13s: ''%s''\n',StrL,L_precond); - if ok - if U_precond~=0 & ~strcmp(U_precond,'preconditioner') - fprintf('%13s: ''%s''\n',StrU,U_precond); - else - fprintf('%13s: ''%s''\n',StrU,L_precond); - end - end - else - fprintf('%13s: [%ix%i %s]\n',StrL,n,n,Ls); - if ok & Ud, fprintf('%13s: [%ix%i %s]\n',StrU,n,n,Us); end - end - end - fprintf('\n') - - string1='%13s: ''%s'''; string2='\n\t %s'; - switch INTERIOR - case 0 - fprintf(string1,'TestSpace','Standard, W = V ') - fprintf(string2,'V W: V orthogonal') - fprintf(string2,'W=A*V') - case 1 - fprintf(string1,'TestSpace','Harmonic, W = A*V - sigma*V') - fprintf(string2,'V W: V and W orthogonal') - fprintf(string2,'AV-Q*E=W*R where AV=A*V-sigma*V and E=Q''*AV') - case 1.1 - fprintf(string1,'TestSpace','Harmonic, W = A*V - sigma*V') - fprintf(string2,'V W AV: V and W orthogonal') - fprintf(string2,'AV=A*V-sigma*V, AV-Q*Q''*AV=W*R') - case 1.2 - fprintf(string1,'TestSpace','Harmonic, W = A*V - sigma*V') - fprintf(string2,'V W: W orthogonal') - fprintf(string2,'W=AV-Q*E where AV=A*V-sigma*V and E=Q''*AV') - otherwise - fprintf(string1,'TestSpace','Experimental') - end % switch INTERIOR - fprintf('\n\n') -end % if SHOW - -if ischar(sigma) & INTERIOR >=1 - msg1=sprintf('\n The choice sigma = ''%s'' does not match',sigma); - msg2=sprintf('\n the search for INTERIOR eigenvalues.'); - msg3=sprintf('\n Specify a numerical value for sigma'); - msg4=sprintf(',\n for instance, a value that is '); - switch sigma - case {'LM'} - % sigma='SM'; - msg5=sprintf('absolute large.\n'); - msg4=[msg4,msg5]; - case {'LR'} - % sigma='SP'; % smallest positive real - msg5=sprintf('positive large.\n'); - msg4=[msg4,msg5]; - case {'SR'} - % sigma='LN'; % largest negative real - msg5=sprintf('negative and absolute large.\n'); - msg4=[msg4,msg5]; - case {'BE'} - % sigma='AS'; % alternating smallest pos., largest neg - msg4=sprintf('.\n'); - end - msg=[msg1,msg2,msg3,msg4]; - msg5=sprintf(' Do you want to continue with sigma=0?'); - msg=[msg,msg5]; - button=questdlg(msg,'Finding Interior Eigenvalues','Yes','No','Yes'); - if strcmp(button,'Yes'), sigma=0, else, n=-1; end -end - -return - -%------------------------------------------------------------------- -function x = boolean(x,gamma,string) -%Y = BOOLEAN(X,GAMMA,STRING) -% GAMMA(1) is the default. -% If GAMMA is not specified, GAMMA = 0. -% STRING is a matrix of accepted strings. -% If STRING is not specified STRING = ['no ';'yes'] -% STRING(I,:) and GAMMA(I) are accepted expressions for X -% If X=GAMMA(I) then Y=X. If X=STRING(I,:), then Y=GAMMA(I+1). -% For other values of X, Y=GAMMA(1); - -if nargin < 2, gamma=0; end -if nargin < 3, string=strvcat('no','yes'); gamma=[gamma,0,1]; end - -if ischar(x) - i=strmatch(lower(x),string,'exact'); - if isempty(i),i=1; else, i=i+1; end, x=gamma(i); -elseif max((gamma-x)==0) -elseif gamma(end) == inf -else, x=gamma(1); -end - -return -%------------------------------------------------------------------- -function possibilities - fprintf('\n') - fprintf('PROBLEM\n') - fprintf(' A: [ square matrix | string ]\n'); - fprintf(' nselect: [ positive integer {5} ]\n\n'); - fprintf('TARGET\n') - fprintf(' sigma: [ scalar | vector of scalars |\n'); - fprintf(' ''LM'' | {''SM''} | ''LR'' | ''SR'' | ''BE'' ]\n\n'); - - fprintf('OPTIONS\n'); - fprintf(' Schur: [ yes | {no} ]\n'); - fprintf(' Tol: [ positive scalar {1e-8} ]\n'); - fprintf(' Disp: [ yes | {no} | 2 ]\n'); - fprintf(' jmin: [ positive integer {nselect+5} ]\n'); - fprintf(' jmax: [ positive integer {jmin+5} ]\n'); - fprintf(' MaxIt: [ positive integer {200} ]\n'); - fprintf(' v0: [ size(A,1) by p vector of scalars {rand(size(A,1),1)} ]\n'); - fprintf(' TestSpace: [ Standard | {Harmonic} ]\n'); - fprintf(' Pairs: [ yes | {no} ]\n'); - fprintf(' AvoidStag: [ yes | {no} ]\n'); - fprintf(' Track: [ {yes} | no | non-negative scalar {1e-4} ]\n'); - fprintf(' LSolver: [ {gmres} | bicgstab ]\n'); - fprintf(' LS_Tol: [ row of positive scalars {[1,0.7]} ]\n'); - fprintf(' LS_MaxIt: [ positive integer {5} ]\n'); - fprintf(' LS_ell: [ positive integer {4} ]\n'); - fprintf(' Precond: [ n by 2n matrix | string {identity} ]\n'); - fprintf('\n') - -return -%=========================================================================== -%============= OUTPUT FUNCTIONS ============================================ -%=========================================================================== -function varargout=ShowLambda(lambda,kk) - -for k=1:size(lambda,1); - if k>1, Str=[Str,sprintf('\n%15s','')]; else, Str=[]; end - rlambda=real(lambda(k,1)); ilambda=imag(lambda(k,1)); - Str=[Str,sprintf(' %+11.4e',rlambda)]; - if abs(ilambda)>100*eps*abs(rlambda) - if ilambda>0 - Str=[Str,sprintf(' + %10.4ei',ilambda)]; - else - Str=[Str,sprintf(' - %10.4ei',-ilambda)]; - end - end -end - -if nargout == 0 - if nargin == 2 - Str=[sprintf('\nlambda(%i) =',kk),Str]; - else - Str=[sprintf('\nDetected eigenvalues:\n\n%15s',''),Str]; - end - fprintf('%s\n',Str) -else - varargout{1}=Str; -end - -return -%=========================================================================== -function DispResult(s,nr,gamma) - - if nargin<3, gamma=0; end - - extra=''; - if nr > 100*eps & gamma - extra=' norm > 100*eps !!! '; - end - - if gamma<2 | nr>100*eps - fprintf('\n %35s: %0.5g\t%s',s,nr,extra) - end - -return -%=========================================================================== -function STATUS0=MovieTheta(n,nit,Lambda,jmin,tau,LOCKED,SHRINK) -% MovieTheta(n,nit,Lambda,jmin,tau,nr0, axis(MovieAxis), end, hold on -pls='bo'; if SHRINK, pls='mo'; end -%plot(real(Lambda(jmin+1:end)),imag(Lambda(jmin+1:end)),pls) -%plot(real(EigMATLAB),imag(EigMATLAB),'cp'); -THETA=diag(Rschur); %plot(real(THETA),imag(THETA),'k*'); - -x=real(Lambda(1)); y=imag(Lambda(1)); -%plot(x,y,'kd'), pls='ks'; -if LOCKED, plot(x,y,'ks'), pls='ms'; end - -if ischar(tau), tau=0; end -delta=Lambda([1,jmin])-tau; -if length(CIRCLE)~=2, delta=abs(delta); -% plot(real(tau),imag(tau),pls) -else, delta=real(delta); end -for i=1:1+SHRINK, - zeta=delta(i)*CIRCLE+tau; -% plot(real(zeta),imag(zeta),'r:'), -end - -if nit==0 - buttons(f,-1); hold off, zoom on -end -title('legend see figure(255)') -if SHRINK, STATUS0=buttons(f,2); if STATUS0, return, end, end -STATUS0=buttons(f,1); drawnow, hold off - -return - -%============================================================= -function Explanation(E,f) - - %if gcf~=f, figure(f), end - - HL=plot(0,0,'kh',0,0,'bo'); hold on - StrL=str2mat('Detected eigenvalues','Approximate eigenvalues'); - if E - HL=[HL;plot(0,0,'cp')]; - StrL=str2mat(StrL,'Exact eigenvenvalues'); - end - HL=[HL;plot(0,0,'kd',0,0,'ks',0,0,'r:')]; - % StrL=str2mat(StrL,'Tracked app. eig.','target',... - % 'inner/outer bounds for restart'); - StrL=str2mat(StrL,'Selected approximate eigenvalue','target',... - 'inner/outer bounds for restart'); - - legend(HL,StrL), hold on, drawnow, hold off - title('legend for figure(256)') - -return - -%============================================================= -function STATUS0=buttons(f,push) -% push=0: do nothing -% push>0: check status buttons, -% STATUS0=1 if break else STATUS0=0. -% push=-1: make buttons for pause and break -% push=-2: remove buttons - -global M_STATUS MovieAxis - - if push>0 % check status buttons - - ud = get(f,'UserData'); - if ud.pause ==1, M_STATUS=1; end - if ud.break ==1, STATUS0=1; - ud.pause=0; ud.break=0; set(f,'UserData',ud); return, - else, STATUS0=0; end - - if push>1 - ud.pause=0; set(f,'UserData',ud); - while M_STATUS - ud = get(f,'UserData'); pause(0.1) - if ud.pause, M_STATUS=0; end - if ud.break, M_STATUS=0; STATUS0=1; end - MovieAxis=axis; - end - ud.pause=0; ud.break=0; set(f,'UserData',ud); - end - - - elseif push==0, STATUS0=0; return - elseif push==-1 % make buttons - - ud = []; - h = findobj(f,'Tag','pause'); - if isempty(h) - ud.pause = 0; - pos = get(0,'DefaultUicontrolPosition'); - pos(1) = pos(1) - 15; - pos(2) = pos(2) - 15; - str = 'ud=get(gcf,''UserData''); ud.pause=1; set(gcf,''UserData'',ud);'; - uicontrol( ... - 'Style','push', ... - 'String','Pause', ... - 'Position',pos, ... - 'Callback',str, ... - 'Tag','pause'); - else - set(h,'Visible','on'); % make sure it's visible - if ishold - oud = get(f,'UserData'); - ud.pause = oud.pause; % don't change old ud.pause status - else - ud.pause = 0; - end - end - h = findobj(f,'Tag','break'); - if isempty(h) - ud.break = 0; - pos = get(0,'DefaultUicontrolPosition'); - pos(1) = pos(1) + 50; - pos(2) = pos(2) - 15; - str = 'ud=get(gcf,''UserData''); ud.break=1; set(gcf,''UserData'',ud);'; - uicontrol( ... - 'Style','push', ... - 'String','Break', ... - 'Position',pos, ... - 'Callback',str, ... - 'Tag','break'); - else - set(h,'Visible','on'); % make sure it's visible - if ishold - oud = get(f,'UserData'); - ud.break = oud.break; % don't change old ud.break status - else - ud.break = 0; - end - end - set(f,'UserData',ud); M_STATUS=0; - - STATUS0=0; hold off, zoom on - - MA=axis; nl=MA/10; - MovieAxis = MA-max(nl([2,4])-nl([1,3]))*[1,-1,1,-1]; - - else % remove buttons - - set(findobj(f,'Tag','pause'),'Visible','off'); - set(findobj(f,'Tag','break'),'Visible','off'); - STATUS0=0; return, refresh - - end -return diff --git a/code/dimReducMethods/jdqz.m b/code/dimReducMethods/jdqz.m deleted file mode 100644 index 6f95bbc..0000000 --- a/code/dimReducMethods/jdqz.m +++ /dev/null @@ -1,2507 +0,0 @@ -function varargout=jdqz(varargin) -%JDQZ computes a partial generalized Schur decomposition (or QZ -% decomposition) of a pair of square matrices or operators. -% -% LAMBDA=JDQZ(A,B) and JDQZ(A,B) return K eigenvalues of the matrix pair -% (A,B), where K=min(5,N) and N=size(A,1) if K has not been specified. -% -% [X,JORDAN]=JDQZ(A,B) returns the eigenvectors X and the Jordan -% structure JORDAN: A*X=B*X*JORDAN. The diagonal of JORDAN contains the -% eigenvalues: LAMBDA=DIAG(JORDAN). JORDAN is an K by K matrix with the -% eigenvalues on the diagonal and zero or one on the first upper diagonal -% elements. The other entries are zero. -% -% [X,JORDAN,HISTORY]=JDQZ(A,B) returns also the convergence history. -% -% [X,JORDAN,Q,Z,S,T,HISTORY]=JDQZ(A,B) -% If between four and seven output arguments are required, then Q and Z -% are N by K orthonormal, S and T are K by K upper triangular such that -% they form a partial generalized Schur decomposition: A*Q=Z*S and -% B*Q=Z*T. Then LAMBDA=DIAG(S)./DIAG(T) and X=Q*Y with Y the eigenvectors -% of the pair (S,T): S*Y=T*Y*JORDAN (see also OPTIONS.Schur). -% -% JDQZ(A,B) -% JDQZ('Afun','Bfun') -% The first input argument is either a square matrix (which can be full -% or sparse, symmetric or nonsymmetric, real or complex), or a string -% containing the name of an M-file which applies a linear operator to the -% columns of a given matrix. In the latter case, the M-file, say Afun.m, -% must return the dimension N of the problem with N = Afun([],'dimension'). -% For example, JDQZ('fft',...) is much faster than JDQZ(F,...), where F is -% the explicit FFT matrix. -% If another input argument is a square N by N matrix or the name of an -% M-file, then B is this argument (regardless whether A is an M-file or a -% matrix). If B has not been specified, then B is assumed to be the -% identity unless A is an M-file with two output vectors of dimension N -% with [AV,BV]=Afun(V), or with AV=Afun(V,'A') and BV=Afun(V,'B'). -% -% The remaining input arguments are optional and can be given in -% practically any order: -% -% [X,JORDAN,Q,Z,S,T,HISTORY] = JDQZ(A,B,K,SIGMA,OPTIONS) -% [X,JORDAN,Q,Z,S,T,HISTORY] = JDQZ('Afun','Bfun',K,SIGMA,OPTIONS) -% -% where -% -% K an integer, the number of desired eigenvalues. -% SIGMA a scalar shift or a two letter string. -% OPTIONS a structure containing additional parameters. -% -% If K is not specified, then K = MIN(N,5) eigenvalues are computed. -% -% If SIGMA is not specified, then the Kth eigenvalues largest in -% magnitude are computed. If SIGMA is a real or complex scalar, then the -% Kth eigenvalues nearest SIGMA are computed. If SIGMA is column vector -% of size (L,1), then the Jth eigenvalue nearest to SIGMA(MIN(J,L)) -% is computed for J=1:K. SIGMA is the "target" for the desired eigenvalues. -% If SIGMA is one of the following strings, then it specifies the desired -% eigenvalues. -% -% SIGMA Specified eigenvalues -% -% 'LM' Largest Magnitude -% 'SM' Smallest Magnitude (same as SIGMA = 0) -% 'LR' Largest Real part -% 'SR' Smallest Real part -% 'BE' Both Ends. Computes K/2 eigenvalues -% from each end of the spectrum (one more -% from the high end if K is odd.) -% -% If 'TestSpace' is 'Harmonic' (see OPTIONS), then SIGMA = 0 is the -% default, otherwise SIGMA = 'LM' is the default. -% -% -% The OPTIONS structure specifies certain parameters in the algorithm. -% -% Field name Parameter Default -% -% OPTIONS.Tol Convergence tolerance: 1e-8 -% norm(r) <= Tol/SQRT(K) -% OPTIONS.jmin Minimum dimension search subspace V K+5 -% OPTIONS.jmax Maximum dimension search subspace V jmin+5 -% OPTIONS.MaxIt Maximum number of iterations. 100 -% OPTIONS.v0 Starting space ones+0.1*rand -% OPTIONS.Schur Gives schur decomposition 'no' -% If 'yes', then X and JORDAN are -% not computed and [Q,Z,S,T,HISTORY] -% is the list of output arguments. -% OPTIONS.TestSpace Defines the test subspace W 'Harmonic' -% 'Standard': W=sigma*A*V+B*V -% 'Harmonic': W=A*V-sigma*B*V -% 'SearchSpace': W=V -% W=V is justified if B is positive -% definite. -% OPTIONS.Disp Shows size of intermediate residuals 'no' -% and the convergence history -% OPTIONS.NSigma Take as target for the second and 'no' -% following eigenvalues, the best -% approximate eigenvalues from the -% test subspace. -% OPTIONS.Pairs Search for conjugated eigenpairs 'no' -% OPTIONS.LSolver Linear solver 'GMRES' -% OPTIONS.LS_Tol Residual reduction linear solver 1,0.7,0.7^2,.. -% OPTIONS.LS_MaxIt Maximum number it. linear solver 5 -% OPTIONS.LS_ell ell for BiCGstab(ell) 4 -% OPTIONS.Precond Preconditioner (see below) identity. -% OPTIONS.Type_Precond Way of using preconditioner 'left' -% -% For instance -% -% options=struct('Tol',1.0e-8,'LSolver','BiCGstab','LS_ell',4,'Precond',M); -% -% changes the convergence tolerance to 1.0e-8, takes BiCGstab as linear -% solver, and takes M as preconditioner (for ways of defining M, see below). -% -% -% PRECONDITIONING. The action M-inverse of the preconditioner M (an -% approximation of A-lamda*B) on an N-vector V can be defined in the -% OPTIONS -% -% OPTIONS.Precond -% OPTIONS.L_Precond same as OPTIONS.Precond -% OPTIONS.U_Precond -% OPTIONS.P_Precond -% -% If no preconditioner has been specified (or is []), then M\V=V (M is -% the identity). -% If Precond is an N by N matrix, say, K, then -% M\V = K\V. -% If Precond is an N by 2*N matrix, say, K, then -% M\V = U\L\V, where K=[L,U], and L and U are N by N matrices. -% If Precond is a string, say, 'Mi', then -% if Mi(V,'L') and Mi(V,'U') return N-vectors -% M\V = Mi(Mi(V,'L'),'U') -% otherwise -% M\V = Mi(V) or M\V=Mi(V,'preconditioner'). -% Note that Precond and A can be the same string. -% If L_Precond and U_Precond are strings, say, 'Li' and 'Ui', -% respectively, then -% M\V=Ui(Li(V)). -% If (P_precond,) L_Precond, and U_precond are N by N matrices, say, -% (P,) L, and U, respectively, then -% M\V=U\L\(P*V) (P*M=L*U) -% -% OPTIONS.Type_Precond -% The preconditioner can be used as explicit left preconditioner -% ('left', default), as explicit right preconditioner ('right') or -% implicitly ('impl'). -% -% -% JDQZ without input arguments returns the options and its defaults. -% - -% Gerard Sleijpen. -% Copyright (c) 2002 -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - -global Qschur Zschur Sschur Tschur ... - Operator_MVs Precond_Solves ... - MinvZ QastMinvZ - -if nargin==0 - possibilities, return, -end - -%%% Read/set parameters -[n,nselect,Sigma,kappa,SCHUR,... - jmin,jmax,tol0,maxit,V,AV,BV,TS,DISP,PAIRS,JDV0,FIX_tol,track,NSIGMA,... - lsolver,LSpar] = ReadOptions(varargin{1:nargin}); - -Qschur = zeros(n,0); Zschur=zeros(n,0);; -MinvZ = zeros(n,0); QastMinvZ=zeros(0,0); -Sschur = []; Tschur=[]; history = []; - -%%% Return if eigenvalueproblem is trivial -if n<2 - if n==1, Qschur=1; Zschur=1; [Sschur,Tschur]=MV(1); end - if nargout == 0, Lambda=Sschur/Tschur, else - [varargout{1:nargout}]=output(history,SCHUR,1,Sschur/Tschur); end, -return, end - -%---------- SET PARAMETERS & STRINGS FOR OUTPUT ------------------------- - -if TS==0, testspace='sigma(1)''*Av+sigma(2)''*Bv'; -elseif TS==1, testspace='sigma(2)*Av-sigma(1)*Bv'; -elseif TS==2, testspace='v'; -elseif TS==3, testspace='Bv'; -elseif TS==4, testspace='Av'; -end - -String=['\r#it=%i #MV=%3i, dim(V)=%2i, |r_%2i|=%6.1e ']; - -%------------------- JDQZ ----------------------------------------------- - -% fprintf('Scaling with kappa=%6.4g.',kappa) - -k=0; nt=0; j=size(V,2); nSigma=size(Sigma,1); -it=0; extra=0; Zero=[]; target=[]; tol=tol0/sqrt(nselect); - -INITIATE=1; JDV=0; -rKNOWN=0; EXPAND=0; USE_OLD=0; DETECTED=0; - -time=clock; -if TS ~=2 -while (k1 & ~ischar(target), theta=target; else, FIX_tol=0; end - t=SolvePCE(theta,q,z,r,lsolver,LSpar,lit); - nlit=nlit+1; lit=lit+1; it=it+1; - EXPAND=1; rKNOWN=0; JDV=0; - end % if rKNOWN - - %%% Expand the subspaces and the interaction matrices - if EXPAND - [v,zeta]=RepGS([Qschur,V],t); - V=[V,v]; - [Av,Bv]=MV(v); AV=[AV,Av]; BV=[BV,Bv]; - w=eval(testspace); w=RepGS([Zschur,W],w); - WAV=[WAV,W'*Av;w'*AV]; WBV=[WBV,W'*Bv;w'*BV]; W=[W,w]; - j=j+1; EXPAND=0; - - %%% Check for stagnation - if abs(zeta(size(zeta,1),1))/norm(zeta)<0.06, JDV=JDV0; end - - end % if EXPAND - - %%% Solve projected eigenproblem - if USE_OLD - [Ur,Ul,St,Tt]=SortQZ(WAV,WBV,ttarget,kappa,(j>=jmax)*jmin,y); - else - [Ur,Ul,St,Tt]=SortQZ(WAV,WBV,ttarget,kappa,(j>=jmax)*jmin); - end - - %%% Compute approximate eigenpair and residual - y=Ur(:,1); q=V*y; Av=AV*y; Bv=BV*y; - [r,z,nr,theta]=Comp_rz(RepGS(Zschur,[Av,Bv],0),kappa); - %%%=== an alternative, but less stable way of computing z ===== - % beta=Tt(1,1); alpha=St(1,1); theta=[alpha,beta]; - % r=RepGS(Zschur,beta*Av-alpha*Bv,0); nr=norm(r); z=W*Ul(:,1); - rKNOWN=1; if nr=nselect), break; end; - %%% Expand preconditioned Schur matrix MinvZ=M\Zschur - UpdateMinvZ; - J=[2:j]; j=j-1; Ur=Ur(:,J); Ul=Ul(:,J); - V=V*Ur; AV=AV*Ur; BV=BV*Ur; W=W*Ul; - WAV=St(J,J); WBV=Tt(J,J); - - rKNOWN=0; DETECTED=1; USE_OLD=0; - - %%% check for conjugate pair - if PAIRS & (abs(imag(theta(1)/theta(2)))>tol) - t=ImagVector(q); % t=conj(q); t=t-q*(q'*t); - if norm(t)>tol, t=RepGS([Qschur,V],t,0); - if norm(t)>200*tol - target=ScaleEig(conj(theta)); - EXPAND=1; DETECTED=0; - if DISP, fprintf('--- Checking for conjugate pair ---\n'), end - end - end - end - - INITIATE = ( j==0 & DETECTED); - - elseif DETECTED %%% To detect whether another eigenpair is accurate enough - INITIATE=1; - end % if (nr jmax - if j==jmax - j=jmin; J=[1:j]; - Ur=Ur(:,J); Ul=Ul(:,J); - V=V*Ur; AV=AV*Ur; BV=BV*Ur; W=W*Ul; - WAV=St(J,J); WBV=Tt(J,J); - end % if j==jmax - -end % while k -end % if TS~=2 - - -if TS==2 -Q0=Qschur; ZastQ=[]; -% WAV=V'*AV; WBV=V'*BV; -while (kk | NSIGMA), % set new target - nt=min(nt+1,nSigma); sigma = Sigma(nt,:); nlit=0; lit=0; - if j<2 - [V,AV,BV]=Arnoldi(V,AV,BV,sigma,jmin,nselect,tol); - rKNOWN=0; EXPAND=0; USE_OLD=0; DETECTED=0; target=[]; - j=min(jmin,n-k);; - end - if DETECTED & NSIGMA - [Ur,Ul,St,Tt]=SortQZ(WAV,WBV,sigma,kappa,1); - q=RepGS(Zschur,V*Ur(:,1)); [Av,Bv]=MV(q); - [r,z,nr,theta]=Comp_rz(RepGS(Zschur,[Av,Bv],0),kappa); - sigma=ScaleEig(theta); - USE_OLD=NSIGMA; rKNOWN=1; lit=10; - end - target=sigma; ttarget=sigma; - if ischar(ttarget), ttrack=0; else, ttrack=track; end - if ~DETECTED - %%% additional stabilisation. May not be needed - %%% V=RepGS(Zschur,V); [AV,BV]=MV(V); - %%% end add. stab. - WAV=V'*AV; WBV=V'*BV; - end - DETECTED=0; INITIATE=0; JDV=0; - end % if INITIATE - - %%% Solve the preconditioned correction equation - if rKNOWN, - if JDV, z=V; q=V; extra=extra+1; - if DISP, fprintf(' %2i-d proj.\n',k+j-1), end - end - if FIX_tol*nr>1 & ~ischar(target), theta=target; else, FIX_tol=0; end - t=SolvePCE(theta,q,z,r,lsolver,LSpar,lit); - nlit=nlit+1; lit=lit+1; it=it+1; - EXPAND=1; rKNOWN=0; JDV=0; - end % if rKNOWN - - %%% expand the subspaces and the interaction matrices - if EXPAND - [v,zeta]=RepGS([Zschur,V],t); [Av,Bv]=MV(v); - WAV=[WAV,V'*Av;v'*AV,v'*Av]; WBV=[WBV,V'*Bv;v'*BV,v'*Bv]; - V=[V,v]; AV=[AV,Av]; BV=[BV,Bv]; - j=j+1; EXPAND=0; - - %%% Check for stagnation - if abs(zeta(size(zeta,1),1))/norm(zeta)<0.06, JDV=JDV0; end - - end % if EXPAND - - %%% compute approximate eigenpair - if USE_OLD - [Ur,Ul]=SortQZ(WAV,WBV,ttarget,kappa,(j>=jmax)*jmin,Ur(:,1)); - else - [Ur,Ul]=SortQZ(WAV,WBV,ttarget,kappa,(j>=jmax)*jmin); - end - - %%% Compute approximate eigenpair and residual - q=V*Ur(:,1); Av=AV*Ur(:,1); Bv=BV*Ur(:,1); - [r,z,nr,theta]=Comp_rz(RepGS(Zschur,[Av,Bv],0),kappa); - rKNOWN=1; if nr=nselect), break; end; - UpdateMinvZ; - J=[2:j]; j=j-1; rKNOWN=0; DETECTED=1; - Ul=Ul(:,J); - V=V*Ul; AV=AV*Ul; BV=BV*Ul; - WAV=Ul'*WAV*Ul; WBV=Ul'*WBV*Ul; - Ul=eye(j); Ur=Ul; - - %%% check for conjugate pair - if PAIRS & (abs(imag(theta(2)/theta(1)))>tol) - t=ImagVector(q); - if norm(t)>tol, - %%% t perp Zschur, t in span(Q0,imag(q)) - t=t-Q0*(ZastQ\(Zschur'*t)); - if norm(t)>100*tol - target=ScaleEig(conj(theta)); - EXPAND=1; DETECTED=0; USE_OLD=0; - if DISP, fprintf('--- Checking for conjugate pair ---\n'), end - end - end - end - INITIATE = ( j==0 & DETECTED); - - elseif DETECTED %%% To detect whether another eigenpair is accurate enough - INITIATE=1; - end % if (nr jmax - if j==jmax - j=jmin; J=[1:j]; - Ur=Ur(:,J); - V=V*Ur; AV=AV*Ur; BV=BV*Ur; - WAV=Ur'*WAV*Ur; WBV=Ur'*WBV*Ur; - Ur=eye(j); - end % if jmax - -end % while k -Qschur=Q0; -end - -time_needed=etime(clock,time); - -if JDV0 & extra>0 & DISP - fprintf('\n\n# j-dim. proj.: %2i\n\n',extra) -end - -I=CheckSortSchur(Sigma,kappa); Target(1:length(I),:)=Target(I,:); - -XKNOWN=0; - -if nargout == 0 - if ~DISP - eigenvalues=diag(Sschur)./diag(Tschur) - % Result(eigenvalues) - return, end -else - Jordan=[]; X=zeros(n,0); - if SCHUR ~= 1 - if k>0 - [Z,D,Jor]=FindJordan(Sschur,Tschur,SCHUR); - DT=abs(diag(D)); DS=abs(diag(Jor)); - JT=find(DT<=tol & DS>tol); JS=find(DS<=tol & DT<=tol); - msg=''; DT=~isempty(JT); DS=~isempty(JS); - if DT - msg1='The eigenvalues'; msg2=sprintf(', %i',JT); - msg=[msg1,msg2,' are numerically ''Inf''']; - end, - if DS - msg1='The pencil is numerically degenerated in the directions'; - msg2=sprintf(', %i',JS); - if DT, msg=[msg,sprintf('\n\n')]; end, msg=[msg,msg1,msg2,'.']; - end, - if (DT | DS), warndlg(msg,'Unreliable directions'), end - Jordan=Jor/D; X=Qschur*Z; XKNOWN=1; - end - end - [varargout{1:nargout}]=output(history,SCHUR,X,Jordan); - -end - -%-------------- display results ----------------------------------------- -if DISP & size(history,1)>0 - rs=history(:,1); mrs=max(rs); - if mrs>0, rs=rs+0.1*eps*mrs; - subplot(2,1,1); t=history(:,2); - plot(t,log10(rs),'*-',t,log10(tol)+0*t,':') - legend('log_{10} || r_{#it} ||_2') - String=sprintf('The test subspace is computed as %s.',testspace); - title(String) - - subplot(2,1,2); t=history(:,3); - plot(t,log10(rs),'-*',t,log10(tol)+0*t,':') - legend('log_{10} || r_{#MV} ||_2') - - - String=sprintf('JDQZ with jmin=%g, jmax=%g, residual tolerance %g.',... - jmin,jmax,tol); - title(String) - String=sprintf('Correction equation solved with %s.',lsolver); - xlabel(String), - - date=fix(clock); - String=sprintf('%2i-%2i-%2i, %2i:%2i:%2i',date(3:-1:1),date(4:6)); - ax=axis; text(0.2*ax(1)+0.8*ax(2),1.2*ax(3)-0.2*ax(4),String) - drawnow - end - - Result(Sigma,Target,diag(Sschur),diag(Tschur),tol) - -end - -%------------------------ TEST ACCURACY --------------------------------- -if k>nselect & DISP - fprintf('\n%i additional eigenpairs have been detected.\n',k-nselect) -end -if k0) & DISP - Str='time_needed'; texttest(Str,eval(Str)) - fprintf('\n%39s: %9i','Number of Operator actions',Operator_MVs) - if Precond_Solves - fprintf('\n%39s: %9i','Number of preconditioner solves',Precond_Solves) - end - if 1 - if SCHUR ~= 1 & XKNOWN - % Str='norm(Sschur*Z-Tschur*Z*Jordan)'; texttest(Str,eval(Str),tol0) - ok=1; eval('[AX,BX]=MV(X);','ok=0;') - if ~ok, for j=1:size(X,2), [AX(:,j),BX(:,j)]=MV(X(:,j)); end, end - Str='norm(AX*D-BX*Jor)'; texttest(Str,eval(Str),tol0) - end - ok=1; eval('[AQ,BQ]=MV(Qschur);','ok=0;') - if ~ok, for j=1:size(Qschur,2), [AQ(:,j),BQ(:,j)]=MV(Qschur(:,j)); end, end - if kappa == 1 - Str='norm(AQ-Zschur*Sschur)'; texttest(Str,eval(Str),tol0) - else - Str='norm(AQ-Zschur*Sschur)/kappa'; texttest(Str,eval(Str),tol0) - end - Str='norm(BQ-Zschur*Tschur)'; texttest(Str,eval(Str),tol0) - I=eye(k); - Str='norm(Qschur''*Qschur-I)'; texttest(Str,eval(Str)) - Str='norm(Zschur''*Zschur-I)'; texttest(Str,eval(Str)) - nrmSschur=max(norm(Sschur),1.e-8); - nrmTschur=max(norm(Tschur),1.e-8); - Str='norm(tril(Sschur,-1))/nrmSschur'; texttest(Str,eval(Str)) - Str='norm(tril(Tschur,-1))/nrmTschur'; texttest(Str,eval(Str)) - end - fprintf('\n==================================================\n') -end -if k==0 - disp('no eigenvalue could be detected with the required precision') -end - -return -%%%======== END JDQZ ==================================================== - -%%%====================================================================== -%%%======== PREPROCESSING =============================================== -%%%====================================================================== - -%%%======== ARNOLDI (for initial spaces) ================================ -function [V,AV,BV]=Arnoldi(v,Av,Bv,sigma,jmin,nselect,tol) -% Apply Arnoldi with M\(A*sigma(1)'+B*sigma(2)'), to construct an -% initial search subspace -% - -global Qschur - -if ischar(sigma), sigma=[0,1]; end - -[n,j]=size(v); k=size(Qschur,2); jmin=min(jmin,n-k); - -if j==0 & k>0 - v=RepGS(Qschur,rand(n,1)); [Av,Bv]=MV(v); j=1; -end - -V=v; AV=Av; BV=Bv; -while jeps*abs(RT))*sqrt(-1); -return -%%%======== COMPUTE SORTED JORDAN FORM ================================== -function [X,D,Jor]=FindJordan(S,T,SCHUR) -% [X,D,J]=FINDJORDAN(S,T) -% For S and T k by k upper triangular matrices -% FINDJORDAN computes the Jordan decomposition. -% X is a k by k matrix of eigenvectors and principal vectors -% D and J are k by matrices, D is diagonal, J is Jordan -% such that S*X*D=T*X*J. (diag(D),diag(J)) are the eigenvalues. -% If D is non-singular then Lambda=diag(J)./diag(D) -% are the eigenvalues. - -% coded by Gerard Sleijpen, May, 2002 - -k=size(S,1); -s=diag(S); t=diag(T); n=sign(t); n=n+(n==0); -D=sqrt(conj(s).*s+conj(t).*t).*n; -S=diag(D)\S; T=diag(D)\T; D=diag(diag(T)); - -if k<1, - if k==0, X=[]; D=[]; Jor=[]; end - if k==1, X=1; Jor=s; end - return -end - -tol=k*(norm(S,1)+norm(T,1))*eps; -[X,Jor,I]=PseudoJordan(S,T,tol); - - -if SCHUR == 0 -for l=1:length(I)-1 - if I(l)tol); - -return -%================================================== -function [X,Jor,J]=PseudoJordan(S,T,delta) -% Computes a pseudo-Jordan decomposition for the upper triangular -% matrices S and T with ordered diagonal elements. -% S*X*(diag(diag(T)))=T*X*(diag(diag(S))+Jor) -% with X(:,i:j) orthonormal if its -% columns span an invariant subspace of (S,T). - -k=size(S,1); s=diag(S); t=diag(T); - -Jor=zeros(k); X=eye(k); J=1; - -for i=2:k - I=[1:i]; - C=t(i,1)*S(I,I)-s(i,1)*T(I,I); C(i,i)=norm(C,inf); - if C(i,i)>0 - tol=delta*C(i,i); - for j=i:-1:1 - if j==1 | abs(C(j-1,j-1))>tol, break; end - end - e=zeros(i,1); e(i,1)=1; - if j==i - J=[J,i]; q=C\e; X(I,i)=q/norm(q); - else - q=X(I,j:i-1); - q=[C,T(I,I)*q;q',zeros(i-j)]\[e;zeros(i-j,1)]; - q=q/norm(q(I,1)); X(I,i)=q(I,1); - Jor(j:i-1,i)=-q(i+1:2*i-j,1); - end - end -end -J=[J,k+1]; - -return -%================================================== -function [X,Jor,U]=JordanBlock(A,tol) -% If A is nilpotent, then A*X=X*Jor with -% Jor a Jordan block -% - -k=size(A,1); Id=eye(k); -U=Id; aa=A; j=k; jj=[]; J=1:k; - -while j>0 - [u,s,v]=svd(aa); U(:,J)=U(:,J)*v; - sigma=diag(s); delta=tol; - J=find(sigmatol); -l=length(jj); jj=[jj(l:-1:1),k]; - -l2=jj(2)-jj(1); J=jj(1)+(1:l2); -JX=Id(:,J); X=Id; -for j=2:l - l1=l2+1; l2=jj(j+1)-jj(j); - J2=l1:l2; J=jj(j)+(1:l2); - JX=Jor*JX; D=diag(sqrt(diag(JX'*JX))); JX=JX/D; - [Q,S,V]=svd(JX(J,:)); - JX=[JX,Id(:,J)*Q(:,J2)]; X(:,J)=JX; -end - -J=[]; -for i=1:l2 - for k=l:-1:1 - j=jj(k)+i; if j<=jj(k+1), J=[J,j]; end - end -end - -X=X(:,J); Jor=X\(Jor*X); X=U*X; -Jor=Jor.*(abs(Jor)>100*tol); - -return -%%%======== END JORDAN FORM ============================================= - -%%%======== OUTPUT ====================================================== -function varargout=output(history,SCHUR,X,Lambda) - -global Qschur Zschur Sschur Tschur - -if nargout == 1, varargout{1}=diag(Sschur)./diag(Tschur); return, end -if nargout > 2, varargout{nargout}=history; end -if nargout < 6 & SCHUR == 1 - if nargout >1, varargout{1}=Qschur; varargout{2}=Zschur; end - if nargout >2, varargout{3}=Sschur; end - if nargout >3, varargout{4}=Tschur; end -end - -%-------------- compute eigenpairs -------------------------------------- - -if SCHUR ~= 1 - varargout{1}=X; varargout{2}=Lambda; - if nargout >3, varargout{3}=Qschur; varargout{4}=Zschur; end - if nargout >4, varargout{5}=Sschur; end - if nargout >5, varargout{6}=Tschur; end -end - -return -%%%====================================================================== -%%%======== UPDATE PRECONDITIONED SCHUR VECTORS ========================= -%%%====================================================================== -function UpdateMinvZ - -global Qschur Zschur MinvZ QastMinvZ - - [n,k]=size(Qschur); - if k==1, MinvZ=zeros(n,0); QastMinvZ = []; end - Minv_z=SolvePrecond(Zschur(:,k)); - QastMinvZ=[[QastMinvZ;Qschur(:,k)'*MinvZ],Qschur'*Minv_z]; - MinvZ=[MinvZ,Minv_z]; - -return -%%%====================================================================== -%%%======== SOLVE CORRECTION EQUATION =================================== -%%%====================================================================== - -function [t,xtol]=SolvePCE(theta,q,z,r,lsolver,par,nit) - -global Qschur Zschur - - Q=[Qschur,q]; Z=[Zschur,z]; - - switch lsolver - case 'exact' - [t,xtol] = exact(theta,Q,Z,r); - - case {'gmres','cgstab','olsen'} - - [MZ,QMZ]=FormPM(q,z); - %%% solve preconditioned system - [t,xtol] = feval(lsolver,theta,Q,Z,MZ,QMZ,r,spar(par,nit)); - - end - -return -%------------------------------------------------------------------------ -function [MZ,QMZ]=FormPM(q,z) -% compute vectors and matrices for skew projection - -global Qschur MinvZ QastMinvZ - - Minv_z=SolvePrecond(z); - QMZ=[QastMinvZ,Qschur'*Minv_z;q'*MinvZ,q'*Minv_z]; - MZ=[MinvZ,Minv_z]; - -return -%%%====================================================================== -%%%======== LINEAR SOLVERS ============================================== -%%%====================================================================== -function [x,xtol] = exact(theta,Q,Z,r) -% produces the exact solution if matrices are given -% Is only feasible for low dimensional matrices -% Only of interest for experimental purposes -% -global Operator_A Operator_B - -n=size(r,1); - -if ischar(Operator_A) - [MZ,QMZ]=FormPM(Q(:,end),Z(:,end)); - if n>200 - [x,xtol]=SolvePCE(theta,Q,Z,MZ,QMZ,r,'cgstab',[1.0e-10,500,4]); - else - [x,xtol]=SolvePCE(theta,Q,Z,MZ,QMZ,r,'gmres',[1.0e-10,100]); - end - return -end - -k=size(Q,2); -Aug=[theta(2)*Operator_A-theta(1)*Operator_B,Z;Q',zeros(k,k)]; -x=Aug\[r;zeros(k,1)]; x([n+1:n+k],:)=[]; xtol=1; - -% L=eig(full(Aug)); plot(real(L),imag(L),'*'), pause -%%% [At,Bt]=MV(x); At=theta(2)*At-theta(1)*Bt; -%%% xtol=norm(r-At+Z*(Z'*At))/norm(r); - -return - -%%%===== Iterative methods ============================================== -function [r,xtol] = olsen(theta,Q,Z,MZ,M,r,par) -% returns the preconditioned residual as approximate solution -% May be sufficient in case of an excellent preconditioner - - r=SkewProj(Q,MZ,M,SolvePrecond(r)); xtol=0; - -return -%------------------------------------------------------------------------ -function [x,rnrm] = cgstab(theta,Q,Z,MZ,M,r,par) -% BiCGstab(ell) with preconditioning -% [x,rnrm] = cgstab(theta,Q,Z,MZ,M,r,par) -% Computes iteratively an approximation to the solution -% of the linear system Q'*x = 0 and Atilde*x=r -% where Atilde=(I-Z*Z)*(A-theta*B)*(I-Q*Q'). -% using (I-MZ*(M\Q'))*inv(K) as preconditioner -% -% This function is specialized for use in JDQZ. -% integer nmv: number of matrix multiplications -% rnrm: relative residual norm -% -% par=[tol,mxmv,ell] where -% integer m: max number of iteration steps -% real tol: residual reduction -% -% rnrm: obtained residual reduction -% -% -- References: ETNA - -% Gerard Sleijpen (sleijpen@math.uu.nl) -% Copyright (c) 1998, Gerard Sleijpen - -% -- Initialization -- -% - -global Precond_Type - -tol=par(1); max_it=par(2); l=par(3); n=size(r,1); -rnrm=1; nmv=0; - -if max_it < 2 | tol>=1, x=r; return, end -%%% 0 step of bicgstab eq. 1 step of bicgstab -%%% Then x is a multiple of b - -TP=Precond_Type; -if TP==0, r=SkewProj(Q,MZ,M,SolvePrecond(r)); tr=r; -else, tr=RepGS(Z,r); end -rnrm=norm(r); snrm=rnrm; tol=tol*snrm; - -sigma=1; omega=1; -x=zeros(n,1); u=zeros(n,1); -J1=2:l+1; - -%%% HIST=[0,1]; - -if TP <2 %% explicit preconditioning -% -- Iteration loop -while (nmv < max_it) - - sigma=-omega*sigma; - for j = 1:l, - rho=tr'*r(:,j); bet=rho/sigma; - u=r-bet*u; - u(:,j+1)=PreMV(theta,Q,MZ,M,u(:,j)); - sigma=tr'*u(:,j+1); alp=rho/sigma; - r=r-alp*u(:,2:j+1); - r(:,j+1)=PreMV(theta,Q,MZ,M,r(:,j)); - x=x+alp*u(:,1); - G(1,1)=r(:,1)'*r(:,1); rnrm=sqrt(G(1,1)); - if rnrm1, %%% collect the updates for x in l-space - v(:,1:j-1)=s(:,1:j-1)-bet*v(:,1:j-1); - end - [u(:,j+1),V(:,j)]=PreMV(theta,Q,MZ,M,u(:,j)); - sigma=tr'*u(:,j+1); alp=rho/sigma; - r=r-alp*u(:,2:j+1); - if j>1, - s(:,1:j-1)=s(:,1:j-1)-alp*v(:,2:j); - end - [r(:,j+1),V(:,l+j)]=PreMV(theta,Q,MZ,M,r(:,j)); - y=y+alp*v(:,1); - G(1,1)=r(:,1)'*r(:,1); rnrm=sqrt(G(1,1)); - if rnrm=1, return, end -%%% 0 step of gmres eq. 1 step of gmres -%%% Then x is a multiple of b - -H = zeros(max_it +1,max_it); Rot=[ones(1,max_it);zeros(1,max_it)]; - -TP=Precond_Type; - -TP=Precond_Type; -if TP==0 - v=SkewProj(Q,MZ,M,SolvePrecond(v)); rho0 = norm(v); v = v/rho0; -else - v=RepGS(Z,v); -end - -V = [v]; -tol = tol * rnrm; -y = [ rnrm ; zeros(max_it,1) ]; - -while (j < max_it) & (rnrm > tol), - j=j+1; - [v,w]=PreMV(theta,Q,MZ,M,v); - if TP - if TP == 2, W=[W,w]; end - v=RepGS(Z,v,0); - end - [v,h] = RepGS(V,v); H(1:size(h,1),j) = h; - V = [V, v]; - for i = 1:j-1, - a = Rot(:,i); - H(i:i+1,j) = [a'; -a(2) a(1)]*H(i:i+1,j); - end - J=[j, j+1]; - a=H(J,j); - if a(2) ~= 0 - cs = norm(a); - a = a/cs; Rot(:,j) = a; - H(J,j) = [cs; 0]; - y(J) = [a'; -a(2) a(1)]*y(J); - end - rnrm = abs(y(j+1)); -end - -J=[1:j]; -if TP == 2 - v = W(:,J)*(H(J,J)\y(J)); -else - v = V(:,J)*(H(J,J)\y(J)); -end - -if TP==1, v=SkewProj(Q,MZ,M,SolvePrecond(v)); end - -return -%%%====================================================================== -function [v,rnrm] = gmres(theta,Q,Z,MZ,M,v,par) -% GMRES -% [x,nmv,rnrm] = gmres(theta,Q,Z,MZ,M,v,par) -% Computes iteratively an approximation to the solution -% of the linear system Q'*x = 0 and Atilde*x=r -% where Atilde=(I-Z*Z)*(A-theta*B)*(I-Q*Q'). -% using (I-MZ*(M\Q'))*inv(K) as preconditioner. -% -% If used as implicit preconditioner, then FGMRES. -% -% par=[tol,m] where -% integer m: degree of the minimal residual polynomial -% real tol: residual reduction -% -% nmv: number of MV with Atilde -% rnrm: obtained residual reduction -% -% -- References: Saad -% Same as gmres0. However this variant uses MATLAB built-in functions -% slightly more efficient (see Sleijpen and van den Eshof). -% -% -% Gerard Sleijpen (sleijpen@math.uu.nl) -% Copyright (c) 2002, Gerard Sleijpen - -global Precond_Type - -% -- Initialization -tol=par(1); max_it=par(2); n = size(v,1); -j=0; - -if max_it < 2 | tol>=1, rnrm=1; return, end -%%% 0 step of gmres eq. 1 step of gmres -%%% Then x is a multiple of b - -H = zeros(max_it +1,max_it); Gamma=1; rho=1; - -TP=Precond_Type; -if TP==0 - v=SkewProj(Q,MZ,M,SolvePrecond(v)); rho0 = norm(v); v = v/rho0; -else - v=RepGS(Z,v); rho0=1; -end - -V = zeros(n,0); W=zeros(n,0); -tol0 = 1/(tol*tol); -%% HIST=1; -while (j < max_it) & (rho < tol0) - - V=[V,v]; j=j+1; - [v,w]=PreMV(theta,Q,MZ,M,v); - if TP - if TP == 2, W=[W,w]; end - v=RepGS(Z,v,0); - end - [v,h] = RepGS(V,v); - H(1:size(h,1),j)=h; gamma=H(j+1,j); - - if gamma==0, break %%% Lucky break-down - else - gamma= -Gamma*h(1:j)/gamma; - Gamma=[Gamma,gamma]; - rho=rho+gamma'*gamma; - end - - %% HIST=[HIST;(gamma~=0)/sqrt(rho)]; - -end - -if gamma==0; %%% Lucky break-down - e1=zeros(j,1); e1(1)=rho0; rnrm=0; - if TP == 2 - v=W*(H(1:j,1:j)\e1); - else - v=V*(H(1:j,1:j)\e1); - end -else %%% solve in least square sense - e1=zeros(j+1,1); e1(1)=rho0; rnrm=1/sqrt(rho); - if TP == 2 - v=W*(H(1:j+1,1:j)\e1); - else - v=V*(H(1:j+1,1:j)\e1); - end -end - -if TP==1, v=SkewProj(Q,MZ,M,SolvePrecond(v)); end -%% HIST=log10(HIST+eps); J=[0:size(HIST,1)-1]'; -%% plot(J,HIST(:,1),'*'); drawnow -return -%%%======== END SOLVE CORRECTION EQUATION =============================== - -%%%====================================================================== -%%%======== BASIC OPERATIONS ============================================ -%%%====================================================================== -function [Av,Bv]=MV(v) -% [y,z]=MV(x) -% y=A*x, z=B*x - -% y=MV(x,theta) -% y=(A-theta*B)*x -% - -global Operator_Form Operator_MVs Operator_A Operator_B Operator_Params - - Bv=v; - switch Operator_Form - case 1 % both Operator_A and B are strings - Operator_Params{1}=v; - Av=feval(Operator_A,Operator_Params{:}); - Bv=feval(Operator_B,Operator_Params{:}); - case 2 - Operator_Params{1}=v; - [Av,Bv]=feval(Operator_A,Operator_Params{:}); - case 3 - Operator_Params{1}=v; - Operator_Params{2}='A'; - Av=feval(Operator_A,Operator_Params{:}); - Operator_Params{2}='B'; - Bv=feval(Operator_A,Operator_Params{:}); - case 4 - Operator_Params{1}=v; - Av=feval(Operator_A,Operator_Params{:}); - Bv=Operator_B*v; - case 5 - Operator_Params{1}=v; - Av=feval(Operator_A,Operator_Params{:}); - case 6 - Av=Operator_A*v; - Operator_Params{1}=v; - Bv=feval(Operator_B,Operator_Params{:}); - case 7 - Av=Operator_A*v; - Bv=Operator_B*v; - case 8 - Av=Operator_A*v; - end - - Operator_MVs = Operator_MVs +size(v,2); - -% [Av(1:5,1),Bv(1:5,1)], pause -return -%------------------------------------------------------------------------ -function y=SolvePrecond(y); - -global Precond_Form Precond_L Precond_U Precond_P Precond_Params Precond_Solves - - switch Precond_Form - case 0, - case 1, Precond_Params{1}=y; - y=feval(Precond_L,Precond_Params{:}); - case 2, Precond_Params{1}=y; Precond_Params{2}='preconditioner'; - y=feval(Precond_L,Precond_Params{:}); - case 3, Precond_Params{1}=y; - Precond_Params{1}=feval(Precond_L,Precond_Params{:}); - y=feval(Precond_U,Precond_Params{:}); - case 4, Precond_Params{1}=y; Precond_Params{2}='L'; - Precond_Params{1}=feval(Precond_L,Precond_Params{:}); - Precond_Params{2}='U'; - y=feval(Precond_L,Precond_Params{:}); - case 5, y=Precond_L\y; - case 6, y=Precond_U\(Precond_L\y); - case 7, y=Precond_U\(Precond_L\(Precond_P*y)); - end - - if Precond_Form - Precond_Solves = Precond_Solves +size(y,2); - end -%% y(1:5,1), pause -return -%------------------------------------------------------------------------ -function [v,u]=PreMV(theta,Q,Z,M,v) -% v=Atilde*v - -global Precond_Type - - if Precond_Type - u=SkewProj(Q,Z,M,SolvePrecond(v)); - [v,w]=MV(u); v=theta(2)*v-theta(1)*w; - else - [v,u]=MV(v); u=theta(2)*v-theta(1)*u; - v=SkewProj(Q,Z,M,SolvePrecond(u)); - end - -return -%------------------------------------------------------------------------ -function r=SkewProj(Q,Z,M,r); - - if ~isempty(Q), - r=r-Z*(M\(Q'*r)); - end - -return -%------------------------------------------------------------------------ -function ppar=spar(par,nit) - -k=size(par,2)-2; -ppar=par(1,k:k+2); - -if k>1 - if nit>k - ppar(1,1)=par(1,k)*((par(1,k)/par(1,k-1))^(nit-k)); - else - ppar(1,1)=par(1,max(nit,1)); - end -end - -ppar(1,1)=max(ppar(1,1),1.0e-8); - -return -%------------------------------------------------------------------------ -function u=ImagVector(u) -% computes "essential" imaginary part of a vector - maxu=max(u); maxu=maxu/abs(maxu); u=imag(u/maxu); -return -%------------------------------------------------------------------------ -function Sigma=ScaleEig(Sigma) -% -% - n=sign(Sigma(:,2)); n=n+(n==0); - d=sqrt((Sigma.*conj(Sigma))*[1;1]).*n; - Sigma=diag(d)\Sigma; - -return -%%%======== COMPUTE r AND z ============================================= -function [r,z,nrm,theta]=Comp_rz(E,kappa) -% -% [r,z,nrm,theta]=Comp_rz(E) -% computes the direction r of the minimal residual, -% the left projection vector z, -% the approximate eigenvalue theta -% -% [r,z,nrm,theta]=Comp_rz(E,kappa) -% kappa is a scaling factor. -% - -% coded by Gerard Sleijpen, version Januari 7, 1998 - - if nargin == 1 - kappa=norm(E(:,1))/norm(E(:,2)); kappa=2^(round(log2(kappa))); - end - - if kappa ~=1, E(:,1)=E(:,1)/kappa; end - - [Q,sigma,u]=svd(E,0); %%% E*u=Q*sigma, sigma(1,1)>sigma(2,2) - r=Q(:,2); z=Q(:,1); nrm=sigma(2,2); - % nrm=nrm/sigma(1,1); nrmz=sigma(1,1) - - u(1,:)=u(1,:)/kappa; theta=[-u(2,2),u(1,2)]; - -return -%%%======== END computation r and z ===================================== -%%%====================================================================== -%%%======== Orthogonalisation =========================================== -%%%====================================================================== -function [V,R]=RepGS(Z,V,gamma) -% -% Orthonormalisation using repeated Gram-Schmidt -% with the Daniel-Gragg-Kaufman-Stewart (DGKS) criterion -% -% Q=RepGS(V) -% The n by k matrix V is orthonormalized, that is, -% Q is an n by k orthonormal matrix and -% the columns of Q span the same space as the columns of V -% (in fact the first j columns of Q span the same space -% as the first j columns of V for all j <= k). -% -% Q=RepGS(Z,V) -% Assuming Z is n by l orthonormal, V is orthonormalized against Z: -% [Z,Q]=RepGS([Z,V]) -% -% Q=RepGS(Z,V,gamma) -% With gamma=0, V is only orthogonalized against Z -% Default gamma=1 (the same as Q=RepGS(Z,V)) -% -% [Q,R]=RepGS(Z,V,gamma) -% if gamma == 1, V=[Z,Q]*R; else, V=Z*R+Q; end - -% coded by Gerard Sleijpen, March, 2002 - -% if nargin == 1, V=Z; Z=zeros(size(V,1),0); end -if nargin <3, gamma=1; end - -[n,dv]=size(V); [m,dz]=size(Z); - -if gamma, l0=min(dv+dz,n); else, l0=dz; end -R=zeros(l0,dv); - -if dv==0, return, end -if dz==0 & gamma==0, return, end - -% if m~=n -% if mn, V=[V;zeros(m-n,dv)]; n=m; end -% end - -if (dz==0 & gamma) - j=1; l=1; J=1; - q=V(:,1); nr=norm(q); R(1,1)=nr; - while nr==0, q=rand(n,1); nr=norm(q); end, V(:,1)=q/nr; - if dv==1, return, end -else - j=0; l=0; J=[]; -end - -while j0, yz=Z'*q; q=q-Z*yz; end - if l>0, y=V(:,J)'*q; q=q-V(:,J)*y; end - nr_n=norm(q); - - while (nr_n<0.5*nr_o & nr_n > nr) - if dz>0, sz=Z'*q; q=q-Z*sz; yz=yz+sz; end - if l>0, s=V(:,J)'*q; q=q-V(:,J)*s; y=y+s; end - nr_o=nr_n; nr_n=norm(q); - end - if dz>0, R(1:dz,j)=yz; end - if l>0, R(dz+J,j)=y; end - - if ~gamma - V(:,j)=q; - elseif l+dz 4, kk=max(1,min(gamma,k-1)); end - - %% kappa=max(norm(A,inf)/max(norm(B,inf),1.e-12),1); - %% kappa=2^(round(log2(kappa))); - -%%%------ compute the qz factorization ------- - [S,T,Z,Q]=qz(A,B); Z=Z'; - % kkappa=max(norm(A,inf),norm(B,inf)); - % Str='norm(A*Q-Z*S)';texttest(Str,eval(Str)) - % Str='norm(B*Q-Z*T)';texttest(Str,eval(Str)) - -%%%------ scale the eigenvalues -------------- - t=diag(T); n=sign(t); n=n+(n==0); D=diag(n); - Q=Q/D; S=S/D; T=T/D; - -%%%------ sort the eigenvalues --------------- - I=SortEig(diag(S),real(diag(T)),tau,kappa); - -%%%------ swap the qz form ------------------- - [Q,Z,S,T]=SwapQZ(Q,Z,S,T,I(1:kk)); - % Str='norm(A*Q-Z*S)';texttest(Str,eval(Str)) - % Str='norm(B*Q-Z*T)';texttest(Str,eval(Str)) - - - - if nargin < 6 | size(u,2) ~= 1 - return - else -%%% repeat SwapQZ if angle is too small - kk=min(size(u,1),k); J=1:kk; u=u(J,1)'*Q(J,:); - if abs(u(1,1))>0.7, return, end - for j=2:kk - J=1:j; - if norm(u(1,J))>0.7 - J0=[j,1:j-1]; - [Qq,Zz,Ss,Tt]=SwapQZ(eye(j),eye(j),S(J,J),T(J,J),J0); - if abs(u(1,J)*Qq(:,1))>0.71 - Q(:,J)=Q(:,J)*Qq; Z(:,J)=Z(:,J)*Zz; - S(J,J)=Ss; S(J,j+1:k)=Zz'*S(J,j+1:k); - T(J,J)=Tt; T(J,j+1:k)=Zz'*T(J,j+1:k); - % Str='norm(A*Q-Z*S)';texttest(Str,eval(Str)) - % Str='norm(B*Q-Z*T)';texttest(Str,eval(Str)) - fprintf(' Took %2i:%6.4g\n',j,S(1,1)./T(1,1)) - return - end - end - end - disp([' Selection problem: took ',num2str(1)]) - return - end - -%%%====================================================================== -function I=SortEig(s,t,sigma,kappa); -% -% I=SortEig(S,T,SIGMA) sorts the indices of [S,T] as prescribed by SIGMA -% S and T are K-vectors. -% -% If SIGMA=[ALPHA,BETA] is a complex pair then -% if CHORDALDISTANCE -% sort [S,T] with increasing chordal distance w.r.t. SIGMA. -% else -% sort S./T with increasing distance w.r.t. SIGMA(1)/SIGMA(2) -% -% The chordal distance D between a pair A and a pair B is -% defined as follows. -% Scale A by a scalar F such that NORM(F*A)=1. -% Scale B by a scalar G such that NORM(G*B)=1. -% Then D(A,B)=SQRT(1-ABS((F*A)*(G*B)')). -% -% I=SortEig(S,T,SIGMA,KAPPA). Kappa is a caling that effects the -% chordal distance: [S,KAPPA*T] w.r.t. [SIGMA(1),KAPPA*SIGMA(2)]. - -% coded by Gerard Sleijpen, version April 2002 - -global CHORDALDISTANCE - -if ischar(sigma) - warning off, s=s./t; warning on - switch sigma - case 'LM' - [s,I]=sort(-abs(s)); - case 'SM' - [s,I]=sort(abs(s)); - case 'LR'; - [s,I]=sort(-real(s)); - case 'SR'; - [s,I]=sort(real(s)); - case 'BE'; - [s,I]=sort(real(s)); I=twistdim(I,1); - end -elseif CHORDALDISTANCE - if kappa~=1, t=kappa*t; sigma(2)=kappa*sigma(2); end - n=sqrt(s.*conj(s)+t.*t); - [s,I]=sort(-abs([s,t]*sigma')./n); -else - warning off, s=s./t; warning on - if sigma(2)==0; [s,I]=sort(-abs(s)); - else, [s,I]=sort(abs(s-sigma(1)/sigma(2))); - end -end - -return -%------------------------------------------------------------------------ -function t=twistdim(t,k) - - d=size(t,k); J=1:d; J0=zeros(1,2*d); - J0(1,2*J)=J; J0(1,2*J-1)=flipdim(J,2); I=J0(1,J); - if k==1, t=t(I,:); else, t=t(:,I); end - -return -%%%====================================================================== -function [Q,Z,S,T]=SwapQZ(Q,Z,S,T,I) -% [Q,Z,S,T]=SwapQZ(QQ,ZZ,SS,TT,P) -% QQ and ZZ are K by K unitary, SS and TT are K by K uper triangular. -% P is the first part of a permutation of (1:K)'. -% -% Then Q and Z are K by K unitary, S and T are K by K upper triangular, -% such that, for A = ZZ*SS*QQ' and B = ZZ*T*QQ', we have -% A*Q = Z*S, B*Q = Z*T and LAMBDA(1:LENGTH(P))=LLAMBDA(P) where -% LAMBDA=DIAG(S)./DIAGg(T) and LLAMBDA=DIAG(SS)./DIAG(TT). -% -% Computation uses Givens rotations. -% - -% coded by Gerard Sleijpen, version October 12, 1998 - - - kk=min(length(I),size(S,1)-1); - j=1; while (j<=kk & j==I(j)), j=j+1; end - while j<=kk - i=I(j); - for k = i-1:-1:j, - %%% i>j, move ith eigenvalue to position j - J = [k,k+1]; - q = T(k+1,k+1)*S(k,J) - S(k+1,k+1)*T(k,J); - if q(1) ~= 0 - q = q/norm(q); - G = [[q(2);-q(1)],q']; - Q(:,J) = Q(:,J)*G; - S(:,J) = S(:,J)*G; T(:,J) = T(:,J)*G; - end - if abs(S(k+1,k)) 0) - nselect = min(n,s); - elseif isempty(Sigma) - Sigma = s; - else - jj=[jj,j]; - end - elseif min(size(varargin{j}))==1 & isempty(Sigma) - Sigma = varargin{j}; if size(Sigma,1)==1, Sigma=Sigma'; end - elseif min(size(varargin{j}))==2 & isempty(Sigma) - Sigma = varargin{j}; if size(Sigma,2)>2 , Sigma=Sigma'; end - else - jj=[jj,j]; - end -end - -%------- find parameters for operators ----------- -Operator_Params=[]; Operator_Params{2}=''; -k=length(jj); -if k>0 - Operator_Params(3:k+2)=varargin(jj); - if ~ischar(Operator_A) - msg=sprintf(', %i',jj); - msg=sprintf('Input argument, number%s, not recognized.',msg); - button=questdlg(msg,'Input arguments','Ignore','Stop','Ignore'); - if strcmp(button,'Stop'), n=-1; return, end - end -end -%------- operator B ----------------------------- -if isempty(Operator_B) - if ischar(Operator_A) - Operator_Form=2; % or Operator_Form=3, or Operator_Form=5; - else - Operator_Form=8; - end -else - if ischar(Operator_B) - if ischar(Operator_A), Operator_Form=1; else, Operator_Form=6; end - elseif ischar(Operator_A) - Operator_Form=4; - else - Operator_Form=7; - end -end -if n<2, return, end - -%------- number of eigs to be computed ---------- -if isempty(nselect), nselect=min(n,nselect0); end - -%------------------------------------------------ -%------- Analyse Options ------------------------ -%------------------------------------------------ -fopts = []; -if ~isempty(options), fopts = fieldnames(options); end - -%------- preconditioner ------------------------- -Precond_L=findfield(options,fopts,'pr',[]); -[L,ok]=findfield(options,fopts,'l_',Precond_L); -if ok & ~isempty(Precond_L), - msg =sprintf('A preconditioner is defined in'); - msg =[msg,sprintf('\n''Precond'', but also in ''L_precond''.')]; - msg=[msg,sprintf('\nWhat is the correct one?')]; - button=questdlg(msg,'Preconditioner','L_Precond','Precond','L_Precond'); - if strcmp(button,'L_Precond'), - Precond_L = L; - end -else - Precond_L = L; -end - -if ~isempty(Precond_L) - Precond_U=findfield(options,fopts,'u_',[]); - Precond_P=findfield(options,fopts,'p_',[]); -end - -Precond_Params=[]; Precond_Params{2}=''; -Params=findfield(options,fopts,'par',[]); -[l,k]=size(Params); -if k>0, - if iscell(Params), Precond_Params(3:k+2)=Params; - else, Precond_Params{3}=Params; end -end -TP=findfield(options,fopts,'ty',TP); -n=SetPrecond(n,TP); if n<2, return, end - -%------- max, min dimension search subspace ------ -jmin=min(n,findfield(options,fopts,'jmi',jmin)); -jmax=min(n,findfield(options,fopts,'jma',jmax)); -if jmax < 0 - if jmin<0, jmin=min(n,nselect+p0); end - jmax=min(n,jmin+p1); -else - if jmin<0, jmin=max(1,jmax-p1); end -end -maxit=findfield(options,fopts,'ma',maxit); - -%------- initial search subspace ---------------- -V=findfield(options,fopts,'v',[]); -[m,d]=size(V); -if m~=n - if m>n, V = V(1:n,:); end - if m0 & (ischar(Operator_A) | ischar(Operator_B)) - msgj=sprintf(', %i',jj); msgo=''; - if ischar(Operator_A), msgo=sprintf(' ''%s''',Operator_A); end - if ischar(Operator_B), msgo=sprintf('%s ''%s''.',msgo,Operator_B); end - fprintf(' The JDQZ input arguments, number%s, are\n',msgj) - fprintf(' taken as input parameters 3:%i for%s.\n\n',length(jj)+2,msgo); - end - - fprintf('TARGET\n') - if ischar(Sigma) - fprintf('%13s: ''%s''\n','sigma',Sigma) - else - fprintf('%13s: %s\n','sigma',mydisp(Sigma(1,:))) - for j=2:size(Sigma,1), - fprintf('%13s: %s\n','',mydisp(Sigma(j,:))) - end - end - - fprintf('\nOPTIONS\n') - fprintf('%13s: %g\n','Schur',SCHUR) - fprintf('%13s: %g\n','Tol',tol) - fprintf('%13s: %i\n','Disp',DISP) - fprintf('%13s: %i\n','jmin',jmin) - fprintf('%13s: %i\n','jmax',jmax) - fprintf('%13s: %i\n','MaxIt',maxit) - fprintf('%13s: %s\n','v0',StrOp(V)) - fprintf('%13s: %i\n','Pairs',PAIRS) - fprintf('%13s: %i\n','AvoidStag',JDV) - fprintf('%13s: %i\n','NSigma',NSIGMA) - fprintf('%13s: %g\n','Track',track) - fprintf('%13s: %g\n','FixShift',FIX) - fprintf('%13s: %i\n','Chord',CHORDALDISTANCE) - fprintf('%13s: ''%s''\n','LSolver',lsolver) - str=sprintf('%g ',ls_tol); - fprintf('%13s: [ %s]\n','LS_Tol',str) - fprintf('%13s: %i\n','LS_MaxIt',ls_maxit) - if strcmp(lsolver,'cgstab') - fprintf('%13s: %i\n','LS_ell',ell) - end - - DisplayPreconditioner(n); fprintf('\n') - - switch TS - case 0, str='Standard, W = alpha''*A*V + beta''*B*V'; - case 1, str='Harmonic, W = beta*A*V - alpha*B*V'; - case 2, str='SearchSpace, W = V'; - case 3, str='Petrov, W = B*V'; - case 4, str='Petrov, W = A*V'; - end - fprintf('%13s: %s\n','TestSpace',str); fprintf('\n\n'); - -end - -return -%------------------------------------------------------------------------ -function msg=StrOp(Op) - - if ischar(Op) - msg=sprintf('''%s''',Op); - elseif issparse(Op), [n,k]=size(Op); - msg=sprintf('[%ix%i sparse]',n,k); - else, [n,k]=size(Op); - msg=sprintf('[%ix%i double]',n,k); - end - -return -%------------------------------------------------------------------------ -function DisplayPreconditioner(n) - global Precond_Form Precond_Type ... - Precond_L Precond_U Precond_P - - FP=Precond_Form; - switch Precond_Form - case 0, - fprintf('%13s: %s\n','Precond','No preconditioner'); - case {1,2,5} - fprintf('%13s: %s','Precond',StrOp(Precond_L)); - if FP==2, fprintf(' (M\\v = %s(v,''preconditioner''))',Precond_L); end - fprintf('\n') - case {3,4,6,7} - fprintf('%13s: %s\n','L precond',StrOp(Precond_L)); - fprintf('%13s: %s\n','U precond',StrOp(Precond_U)); - if FP==7, fprintf('%13s: %s\n','P precond',StrOp(Precond_P)); end - if FP==4,fprintf('%15s(M\\v = %s(%s(v,''L''),''U''))\n',... - '',Precond_L,Precond_L); end - end - - if FP - switch Precond_Type - case 0, str='explicit left'; - case 1, str='explicit right'; - case 2, str='implicit'; - end - fprintf('%15sTo be used as %s preconditioner.\n','',str) - end - -return -%------------------------------------------------------------------------ -function possibilities - - fprintf('\n') - fprintf('PROBLEM\n') - fprintf(' A: [ square matrix | string ]\n'); - fprintf(' B: [ square matrix {identity} | string ]\n'); - fprintf(' nselect: [ positive integer {5} ]\n\n'); - fprintf('TARGET\n') - fprintf(' sigma: [ vector of scalars | \n'); - fprintf(' pair of vectors of scalars |\n'); - fprintf(' {''LM''} | {''SM''} | ''LR'' | ''SR'' | ''BE'' ]\n\n'); - - fprintf('OPTIONS\n'); - fprintf(' Schur: [ yes | {no} ]\n'); - fprintf(' Tol: [ positive scalar {1e-8} ]\n'); - fprintf(' Disp: [ yes | {no} ]\n'); - fprintf(' jmin: [ positive integer {nselect+5} ]\n'); - fprintf(' jmax: [ positive integer {jmin+5} ]\n'); - fprintf(' MaxIt: [ positive integer {200} ]\n'); - fprintf(' v0: '); - fprintf('[ size(A,1) by p vector of scalars {rand(size(A,1),1)} ]\n'); - fprintf(' TestSpace: '); - fprintf('[ Standard | {Harmonic} | SearchSpace | BV | AV ]\n'); - fprintf(' Pairs: [ yes | {no} ] \n'); - fprintf(' AvoidStag: [ yes | {no} ]\n'); - fprintf(' Track: [ {yes} | no non-negative scalar {1e-4} ]\n'); - fprintf(' NSigma: [ yes | {no} ]\n'); - fprintf(' FixShift: [ yes | {no} | non-negative scalar {1e+3} ]\n'); - fprintf(' Chord: [ {yes} | no ]\n'); - fprintf(' Scale: [ positive scalar {1} ]\n'); - fprintf(' LSolver: [ {gmres} | bicgstab ]\n'); - fprintf(' LS_Tol: [ row of positive scalar {[0.7,0.49]} ]\n'); - fprintf(' LS_MaxIt: [ positive integer {5} ]\n'); - fprintf(' LS_ell: [ positive integer {4} ]\n'); - fprintf(' Precond: '); - fprintf('[ n by n matrix {identity} | n by 2n matrix | string ]\n'); - fprintf(' L_Precond: same as ''Precond''\n'); - fprintf(' U_Precond: [ n by n matrix {identity} | string ]\n'); - fprintf(' P_Precond: [ n by n matrix {identity} ]\n'); - fprintf(' Type_Precond: [ {left} | right | implicit ]\n'); - fprintf('\n') - - -return -%------------------------------------------------------------------------ -function x = boolean(x,gamma,string) -%Y = BOOLEAN(X,GAMMA,STRING) -% GAMMA(1) is the default. -% If GAMMA is not specified, GAMMA = 0. -% STRING is a cell of accepted strings. -% If STRING is not specified STRING = {'n' 'y'} -% STRING{I} and GAMMA(I) are accepted expressions for X -% If X=GAMMA(I) then Y=X. If the first L characters -% of X matches those of STRING{I}, then Y=GAMMA(I+1). -% Here L=SIZE({STRING{1},2). -% For other values of X, Y=GAMMA(1); - -if nargin < 2, gamma=[0,0,1]; end -if nargin < 3, string={'n' 'y'}; end - -if ischar(x) - l=size(string{1},2); - i=min(find(strncmpi(x,string,l))); - if isempty(i), i=0; end, x=gamma(i+1); -elseif max((gamma-x)==0) -elseif gamma(end) == inf -else, x=gamma(1); -end - -return -%------------------------------------------------------------------------ -function [a,ok]=findfield(options,fopts,str,default,gamma,stri) -% Searches the fieldnames in FOPTS for the string STR. -% The field is detected if only the first part of the fieldname -% matches the string STR. The search is case insensitive. -% If the field is detected, then OK=1 and A is the fieldvalue. -% Otherwise OK=0 and A=DEFAULT - - l=size(str,2); j=min(find(strncmpi(str,fopts,l))); - if ~isempty(j) - a=getfield(options,char(fopts(j,:))); ok=1; - if nargin == 5, a = boolean(a,[default,gamma]); - elseif nargin == 6, a = boolean(a,[default,gamma],stri); end - elseif nargin>3 - a=default; ok=0; - else - a=[]; ok=0; - end - -return -%%%====================================================================== -function n=CheckMatrix(A,gamma) - - if ischar(A), n=-1; - if exist(A) ~=2 - msg=sprintf(' Can not find the M-file ''%s.m'' ',A); - errordlg(msg,'MATRIX'),n=-2; - end - if n==-1 & gamma, eval('n=feval(A,[],''dimension'');','n=-1;'), end - else, [n,n] = size(A); - if any(size(A) ~= n) - msg=sprintf(' The operator must be a square matrix or a string. '); - errordlg(msg,'MATRIX'),n=-3; - end - end - -return -%------------------------------------------------------------------------ -function [Av,Bv,n]=CheckDimMV(v) -% [Av,Bv]=CheckDimMV(v) -% Av=A*v, Bv=B*v Checks correctness operator definitions - -global Operator_Form Operator_MVs Operator_A Operator_B Operator_Params - -[n,k]=size(v); -if k>1, V=v(:,2:k); v=v(:,1); end - -Bv=v; -switch Operator_Form - case 1 % both Operator_A and B are strings - Operator_Params{1}=v; - Av=feval(Operator_A,Operator_Params{:}); - Bv=feval(Operator_B,Operator_Params{:}); - case 2 %%% or Operator_Form=3 or Operator_Form=5??? - Operator_Params{1}=v; - eval('[Av,Bv]=feval(Operator_A,Operator_Params{:});','Operator_Form=3;') - if Operator_Form==3, - ok=1; Operator_Params{2}='A'; - eval('Av=feval(Operator_A,Operator_Params{:});','ok=0;') - if ok, - Operator_Params{2}='B'; - eval('Bv=feval(Operator_A,Operator_Params{:});','ok=0;'), - end - if ~ok, - Operator_Form=5; Operator_Params{2}=''; - Av=feval(Operator_A,Operator_Params{:}); - end - end - case 3 - Operator_Params{1}=v; - Operator_Params{2}='A'; - Av=feval(Operator_A,Operator_Params{:}); - Operator_Params{2}='B'; - Bv=feval(Operator_A,Operator_Params{:}); - case 4 - Operator_Params{1}=v; - Av=feval(Operator_A,Operator_Params{:}); - Bv=Operator_B*v; - case 5 - Operator_Params{1}=v; - Av=feval(Operator_A,Operator_Params{:}); - case 6 - Av=Operator_A*v; - Operator_Params{1}=v; - Bv=feval(Operator_B,Operator_Params{:}); - case 7 - Av=Operator_A*v; - Bv=Operator_B*v; - case 8 - Av=Operator_A*v; -end - -Operator_MVs = 1; - -ok_A=min(size(Av)==size(v)); -ok_B=min(size(Bv)==size(v)); - -if ok_A & ok_B - if k>1, - ok=1; eval('[AV,BV]=MV(V);','ok=0;') - if ok - Av=[Av,AV]; Bv=[Bv,BV]; - else - for j=2:k, [Av(:,j),Bv(:,j)]=MV(V(:,j-1)); end - end - end - return -end - -if ~ok_A - Operator=Operator_A; -elseif ~ok_B - Operator=Operator_B; -end -msg=sprintf(' %s does not produce a vector of size %d',Operator,n) -errordlg(msg,'MATRIX'), n=-1; - -return -%------------------------------------------------------------------------ -function n=SetPrecond(n,TP) -% finds out how the preconditioners are defined (Precond_Form) -% and checks consistency of the definitions. -% -% If M is the preconditioner then P*M=L*U. Defaults: L=U=P=I. -% -% Precond_Form -% 0: no L -% 1: L M-file, no U, L ~= A -% 2: L M-file, no U, L == A -% 3: L M-file, U M-file, L ~= A, U ~= A, L ~=U -% 4: L M-file, U M-file, L == U -% 5: L matrix, no U -% 6: L matrix, U matrix no P -% 7: L matrix, U matrix, P matrix -% -% Precond_Type -% 0: Explicit left -% 1: Explicit right -% 2: Implicit -% - global Operator_A ... - Precond_Form Precond_Solves ... - Precond_Type ... - Precond_L Precond_U Precond_P Precond_Params - - Precond_Type = 0; - if ischar(TP) - TP=lower(TP(1,1)); - switch TP - case 'l' - Precond_Type = 0; - case 'r' - Precond_Type = 1; - case 'i' - Precond_Type = 2; - end - else - Precond_Type=max(0,min(fix(TP),2)); - end - - Precond_Solves = 0; - - % Set type preconditioner - Precond_Form=0; - if isempty(Precond_L), return, end - - if ~isempty(Precond_U) & ischar(Precond_L)~=ischar(Precond_U) - msg=sprintf(' L and U should both be strings or matrices'); - errordlg(msg,'PRECONDITIONER'), n=-1; return - end - if ~isempty(Precond_P) & (ischar(Precond_P) | ischar(Precond_L)) - msg=sprintf(' P can be specified only if P, L and U are matrices'); - errordlg(msg,'PRECONDITIONER'), n=-1; return - end - tp=1+4*~ischar(Precond_L)+2*~isempty(Precond_U)+~isempty(Precond_P); - if tp==1, tp = tp + strcmp(Precond_L,Operator_A); end - if tp==3, tp = tp + strcmp(Precond_L,Precond_U); end - if tp==3 & strcmp(Precond_U,Operator_A) - msg=sprintf(' If L and A use the same M-file,') - msg=[msg,sprintf('\n then so should U.')]; - errordlg(msg,'PRECONDITIONER'), n=-1; return - end - if tp>5, tp=tp-1; end, Precond_Form=tp; - - % Check consistency definitions - if tp<5 & exist(Precond_L) ~=2 - msg=sprintf(' Can not find the M-file ''%s.m'' ',Precond_L); - errordlg(msg,'PRECONDITIONER'), n=-1; return - end - - ok=1; - if tp == 2 - Precond_Params{1}=zeros(n,1); - Precond_Params{2}='preconditioner'; - eval('v=feval(Operator_A,Precond_Params{:});','ok=0;') - if ~ok - msg='Preconditioner and matrix use the same M-file'; - msg=[msg,sprintf(' ''%s.m'' \n',Precond_L)]; - msg=[msg,'Therefore the preconditioner is called as']; - msg=[msg,sprintf('\n\n\tw=%s(v,''preconditioner'')\n\n',Precond_L)]; - msg=[msg,sprintf('Put this "switch" in ''%s.m''.',Precond_L)]; - end - end - - if tp == 4 | ~ok - ok1=1; - Precond_Params{1}=zeros(n,1); - Precond_Params{2}='L'; - eval('v=feval(Precond_L,Precond_Params{:});','ok1=0;') - Precond_Params{2}='U'; - eval('v=feval(Precond_L,Precond_Params{:});','ok1=0;') - if ok1 - Precond_Form = 4; Precond_U = Precond_L; ok=1; - else - if tp == 4 - msg='L and U use the same M-file'; - msg=[msg,sprintf(' ''%s.m'' \n',Precond_L)]; - msg=[msg,'Therefore L and U are called']; - msg=[msg,sprintf(' as\n\n\tw=%s(v,''L'')',Precond_L)]; - msg=[msg,sprintf(' \n\tw=%s(v,''U'')\n\n',Precond_L)]; - msg=[msg,sprintf('Check the dimensions and/or\n')]; - msg=[msg,sprintf('put this "switch" in ''%s.m''.',Precond_L)]; - end - errordlg(msg,'PRECONDITIONER'), n=-1; return - end - end - - if tp==1 | tp==3 - Precond_Params{1}=zeros(n,1); Precond_Params{2}=''; - eval('v=feval(Precond_L,Precond_Params{:});','ok=0') - if ~ok - msg=sprintf('''%s'' should produce %i-vectors',Precond_L,n); - errordlg(msg,'PRECONDITIONER'), n=-1; return - end - end - - if tp==3 - if exist(Precond_U) ~=2 - msg=sprintf(' Can not find the M-file ''%s.m'' ',Precond_U); - errordlg(msg,'PRECONDITIONER'), n=-1; return - else - Precond_Params{1}=zeros(n,1); Precond_Params{2}=''; - eval('v=feval(Precond_U,Precond_Params{:});','ok=0') - if ~ok - msg=sprintf('''%s'' should produce %i-vectors',Precond_U,n); - errordlg(msg,'PRECONDITIONER'), n=-1; return - end - end - end - - if tp==5 - if min([n,2*n]==size(Precond_L)) - Precond_U=Precond_L(:,n+1:2*n); Precond_L=Precond_L(:,1:n); - Precond_Form=6; - elseif min([n,3*n]==size(Precond_L)) - Precond_U=Precond_L(:,n+1:2*n); Precond_P=Precond_L(:,2*n+1:3*n); - Precond_L=Precond_L(:,1:n); Precond_Form=7; - elseif ~min([n,n]==size(Precond_L)) - msg=sprintf('The preconditioning matrix\n'); - msg2=sprintf('should be %iX%i or %ix%i ([L,U])\n',n,n,n,2*n); - msg3=sprintf('or %ix%i ([L,U,P])\n',n,3*n); - errordlg([msg,msg2,msg3],'PRECONDITIONER'), n=-1; return - end - end - - if tp==6 & ~min([n,n]==size(Precond_L) & [n,n]==size(Precond_U)) - msg=sprintf('Both L and U should be %iX%i.',n,n); n=-1; - errordlg(msg,'PRECONDITIONER'), n=-1; return - end - - if tp==7 & ~min([n,n]==size(Precond_L) & ... - [n,n]==size(Precond_U) & [n,n]==size(Precond_P)) - msg=sprintf('L, U, and P should all be %iX%i.',n,n); n=-1; - errordlg(msg,'PRECONDITIONER'), n=-1; return - end - -return -%%%====================================================================== -%%%========= DISPLAY FUNCTIONS =========================================== -%%%====================================================================== -function Result(Sigm,Target,S,T,tol) - - if nargin == 1 - fprintf('\n\n %20s\n','Eigenvalues') - for j=1:size(Sigm,1), - fprintf('%2i %s\n',j,mydisp(Sigm(j,:),5)) - end - return - end - - fprintf('\n\n%17s %25s%18s\n','Targets','Eigenvalues','RelErr/Cond') - for j=1:size(S,1), - l=Target(j,1); s=S(j,:); t=T(j,:); lm=mydisp(s/t,5); - if l>0 - fprintf('%2i %8s ''%s'' %9s %23s',j,'',Sigm(l,:),'',lm) - else - fprintf('%2i %23s %23s',j,mydisp(Target(j,2:3),5),lm) - end - re=1-tol/abs(t); - if re>0, re=(1+tol/abs(s))/re; re=min(re-1,1); else, re=1; end - if re>0.999, fprintf(' 1\n'), else, fprintf(' %5.0e\n',re), end - end - -return - -%------------------------------------------------------------------------ -function s=mydisp(lambda,d) - - if nargin <2, d=4; end - - if size(lambda,2)==2, - if lambda(:,2)==0, s='Inf'; return, end - lambda=lambda(:,1)/lambda(:,2); - end - - a=real(lambda); b=imag(lambda); - if max(a,b)==inf, s='Inf'; return, end - - e=0; - if abs(a)>0; e= floor(log10(abs(a))); end - if abs(b)>0; e= max(e,floor(log10(abs(b)))); end - p=10^d; q=p/(10^e); a=round(a*q)/p; b=round(b*q)/p; - - st=['%',num2str(d+2),'.',num2str(d),'f']; - ab=abs(b)==0; - if ab, str=[''' ']; else, str=['''(']; end - if a>=0, str=[str,'+']; a=abs(a); end, str=[str,st]; - if ab, str=[str,'e']; else - if b>=0, str=[str,'+']; b=abs(b); end, - str=[str,st,'i)e']; end - if e>=0, str=[str,'+']; else, str=[str,'-']; e=-e; end - if e<10, str=[str,'0%i''']; else, str=[str,'%i''']; end - if ab, s=eval(sprintf(str,a,e)); - else, s=eval(sprintf(str,a,b,e)); end - -return -%%%====================================================================== -function ShowEig(theta,target,k) - - if ischar(target) - fprintf('\n target=''%s'', ',target) - else - fprintf('\n target=%s, ',mydisp(target,5)) - end - fprintf('lambda_%i=%s\n',k,mydisp(theta,5)); - -return -%%%====================================================================== -function texttest(s,nr,gamma) - - if nargin<3, gamma=100*eps; end - - if nr > gamma - % if nr>100*eps - fprintf('\n %35s is: %9.3g\t',s,nr) - end - -return -%%%====================================================================== - - diff --git a/code/dimReducMethods/kernel_function.c b/code/dimReducMethods/kernel_function.c deleted file mode 100644 index c5b7dfc..0000000 --- a/code/dimReducMethods/kernel_function.c +++ /dev/null @@ -1,253 +0,0 @@ -#include "mex.h" -#include "math.h" -#include "string.h" - - -void computeKernelRow(double* X, int n, int d, int index, const char* function, int param1, int param2, double* row); -void computeColumnSums(double* X, int n, int d, const char* function, int param1, int param2, double* column_sums, double *total_sum); -void centerKernelRow(double* row, int index, int n, double* column_sums, double *total_sum); - - -void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { - - // Initialize variables - int i, j, n, d; - double *v, *X, *column_sums, *total_sum, *row, *res; - bool center; - char *function, *type; - double param1, param2; - - // Check and process inputs - if(nrhs < 2) { - mexErrMsgTxt("Not enough inputs."); - } - if(mxIsClass(prhs[0], "double")) { - v = (double*) mxGetPr(prhs[0]); - } - else { - mexErrMsgTxt("First input should be of type double."); - } - if(mxIsClass(prhs[1], "double")) { - X = (double*) mxGetPr(prhs[1]); - } - else { - mexErrMsgTxt("Second input should be of type double."); - } - if(nrhs < 3) { - center = true; - } - else { - if(mxIsClass(prhs[2], "logical")) { - center = *((bool*) mxGetPr(prhs[2])); - } - else if(mxIsClass(prhs[2], "uint8")) { - if (*((char*) mxGetPr(prhs[2])) == 0) center = false; - else center = true; - } - else if(mxIsClass(prhs[2], "double")) { - if (*((double*) mxGetPr(prhs[2])) == 0.0) center = false; - else center = true; - } - else { - mexErrMsgTxt("Third input should be of type logical, uint8, or double."); - } - } - if(nrhs < 4) { - function = "kernel"; - } - else { - if(mxIsClass(prhs[3], "char")) { - function = (char*) mxGetPr(prhs[3]); - } - else { - mexErrMsgTxt("Fourth input should be of type char."); - } - } - if(nrhs < 5) { - param1 = 1.0; - } - else { - if(mxIsClass(prhs[4], "double")) { - param1 = *((double*) mxGetPr(prhs[4])); - } - else { - mexErrMsgTxt("Fifth input should be of type double."); - } - } - if(nrhs < 6) { - param2 = 3.0; - } - else { - if(mxIsClass(prhs[5], "double")) { - param2 = *((double*) mxGetPr(prhs[5])); - } - else { - mexErrMsgTxt("Fifth input should be of type double."); - } - } - if(nrhs < 7) { - type = "Normal"; - } - else { - if(mxIsClass(prhs[6], "char")) { - type = (char*) mxGetPr(prhs[6]); - } - else { - mexErrMsgTxt("Sixth input should be of type char."); - } - } - if(mxGetN(prhs[1]) != mxGetM(prhs[0]) && mxGetM(prhs[0]) != 0) { - mexErrMsgTxt("Number of instances does not equal length of vector v."); - } - - // Allocate some memory and set some variables - n = mxGetN(prhs[1]); - d = mxGetM(prhs[1]); - plhs[0] = mxCreateDoubleMatrix(1, n, mxREAL); - res = mxGetPr(plhs[0]); - - // Compute column sums and total sum - if(center || strcmp(type, "C") == 0) { - column_sums = (double*) malloc(n * sizeof(double)); - total_sum = (double*) malloc(sizeof(double)); - for(i = 0; i < n; i++) *(column_sums + i) = 0.0; - *total_sum = 0.0; - computeColumnSums(X, n, d, function, param1, param2, column_sums, total_sum); - - // Return only the column sums if type set to "ColumnSums" - if(strcmp(type, "C") == 0) { - for(i = 0; i < n; i++) { - *(res + i) = *(column_sums + i); - } - free(column_sums); - free(total_sum); - return; - } - } - - // Compute all rows and multiply by v - row = (double*) malloc(n * sizeof(double)); - for(i = 0; i < n; i++) { - - // Compute rows - computeKernelRow(X, n, d, i, function, param1, param2, row); - if(center) { - centerKernelRow(row, i, n, column_sums, total_sum); - } - - // Multiply row by v - *(res + i) = 0.0; - for(j = 0; j < n; j++) { - *(res + i) += (*(row + j) * *(v + j)); - } - } - mexPrintf("."); - - // Clean up some memory - free(row); - if(center) { - free(column_sums); - free(total_sum); - } -} - - -/** - * - * Computes a single row of the kernel matrix, viz. row index. - * - */ -void computeKernelRow(double* X, int n, int d, int index, const char* function, int param1, int param2, double* row) { - - // Initialize variables - int i, j; - - // Compute linear kernel - if(strcmp(function, "l") == 0) { - for(i = 0; i < n; i++) { - *(row + i) = 0.0; - for(j = 0; j < d; j++) { - *(row + i) += *(X + (index * d) + j) * *(X + (i * d) + j); - } - } - } - - // Compute polynomial kernel - else if(strcmp(function, "p") == 0) { - for(i = 0; i < n; i++) { - *(row + i) = 0.0; - for(j = 0; j < d; j++) { - *(row + i) += *(X + (index * d) + j) * *(X + (i * d) + j); - } - *(row + i) = pow(*(row + i) + param1, param2); - } - } - - // Compute Gaussian kernel - else if(strcmp(function, "g") == 0) { - for(i = 0; i < n; i++) { - *(row + i) = 0.0; - for(j = 0; j < d; j++) { - *(row + i) += pow(*(X + (index * d) + j) - *(X + (i * d) + j), 2); - } - *(row + i) = exp(-(*(row + i) / (2 * pow(param1, 2)))); - } - } - - // Unknown kernel function - else { - mexErrMsgTxt("Unknown kernel function."); - } -} - - -/** - * - * Compute all column sums and the total sum of a kernel matrix. - * - */ -void computeColumnSums(double* X, int n, int d, const char* function, int param1, int param2, double* column_sums, double* total_sum) { - - // Initialize variables - int i, j; - double *row; - - // Preallocate memory - row = (double*) malloc(n * sizeof(double)); - for(i = 0; i < n; i++) *(row + i) = 0.0; - *total_sum = 0.0; - - // Compute column sums and total sum - for(i = 0; i < n; i++) { - - // Compute kernel row - computeKernelRow(X, n, d, i, function, param1, param2, row); - - // Update sums - for(j = 0; j < n; j++) { - *(column_sums + j) += *(row + j); - *total_sum += *(row + j); - } - } - *total_sum = *total_sum / pow(n, 2); - - // Clean up memory - free(row); -} - - -/** - * - * Centers a kernel row as computed by computeKernelRow() using precomputed sums (e.g., sums as given by computeColumnSums(...)). - * - */ -void centerKernelRow(double* row, int index, int n, double* column_sums, double* total_sum) { - - // Initialize variables - int i; - - // Update kernel row - for(i = 0; i < n; i++) { - *(row + i) = *(row + i) - (*(column_sums + i) / (double) n) - (*(column_sums + index) / (double) n) + *total_sum; - } -} diff --git a/code/dimReducMethods/kernel_function.m b/code/dimReducMethods/kernel_function.m deleted file mode 100644 index ddf4055..0000000 --- a/code/dimReducMethods/kernel_function.m +++ /dev/null @@ -1,152 +0,0 @@ -function y = kernel_function(v, X, center, kernel, param1, param2, type) -%KERNEL_FUNCTION Computes sum of (K * X) where X is a possible eigenvector -% -% y = kernel_function(v, X, center, kernel, param1, param2) -% -% The function computes the sum of the elements of (K * v), where v is a -% possible eigenvector of K. This function is used to enable the use of -% EIGS in Kernel PCA. The other parameters of the function are the dataset -% X, the name of the kernel function (default = 'gauss'), and its -% corresponding parameters in param1 and param2. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('center', 'var') - center = 0; - end - if ~exist('type', 'var') - type = 'Normal'; - end - if ~strcmp(type, 'ColumnSums'), fprintf('.'); end - - % If no kernel function is specified - if nargin == 2 || strcmp(kernel, 'none') - kernel = 'linear'; - end - - % Construct result vector - y = zeros(1, size(X, 1)); - n = size(X, 2); - - switch kernel - - case 'linear' - % Retrieve information for centering of K - if center || strcmp(type, 'ColumnSums') - column_sum = zeros(1, n); - for i=1:n - % Compute single row of the kernel matrix - K = X(:,i)' * X; - column_sum = column_sum + K; - end - % Compute centering constant over entire kernel - total_sum = ((1 / n^2) * sum(column_sum)); - end - - if ~strcmp(type, 'ColumnSums') - % Compute product K*v - for i=1:n - % Compute single row of the kernel matrix - K = X(:,i)' * X; - - % Center row of the kernel matrix - if center - K = K - ((1 / n) .* column_sum) - ((1 / n) .* column_sum(i)) + total_sum; - end - - % Compute sum of products - y(i) = K * v; - end - else - % Return column sums - y = column_sum; - end - - case 'poly' - - % Initialize some variables - if ~exist('param1', 'var'), param1 = 1; param2 = 3; end - - % Retrieve information for centering of K - if center || strcmp(type, 'ColumnSums') - column_sum = zeros(1, n); - for i=1:n - % Compute column sums of the kernel matrix - K = X(:,i)' * X; - K = (K + param1) .^ param2; - column_sum = column_sum + K; - end - % Compute centering constant over entire kernel - total_sum = ((1 / n^2) * sum(column_sum)); - end - - if ~strcmp(type, 'ColumnSums') - % Compute product K*v - for i=1:n - % Compute row of the kernel matrix - K = X(:,i)' * X; - K = (K + param1) .^ param2; - - % Center row of the kernel matrix - if center - K = K - ((1 / n) .* column_sum) - ((1 / n) .* column_sum(i)) + total_sum; - end - - % Compute sum of products - y(i) = K * v; - end - else - % Return column sums - y = column_sum; - end - - case 'gauss' - - % Initialize some variables - if ~exist('param1', 'var'), param1 = 1; end - - % Retrieve information for centering of K - if center || strcmp(type, 'ColumnSums') - column_sum = zeros(1, n); - for i=1:n - % Compute row sums of the kernel matrix - K = L2_distance(X(:,i), X); - K = exp(-(K.^2 / (2 * param1.^2))); - column_sum = column_sum + K; - end - % Compute centering constant over entire kernel - total_sum = ((1 / n^2) * sum(column_sum)); - end - - if ~strcmp(type, 'ColumnSums') - % Compute product K*v - for i=1:n - % Compute single row of the kernel matrix - K = L2_distance(X(:,i), X); - K = exp(-(K.^2 / (2 * param1.^2))); - - % Center row of the kernel matrix - if center - K = K - ((1 / n) .* column_sum) - ((1 / n) .* column_sum(i)) + total_sum; - end - - % Compute sum of products - y(i) = K * v; - end - else - % Return column sums - y = column_sum; - end - - otherwise - error('Unknown kernel function.'); - end \ No newline at end of file diff --git a/code/dimReducMethods/kernel_function.mexmaci b/code/dimReducMethods/kernel_function.mexmaci deleted file mode 100644 index 9e0794b01968dbec5dd2957b6f3542509ff8191c..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 17228 zcmeHPac~sX8Gn~7aBAd&qzH;|W3QDe4Wwm|RA&T}4N_TTfRi|&+e@-Zu3YZYyIl;H zgV;@!^?ASyw56@>Tss+SD>G#Vidc0xAj3h6m|8>}VH&3?lM}6-=qR-`*WdScFB}-L z?SFN4;qCk0_rC9Y-}igpdkc4O@A${>4v%Aum7;i2%22u_#w0&u9?(zXrm8FC`W0vt zUw)^7n)Jswg}AD!YaKdK_I0^_=XH$DxP~#ROA10%ORTfdRMp0W9uG%b9LD7~p1Fy! 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Possible values are 'linear', -% 'gauss', 'poly', 'subsets', or 'princ_angles' (default = 'gauss'). For -% more info on setting the parameters of the kernel function, type HELP -% GRAM. -% The function returns the locations of the embedded trainingdata in -% mappedX. Furthermore, it returns information on the mapping in mapping. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - kernel = 'gauss'; - param1 = 1; - param2 = 3; - if nargin > 2 - kernel = varargin{1}; - if length(varargin) > 1 & strcmp(class(varargin{2}), 'double'), param1 = varargin{2}; end - if length(varargin) > 2 & strcmp(class(varargin{3}), 'double'), param2 = varargin{3}; end - end - - % Store the number of training and test points - ell = size(X, 1); - - if size(X, 1) < 2000 - - % Compute Gram matrix for training points - disp('Computing kernel matrix...'); - K = gram(X, X, kernel, param1, param2); - - % Normalize kernel matrix K - mapping.column_sums = sum(K) / ell; % column sums - mapping.total_sum = sum(mapping.column_sums) / ell; % total sum - J = ones(ell, 1) * mapping.column_sums; % column sums (in matrix) - K = K - J - J'; - K = K + mapping.total_sum; - - % Compute first no_dims eigenvectors and store these in V, store corresponding eigenvalues in L - disp('Eigenanalysis of kernel matrix...'); - K(isnan(K)) = 0; - K(isinf(K)) = 0; - [V, L] = eig(K); - else - % Compute column sums (for out-of-sample extension) - mapping.column_sums = kernel_function([], X', 1, kernel, param1, param2, 'ColumnSums') / ell; - mapping.total_sum = sum(mapping.column_sums) / ell; - - % Perform eigenanalysis of kernel matrix without explicitly - % computing it - disp('Eigenanalysis of kernel matrix (using slower but memory-conservative implementation)...'); - options.disp = 0; - options.isreal = 1; - options.issym = 1; - [V, L] = eigs(@(v)kernel_function(v, X', 1, kernel, param1, param2, 'Normal'), size(X, 1), no_dims, 'LM', options); - disp(' '); - end - - % Sort eigenvalues and eigenvectors in descending order - [L, ind] = sort(diag(L), 'descend'); - L = L(1:no_dims); - V = V(:,ind(1:no_dims)); - - % Compute inverse of eigenvalues matrix L - disp('Computing final embedding...'); - invL = diag(1 ./ L); - - % Compute square root of eigenvalues matrix L - sqrtL = diag(sqrt(L)); - - % Compute inverse of square root of eigenvalues matrix L - invsqrtL = diag(1 ./ diag(sqrtL)); - - % Compute the new embedded points for both K and Ktest-data - mappedX = sqrtL * V'; % = invsqrtL * V'* K - - % Set feature vectors in original format - mappedX = mappedX'; - - % Store information for out-of-sample extension - mapping.X = X; - mapping.V = V; - mapping.invsqrtL = invsqrtL; - mapping.kernel = kernel; - mapping.param1 = param1; - mapping.param2 = param2; - \ No newline at end of file diff --git a/code/dimReducMethods/landmark_isomap.m b/code/dimReducMethods/landmark_isomap.m deleted file mode 100644 index eb5c47a..0000000 --- a/code/dimReducMethods/landmark_isomap.m +++ /dev/null @@ -1,98 +0,0 @@ -function [mappedX, mapping] = landmark_isomap(X, no_dims, k, percentage) -%ISOMAP Runs the Isomap algorithm -% -% [mappedX, mapping] = landmark_isomap(X, no_dims, k, percentage); -% -% The functions runs the Landmark Isomap algorithm on dataset X to reduce the -% dimensionality of the dataset to no_dims. The number of neighbors used in -% the compuations is set by k (default = 12). The variable percentage has to be -% between 0 and 1, and determines the number of landmarks that is used (default = 0.1). -% -% If the neighborhood graph that is constructed is not completely -% connected, only the largest connected component is embedded. The indices -% of this component are returned in mapping.conn_comp. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('percentage', 'var') - percentage = 0.2; - end - - % Construct neighborhood graph - disp('Constructing neighborhood graph...'); - D = find_nn(X, k); - - % Select largest connected component - blocks = components(D)'; - count = zeros(1, max(blocks)); - for i=1:max(blocks) - count(i) = length(find(blocks == i)); - end - [count, block_no] = max(count); - conn_comp = find(blocks == block_no); - D = D(conn_comp, conn_comp); - mapping.D = D; - n = size(D, 1); - - % Compute shortest paths - disp('Computing shortest paths...'); - landmarks = randperm(n); - landmarks = landmarks(1:round(percentage * n)); - nl = length(landmarks); - D = dijkstra(D, landmarks); - D = full(D)'; - mapping.DD = D; - mapping.landmarks = landmarks; - - % Do not embed in more dimensions than (nl - 1) - if no_dims > nl - 1 - no_dims = nl - 1; - warning(['Target dimensionality reduced to ' num2str(no_dims) '...']); - end - - % Performing MDS using eigenvector implementation - disp('Constructing low-dimensional embedding...'); - D = D .^ 2; - subB = -.5 .* (bsxfun(@minus, bsxfun(@minus, D, sum(D, 2) ./ nl), sum(D, 1) ./ n) + sum(D(:)) ./ (n * nl)); - subB2 = subB' * subB; - subB2(isnan(subB2)) = 0; - subB2(isinf(subB2)) = 0; - [alpha, beta] = eig(subB2); - val = beta .^ (1 / 2); - mapping.invVal = inv(val); - vec = subB * alpha * mapping.invVal; - if size(vec, 2) < no_dims - no_dims = size(vec, 2); - warning(['Target dimensionality reduced to ' num2str(no_dims) '...']); - end - - % Computing final embedding - [val, ind] = sort(real(diag(val)), 'descend'); - vec = vec(:,ind(1:no_dims)); - val = val(1:no_dims); - mappedX = real(bsxfun(@times, vec, sqrt(val)')); - - % Store data for out-of-sample extension - mapping.conn_comp = conn_comp; - mapping.k = k; - mapping.X = X(conn_comp,:); - mapping.alpha = alpha; - mapping.beta = beta; - mapping.no_dims = no_dims; - - \ No newline at end of file diff --git a/code/dimReducMethods/laplacian_eigen.m b/code/dimReducMethods/laplacian_eigen.m deleted file mode 100644 index 33e9a4d..0000000 --- a/code/dimReducMethods/laplacian_eigen.m +++ /dev/null @@ -1,111 +0,0 @@ -function [mappedX, mapping] = laplacian_eigen(X, no_dims, k, sigma, eig_impl) -%LAPLACIAN_EIGEN Performs non-linear dimensionality reduction using Laplacian Eigenmaps -% -% [mappedX, mapping] = laplacian_eigen(X, no_dims, k, sigma, eig_impl) -% -% Performs non-linear dimensionality reduction using Laplacian Eigenmaps. -% The data is in matrix X, in which the rows are the observations and the -% columns the dimensions. The variable dim indicates the preferred amount -% of dimensions to retain (default = 2). The variable k is the number of -% neighbours in the graph (default = 12). -% The reduced data is returned in the matrix mappedX. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('sigma', 'var') - sigma = 1; - end - if ~exist('eig_impl', 'var') - eig_impl = 'Matlab'; - end - - % Construct neighborhood graph - disp('Constructing neighborhood graph...'); - if size(X, 1) < 4000 - G = L2_distance(X', X'); - - % Compute neighbourhood graph - [tmp, ind] = sort(G); - for i=1:size(G, 1) - G(i, ind((2 + k):end, i)) = 0; - end - G = sparse(double(G)); - G = max(G, G'); % Make sure distance matrix is symmetric - else - G = find_nn(X, k); - end - G = G .^ 2; - mapping.max_dist = max(max(G)); - G = G ./ mapping.max_dist; - - % Only embed largest connected component of the neighborhood graph - blocks = components(G)'; - count = zeros(1, max(blocks)); - for i=1:max(blocks) - count(i) = length(find(blocks == i)); - end - [count, block_no] = max(count); - conn_comp = find(blocks == block_no); - G = G(conn_comp, conn_comp); - - % Compute weights (W = G) - disp('Computing weight matrices...'); - - % Compute Gaussian kernel (heat kernel-based weights) - G(G ~= 0) = exp(-G(G ~= 0) / (2 * sigma ^ 2)); - - % Construct diagonal weight matrix - D = diag(sum(G, 2)); - - % Compute Laplacian - L = D - G; - L(isnan(L)) = 0; D(isnan(D)) = 0; - L(isinf(L)) = 0; D(isinf(D)) = 0; - - % Construct eigenmaps (solve Ly = lambda*Dy) - disp('Constructing Eigenmaps...'); - tol = 0; - if strcmp(eig_impl, 'JDQR') - options.Disp = 0; - options.LSolver = 'bicgstab'; - [mappedX, lambda] = jdqz(L, D, no_dims + 1, tol, options); % only need bottom (no_dims + 1) eigenvectors - else - options.disp = 0; - options.isreal = 1; - options.issym = 1; - [mappedX, lambda] = eigs(L, D, no_dims + 1, tol, options); % only need bottom (no_dims + 1) eigenvectors - end - - % Sort eigenvectors in ascending order - lambda = diag(lambda); - [lambda, ind] = sort(lambda, 'ascend'); - lambda = lambda(2:no_dims + 1); - - % Final embedding - mappedX = mappedX(:,ind(2:no_dims + 1)); - - % Store data for out-of-sample extension - mapping.K = G; - mapping.vec = mappedX; - mapping.val = lambda; - mapping.X = X(conn_comp,:); - mapping.sigma = sigma; - mapping.k = k; - mapping.conn_comp = conn_comp; - - \ No newline at end of file diff --git a/code/dimReducMethods/lda.m b/code/dimReducMethods/lda.m deleted file mode 100644 index 17a796a..0000000 --- a/code/dimReducMethods/lda.m +++ /dev/null @@ -1,80 +0,0 @@ -function [mappedX, mapping] = lda(X, labels, no_dims) -%LDA Perform the LDA algorithm -% -% [mappedX, mapping] = lda(X, labels, no_dims) -% -% The function runs LDA on a set of datapoints X. The variable -% no_dims sets the number of dimensions of the feature points in the -% embedded feature space (no_dims >= 1, default = 2). The maximum number -% for no_dims is the number of classes in your data minus 1. -% The function returns the coordinates of the low-dimensional data in -% mappedX. Furthermore, it returns information on the mapping in mapping. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') || isempty(no_dims) - no_dims = 2; - end - - % Make sure data is zero mean - mapping.mean = mean(X, 1); - X = bsxfun(@minus, X, mapping.mean); - - % Make sure labels are nice - [classes, bar, labels] = unique(labels); - nc = length(classes); - - % Intialize Sw - Sw = zeros(size(X, 2), size(X, 2)); - - % Compute total covariance matrix - St = cov(X); - - % Sum over classes - for i=1:nc - - % Get all instances with class i - cur_X = X(labels == i,:); - - % Update within-class scatter - C = cov(cur_X); - p = size(cur_X, 1) / (length(labels) - 1); - Sw = Sw + (p * C); - end - - % Compute between class scatter - Sb = St - Sw; - Sb(isnan(Sb)) = 0; Sw(isnan(Sw)) = 0; - Sb(isinf(Sb)) = 0; Sw(isinf(Sw)) = 0; - - % Make sure not to embed in too high dimension - if nc <= no_dims - no_dims = nc - 1; - warning(['Target dimensionality reduced to ' num2str(no_dims) '.']); - end - - % Perform eigendecomposition of inv(Sw)*Sb - [M, lambda] = eig(Sb, Sw); - - % Sort eigenvalues and eigenvectors in descending order - lambda(isnan(lambda)) = 0; - [lambda, ind] = sort(diag(lambda), 'descend'); - M = M(:,ind(1:min([no_dims size(M, 2)]))); - - % Compute mapped data - mappedX = X * M; - - % Store mapping for the out-of-sample extension - mapping.M = M; - mapping.val = lambda; - - \ No newline at end of file diff --git a/code/dimReducMethods/llc.m b/code/dimReducMethods/llc.m deleted file mode 100644 index 39692a0..0000000 --- a/code/dimReducMethods/llc.m +++ /dev/null @@ -1,112 +0,0 @@ -function mappedX = llc(X, neighbor, no_dims, R, Z, eig_impl) -%LLC Runs the LLC algorithm (given information on the formed factor analyzers) -% -% mappedX = llc(X, k, no_dims, R, Z, eig_impl) -% -% Runs the LLC algorithm (given information on the formed factor -% analyzers). The variable X contains the dataset (transposed), and -% neighbor contains the neighborhood indices for every datapoint. The -% matrices R and Z indicate repectively the responsisbiities of clusters to -% points and the cluster centers. The variable eig_impl determines the -% eigenanalysis method that is used. Possible values are 'Matlab' and -% 'JDQR' (default = 'Matlab'). -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('eig_impl', 'var') - eig_impl = 'Matlab'; - end - - % Initialize some variables - [no_dims N no_analyzers] = size(Z); - if numel(neighbor) == 1 || ischar(neighbor) - nn = neighbor; - else - nn = size(neighbor, 1); - end - kf = no_analyzers * (no_dims + 1); - - % Compute pairwise distances and store neighbor indices - disp(['Find ' num2str(nn) ' nearest neighbors...']); - [foo, neighbor] = find_nn(X', nn); - max_k = size(neighbor, 2); - neighbor = neighbor'; - - % Solve for reconstruction weights of the datapoints - disp('Solving for reconstruction weights...'); - tol = 1e-5; - W = zeros(max_k, N); - for ii=1:N - tmp_ind = neighbor(:,ii); - tmp_ind = tmp_ind(tmp_ind ~= 0); - kt = numel(tmp_ind); - z = X(:,tmp_ind) - X(:,ii * ones(kt, 1)); % shift ith pt to origin - C = z' * z; % local covariance - C = C + eye(kt, kt) * tol * trace(C); % regularization (n > D) - wii = C \ ones(kt, 1); % solve Cw=1 - wii = wii / sum(wii); % enforce sum(w)=1 - W(:,ii) = [wii; nan(max_k - kt, 1)]; - end - - % Compute embedding from bottom eigenvectors of cost matrix M=(I-W)'(I-W) - disp('Computing lowdimensional embeddings...'); - M = sparse(1:N, 1:N, ones(1, N), N, N, 4 * max_k * N); - for i=1:N - w = W(:,i); - w(isnan(w)) = 0; - j = neighbor(:,i); - w = w(j ~= 0); - j = j(j ~= 0); - M(i, j) = M(i, j) - w'; - M(j, i) = M(j, i) - w; - M(j, j) = M(j, j) + w * w'; - end - - % Adds last entry = 1 in posterior mean to handle means of factor analyzers - Z(no_dims + 1,:,:) = 1; - Z = permute(Z, [1 3 2]); - - % Construct responsibility weighted local representation matrix U - R = reshape(R, [1 no_analyzers N]); - U = reshape(repmat(R, [no_dims + 1 1 1]) .* Z, [kf N])'; - - % Construct generalized eigenproblem A*LY = lambda*B*LY - A = M' * U; - A = A' * A; - B = U' * U; - - % Eigenanalysis of generalized eigenproblem - if condest(A) > 1e5 || condest(B) > 1e5 - warning('Matrix badly scaled: results may be inaccurate. Maybe you should use more iterations in the EM-algorithm. Using a lower number of factor analyzers might also overcome this problem.'); - end - if strcmp(eig_impl, 'JDQR') - options.Disp = 0; - options.LSolver = 'bicgstab'; - [LY, evals] = jdqz(A, B, no_dims + 1, 'SM', options); - else - options.disp = 0; - options.isreal = 1; - options.issym = 1; - [LY, evals] = eigs(A, B, no_dims + 1, 'SM', options); - end - - % Sort eigenvectors and eigenvalues in ascending order - [evals, ind] = sort(diag(evals), 'ascend'); - LY = LY(:,ind(2:end)); - - % Normalize eigenvectors - s = sqrt(diag(LY' * B * LY) / N)'; - LY = LY ./ repmat(s, [kf 1]); % normalize LY so that cov(mappedX) = I - - % Final lowdimensional data representation - mappedX = (U * LY)'; - diff --git a/code/dimReducMethods/lle.m b/code/dimReducMethods/lle.m deleted file mode 100644 index 240f3a0..0000000 --- a/code/dimReducMethods/lle.m +++ /dev/null @@ -1,133 +0,0 @@ -function [mappedX, mapping] = lle(X, no_dims, k, eig_impl) -%LLE Runs the locally linear embedding algorithm -% -% mappedX = lle(X, no_dims, k, eig_impl) -% -% Runs the local linear embedding algorithm on dataset X to reduces its -% dimensionality to no_dims. In the LLE algorithm, the number of neighbors -% can be specified by k. -% The function returns the embedded coordinates in mappedX. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('eig_impl', 'var') - eig_impl = 'Matlab'; - end - - % Get dimensionality and number of dimensions - [n, d] = size(X); - - % Compute pairwise distances and find nearest neighbors (vectorized implementation) - disp('Finding nearest neighbors...'); - [distance, neighborhood] = find_nn(X, k); - - % Identify largest connected component of the neighborhood graph - blocks = components(distance)'; - count = zeros(1, max(blocks)); - for i=1:max(blocks) - count(i) = length(find(blocks == i)); - end - [count, block_no] = max(count); - conn_comp = find(blocks == block_no); - - % Update the neighborhood relations - tmp = 1:n; - tmp = tmp(conn_comp); - new_ind = zeros(n, 1); - for i=1:n - ii = find(tmp == i); - if ~isempty(ii), new_ind(i) = ii; end - end - neighborhood = neighborhood(conn_comp,:)'; - for i=1:n - neighborhood(neighborhood == i) = new_ind(i); - end - n = numel(conn_comp); - X = X(conn_comp,:)'; - max_k = size(neighborhood, 1); - - % Find reconstruction weights for all points by solving the MSE problem - % of reconstructing a point from each neighbours. A used constraint is - % that the sum of the reconstruction weights for a point should be 1. - disp('Compute reconstruction weights...'); - if k > d - tol = 1e-5; - else - tol = 0; - end - - % Construct reconstruction weight matrix - W = zeros(max_k, n); - for i=1:n - nbhd = neighborhood(:,i); - nbhd = nbhd(nbhd ~= 0); - kt = numel(nbhd); - z = bsxfun(@minus, X(:,nbhd), X(:,i)); % Shift point to origin - C = z' * z; % Compute local covariance - C = C + eye(kt, kt) * tol * trace(C); % Regularization of covariance (if K > D) - wi = C \ ones(kt, 1); % Solve linear system - wi = wi / sum(wi); % Make sure that sum is 1 - W(:,i) = [wi; nan(max_k - kt, 1)]; - end - - % Now that we have the reconstruction weights matrix, we define the - % sparse cost matrix M = (I-W)'*(I-W). - M = sparse(1:n, 1:n, ones(1, n), n, n, 4 * max_k * n); - for i=1:n - w = W(:,i); - j = neighborhood(:,i); - indices = find(j ~= 0 & ~isnan(w)); - j = j(indices); - w = w(indices); - M(i, j) = M(i, j) - w'; - M(j, i) = M(j, i) - w; - M(j, j) = M(j, j) + w * w'; - end - - % For sparse datasets, we might end up with NaNs or Infs in M. We just set them to zero for now... - M(isnan(M)) = 0; - M(isinf(M)) = 0; - - % The embedding is computed from the bottom eigenvectors of this cost matrix - disp('Compute embedding (solve eigenproblem)...'); - tol = 0; - if strcmp(eig_impl, 'JDQR') - options.Disp = 0; - options.LSolver = 'bicgstab'; - [mappedX, eigenvals] = jdqr(M + eps * eye(n), no_dims + 1, tol, options); - else - options.disp = 0; - options.isreal = 1; - options.issym = 1; - [mappedX, eigenvals] = eigs(M + eps * eye(n), no_dims + 1, tol, options); % only need bottom (no_dims + 1) eigenvectors - end - [eigenvals, ind] = sort(diag(eigenvals), 'ascend'); - if size(mappedX, 2) < no_dims + 1 - no_dims = size(mappedX, 2) - 1; - warning(['Target dimensionality reduced to ' num2str(no_dims) '...']); - end - eigenvals = eigenvals(2:no_dims + 1); - mappedX = mappedX(:,ind(2:no_dims + 1)); % throw away zero eigenvector/value - - % Save information on the mapping - mapping.k = k; - mapping.X = X'; - mapping.vec = mappedX; - mapping.val = eigenvals; - mapping.conn_comp = conn_comp; - mapping.nbhd = distance; diff --git a/code/dimReducMethods/lltsa.m b/code/dimReducMethods/lltsa.m deleted file mode 100644 index 9637fdb..0000000 --- a/code/dimReducMethods/lltsa.m +++ /dev/null @@ -1,104 +0,0 @@ -function [mappedX, mapping] = lltsa(X, no_dims, k, eig_impl) -%LLTSA Runs the linear local tangent space alignment algorithm -% -% [mappedX, mapping] = lltsa(X, no_dims, k, eig_impl) -% -% The function runs the linear local tangent space alignment algorithm on -% dataset% X, reducing the data to dimensionality d. The number of neighbors is -% specified by k. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('eig_impl', 'var') - eig_impl = 'Matlab'; - end - - % Make sure data is zero mean - mapping.mean = mean(X, 1); - X = X - repmat(mapping.mean, [size(X, 1) 1]); - - % Compute neighborhood indices - disp('Find nearest neighbors...'); - n = size(X, 1); - [D, ni] = find_nn(X, k); - - % Compute local information matrix for all datapoints - disp('Compute local information matrices for all datapoints...'); - Bi = {}; - for i=1:n - - % Compute correlation matrix W - Ii = ni(i,:); - Ii = Ii(Ii ~= 0); - kt = numel(Ii); - Xi = X(Ii,:) - repmat(mean(X(Ii,:), 1), [kt 1]); - W = Xi * Xi'; - W = (W + W') / 2; - - % Compute local information by computing d largest eigenvectors of W - [Vi, Si] = schur(W); - [s, Ji] = sort(-diag(Si)); - if length(Ji) < no_dims - no_dims = length(Ji); - warning(['Target dimensionality reduced to ' num2str(no_dims) '...']); - end - Vi = Vi(:,Ji(1:no_dims)); - - % Store eigenvectors in G (Vi is the space with the maximum variance, i.e. a good approximation of the tangent space at point Xi) - % The constant 1/sqrt(k) serves as a centering matrix - Gi = [repmat(1 / sqrt(kt), [kt 1]) Vi]; - - % Compute Bi = I - Gi * Gi' - Bi{i} = eye(kt) - Gi * Gi'; - end - - % Construct sparse matrix B (= alignment matrix) - disp('Construct alignment matrix...'); - B = speye(n); - for i=1:n - Ii = ni(i,:); - Ii = Ii(Ii ~= 0); - B(Ii, Ii) = B(Ii, Ii) + Bi{i}; % sum Bi over all points - B(i, i) = B(i, i) - 1; - end - B = (B + B') / 2; % make sure B is symmetric - - % For sparse datasets, we might end up with NaNs in M. We just set them to zero for now... - B(isnan(B)) = 0; - B(isinf(B)) = 0; - - % Solve generalize eigenproblem XBX'v = lambda * XX'v - disp('Solve eigenproblem...'); - if strcmp(eig_impl, 'JDQR') - options.Disp = 0; - options.LSolver = 'bicgstab'; - [map, D] = jdqz(X' * B * X, X' * X, no_dims, 'SR', options); - else - options.disp = 0; - options.isreal = 1; - options.issym = 1; - [map, D] = eigs(X' * B * X, X' * X, no_dims, 'SR', options); - end - - % Sort eigenvalues and eigenvectors - [D, ind] = sort(diag(D), 'ascend'); - mapping.M = map(:,ind(1:no_dims)); - - % Final embedding coordinates - mappedX = X * mapping.M; - \ No newline at end of file diff --git a/code/dimReducMethods/lmnn.m b/code/dimReducMethods/lmnn.m deleted file mode 100644 index a65ddc7..0000000 --- a/code/dimReducMethods/lmnn.m +++ /dev/null @@ -1,146 +0,0 @@ -function [M, L, Y, C] = lmnn(X, labels) -%LMNN Learns a metric using large-margin nearest neighbor metric learning -% -% [M, L, Y, C] = lmnn(X, labels) -% -% The function uses large-margin nearest neighbor (LMNN) metric learning to -% learn a metric on the data set specified by the NxD matrix X and the -% corresponding Nx1 vector labels. The metric is returned in M. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Initialize some variables - [N, D] = size(X); - assert(length(labels) == N); - [lablist, ~, labels] = unique(labels); - K = length(lablist); - label_matrix = false(N, K); - label_matrix(sub2ind(size(label_matrix), (1:length(labels))', labels)) = true; - same_label = logical(double(label_matrix) * double(label_matrix')); - M = eye(D); - C = Inf; prev_C = Inf; - - % Set learning parameters - min_iter = 50; % minimum number of iterations - max_iter = 1000; % maximum number of iterations - eta = .1; % learning rate - mu = .5; % weighting of pull and push terms - tol = 1e-3; % tolerance for convergence - best_C = Inf; % best error obtained so far - best_M = M; % best metric found so far - no_targets = 3; % number of target neighbors - - % Select target neighbors - sum_X = sum(X .^ 2, 2); - DD = bsxfun(@plus, sum_X, bsxfun(@plus, sum_X', -2 * (X * X'))); - DD(~same_label) = Inf; DD(1:N + 1:end) = Inf; - [~, targets_ind] = sort(DD, 2, 'ascend'); - targets_ind = targets_ind(:,1:no_targets); - targets = false(N, N); - targets(sub2ind([N N], vec(repmat((1:N)', [1 no_targets])), vec(targets_ind))) = true; - - % Compute pulling term between target neigbhors to initialize gradient - slack = zeros(N, N, no_targets); - G = zeros(D, D); - for i=1:no_targets - G = G + (1 - mu) .* (X - X(targets_ind(:,i),:))' * (X - X(targets_ind(:,i),:)); - end - - % Perform main learning iterations - iter = 0; - while (prev_C - C > tol || iter < min_iter) && iter < max_iter - - % Compute pairwise distances under current metric - XM = X * M; - sum_X = sum(XM .* X, 2); - DD = bsxfun(@plus, sum_X, bsxfun(@plus, sum_X', -2 * (XM * X'))); - - % Compute value of slack variables - old_slack = slack; - for i=1:no_targets - slack(:,:,i) = ~same_label .* max(0, bsxfun(@minus, 1 + DD(sub2ind([N N], (1:N)', targets_ind(:,i))), DD)); - end - - % Compute value of cost function - prev_C = C; - C = (1 - mu) .* sum(DD(targets)) + ... % push terms between target neighbors - mu .* sum(slack(:)); % pull terms between impostors - - % Maintain best solution found so far (subgradient method) - if C < best_C - best_C = C; - best_M = M; - end - - % Perform gradient update - for i=1:no_targets - - % Add terms for new violations - [r, c] = find(slack(:,:,i) > 0 & old_slack(:,:,i) == 0); - G = G + mu .* ((X(r,:) - X(targets_ind(r, i),:))' * ... - (X(r,:) - X(targets_ind(r, i),:)) - ... - (X(r,:) - X(c,:))' * (X(r,:) - X(c,:))); - - % Remove terms for resolved violations - [r, c] = find(slack(:,:,i) == 0 & old_slack(:,:,i) > 0); - G = G - mu .* ((X(r,:) - X(targets_ind(r, i),:))' * ... - (X(r,:) - X(targets_ind(r, i),:)) - ... - (X(r,:) - X(c,:))' * (X(r,:) - X(c,:))); - end - M = M - (eta ./ N) .* G; - - % Project metric back onto the PSD cone - [V, L] = eig(M); - V = real(V); L = real(L); - ind = find(diag(L) > 0); - if isempty(ind) - warning('Projection onto PSD cone failed. All eigenvalues were negative.'); break - end - M = V(:,ind) * L(ind, ind) * V(:,ind)'; - if any(isinf(M(:))) - warning('Projection onto PSD cone failed. Metric contains Inf values.'); break - end - if any(isnan(M(:))) - warning('Projection onto PSD cone failed. Metric contains NaN values.'); break - end - - % Update learning rate - if prev_C > C - eta = eta * 1.01; - else - eta = eta * .5; - end - - % Print out progress - iter = iter + 1; - no_slack = sum(slack(:) > 0); - if rem(iter, 10) == 0 - [~, sort_ind] = sort(DD, 2, 'ascend'); - disp(['Iteration ' num2str(iter) ': error is ' num2str(C ./ N) ... - ', nearest neighbor error is ' num2str(sum(labels(sort_ind(:,2)) ~= labels) ./ N) ... - ', number of constraints: ' num2str(no_slack)]); - end - end - - % Return best metric and error - M = best_M; - C = best_C; - - % Compute mapped data - [L, S, ~] = svd(M); - L = bsxfun(@times, sqrt(diag(S)), L); - Y = X * L; -end - -function x = vec(x) - x = x(:); -end diff --git a/code/dimReducMethods/lmvu.m b/code/dimReducMethods/lmvu.m deleted file mode 100644 index 44c2c14..0000000 --- a/code/dimReducMethods/lmvu.m +++ /dev/null @@ -1,292 +0,0 @@ -function [mappedX, mapping] = lmvu(X, no_dims, K, LL) -%LMVU Performs Landmark MVU on dataset X -% -% [mappedX, mapping] = lmvu(X, no_dims, k1, k2) -% -% The function performs Landmark MVU on the DxN dataset X. The value of k1 -% represents the number of nearest neighbors that is employed in the MVU -% constraints. The value of k2 represents the number of nearest neighbors -% that is employed to compute the reconstruction weights (for embedding the -% non-landmark points). -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - - if ~exist('K', 'var') - K = 3; - end - if ~exist('LL', 'var') - LL = 12; - end - - % Save some data for out-of-sample extension - if ischar(K) - error('Adaptive neighborhood selection not supported for landmark MVU.'); - end - mapping.k1 = K; - mapping.k2 = LL; - mapping.X = X; - - % Initialize some variables - N = size(X, 2); % number of datapoints - B = ceil(0.02 * N); % number of landmark points - - % Set some parameters parameters - pars.ep = eps; - pars.fastmode = 1; - pars.warmup = K * B / N; - pars.verify = 1; - pars.angles = 1; - pars.maxiter = 100; - pars.noise = 0; - pars.ignore = 0.1; - pars.penalty = 1; - pars.factor = 0.9999; - - % Identify nearest neighbors - disp('Identifying nearest neighbors...'); - KK = max(LL, K); - X = L2_distance(X, X); % memory-intensive: O(n^{2}) !!! - [foo, neighbors] = find_nn(X, KK); - neighbors = neighbors'; - - % Get inverse of reconstruction weight matrix - Pia = getPia(B, LL, X, neighbors); - - % Generate SDP problem - disp('Generating SDP problem...'); - neighbors = neighbors(1:K,:); - clear temp index sorted - nck = nchoosek(1:K + 1, 2); - AA = zeros(N * K, 2); - pos3 = 1; - for i=1:N - ne = neighbors(:,i); - nne = [ne; i]; - pairs = nne(nck); - js = pairs(:,1); - ks = pairs(:,2); - AA(pos3:pos3 + length(js) - 1,:) = sort([js ks], 2); - pos3 = pos3 + length(js); - if i == B - AA = unique(AA, 'rows'); - ForceC = size(AA, 1); - end - if pos3 > size(AA, 1) && i < N - AA = unique(AA, 'rows'); - pos3 = size(AA, 1) + 1; - AA = [AA; zeros(round(N / (N - i) * pos3), 2)]; - fprintf('.'); - end - end - AA = unique(AA, 'rows'); - AA = AA(2:end,:); - clear neighbors ne v2 v3 js ks - bb = zeros(1, size(AA, 1)); - for i=1:size(AA, 1) - bb(i) = sum((X(:,AA(i, 1)) - X(:,AA(i, 2))) .^ 2); - end - disp(' '); - - % Reduce the number of forced vectors - ii = (1:ForceC)'; - jj = zeros(1, size(AA, 1)); - jj(ii) = 1; - jj = find(jj == 0); - jj1 = jj(jj <= ForceC); - jj2 = jj(jj > ForceC); - jj2 = jj2(randperm(length(jj2))); - jj1 = jj1(randperm(length(jj1))); - corder = [ii; jj1'; jj2']; - AA = AA(corder,:); - bb = bb(corder); - ForceC = length(ii); - clear temp jj1 jj2 jj ii - Const = max(round(pars.warmup * size(AA, 1)), ForceC); - [A, b, AA, bb] = getConstraints(AA, Pia, bb, B, Const, pars); - Qt = sum(Pia, 1)' * sum(Pia, 1); - A = [Qt(:)'; A]; - b = [0; b]; - clear K; - solved = 0; - - % Start SDP iterations - disp('Perform semi-definite programming...'); - disp('CSDP OUTPUT ============================================================================='); - while solved == 0 - - % Initialize some variables - c = -vec(Pia' * Pia); - flags.s = B; - flags.l = size(A, 1) - 1; - A = [[zeros(1,flags.l); speye(flags.l)] A]; - - % Set c (employ penalty) - c = [ones(ForceC, 1) .* max(max(c)); zeros(flags.l - ForceC, 1); c]; - - % Launch the CSDP solver - options.maxiter=pars.maxiter; - [x, d, z, info] = csdp(A, b, c, flags, options); - K = mat(x(flags.l + 1:flags.l + flags.s ^ 2)); - - % Check whether a solution is reached - solved = isempty(AA); - A = A(:,flags.l + 1:end); - xx = K(:); - if size(AA, 1) - Aold = size(A,1); - total = 0; - while size(A, 1) - Aold < Const && ~isempty(AA) - [newA, newb, AA, bb] = getConstraints(AA, Pia, bb, B, Const, pars); - jj = find(newA * xx - newb > pars.ignore * abs(newb)); - if info == 2 - jj = 1:size(newA, 1); - end - total = total + length(jj); - A(size(A,1) + 1:size(A,1) + length(jj),:) = newA(jj,:); - b(length(b) + 1:length(b) + length(jj)) = newb(jj); - end - if total == 0 - solved = 1; - end - else - solved=1; - end - if solved == 1 && pars.maxiter < 100 - pars.maxiter = 100; - end - end - disp('========================================================================================='); - - % Perform eigendecomposition of kernel matrix to compute Y - disp('Perform eigendecomposition to obtain low-dimensional data representation...'); - [V, D] = eig(K); - V = V * sqrt(D); - Y = (V(:,end:-1:1))'; - mappedX = Y * Pia'; - - % Reorder data in original order - mappedX = mappedX(1:no_dims,:); - - % Set some information for the out-of-sample extension - mapping.Y = Y; - mapping.D = X; - mapping.no_landmarks = B; - mapping.no_dims = no_dims; - - - -% Function that computes LLE weight matrix -function Q = getPia(B, LL, X, neighbors) - - % Initialize some variables - N = size(X,2); - - % Compute reconstruction weights - disp('Computing reconstruction weights...'); - tol = 1e-7; - Pia = sparse([], [], [], B, N); - for i=1:N - z = X(:,neighbors(:,i)) - repmat(X(:,i), 1, LL); - C = z' * z; - C = C + tol * trace(C) * eye(LL) / LL; - invC = inv(C); - Pia(neighbors(:,i),i) = sum(invC)' / sum(sum(invC)); - end - - % Fill sparse LLE weight matrix - M = speye(N) + sparse([], [], [], N, N, N * LL .^ 2); - for i=1:N - j = neighbors(:,i); - w = Pia(j, i); - M(i, j) = M(i, j) - w'; - M(j, i) = M(j, i) - w; - M(j, j) = M(j, j) + w * w'; - end - - % Invert LLE weight matrix - disp('Invert reconstruction weight matrix...'); - Q = -M(B + 1:end, B + 1:end) \ M(B + 1:end, 1:B); - Q = [eye(B); Q]; - - - -% Functions that constructs the constraints for the SDP -function [A, b, AAomit, bbomit] = getConstraints(AA, Pia, bb, B, Const, pars) - - % Initialize some variables - pos2 = 0; - perm = 1:size(AA,1); - if size(AA, 1) > Const - AAomit = AA(perm(Const + 1:end),:); - bbomit = bb(perm(Const + 1:end)); - AA = AA(perm(1:Const),:); - bb = bb(perm(1:Const)); - else - AAomit = []; - bbomit = []; - end - - % Allocate some memory - persistent reqmem; - if isempty(reqmem) - A2 = zeros(size(AA, 1) * B, 3); - else - A2 = zeros(reqmem, 3); - end - - % Set the constraints - pos = 0; - for j=1:size(AA, 1) - - % Evaluate for current row in AA - ii = AA(j, 1); - jj = AA(j, 2); - Q = Pia(ii,:)' * Pia(ii,:) - 2 .* Pia(jj,:)' * Pia(ii,:) + Pia(jj,:)' * Pia(jj,:); - Q = (Q + Q') ./ 2; - it = find(abs(Q) > pars.ep .^ 2); - - % Constraint found - if ~isempty(it) - - % Allocate more memory if needed - pos = pos + 1; - if pos2 + length(it) > size(A2, 1) - A2 = [A2; zeros(ceil((size(AA, 1) - j) / j * size(A2, 1)), 3)]; - end - - % Set constraint - A2(1 + pos2:pos2 + length(it), 1) = ones(length(it), 1) .* pos; - A2(1 + pos2:pos2 + length(it), 2) = it; - A2(1 + pos2:pos2 + length(it), 3) = full(Q(it)); - pos2 = pos2 + length(it); - end - end - - % Construct sparse constraint matrix - reqmem = pos2; - A2 = A2(1:pos2,:); - A = sparse(A2(:,1), A2(:,2), A2(:,3), size(AA,1), B .^ 2); - b = bb'; - - - -% Function that vectorizes a matrix -function v = vec(M) - v = M(:); - - - -% Function that matrixizes a vector -function M = mat(C) - r = round(sqrt(size(C, 1))); - M = reshape(C, r, r); - diff --git a/code/dimReducMethods/lpp.m b/code/dimReducMethods/lpp.m deleted file mode 100644 index a6f28c8..0000000 --- a/code/dimReducMethods/lpp.m +++ /dev/null @@ -1,99 +0,0 @@ -function [mappedX, mapping] = lpp(X, no_dims, k, sigma, eig_impl) -%LPP Perform linearity preserving projection -% -% [mappedX, mapping] = lpp(X, no_dims, k, sigma, eig_impl) -% -% Perform the Linearity Preserving Projection on dataset X to reduce it to -% dimensionality no_dims. The number of neighbors that is used by LPP is -% specified by k (default = 12). The variable sigma determines the -% bandwidth of the Gaussian kernel (default = 1). -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if size(X, 2) > size(X, 1) - error('Number of samples should be higher than number of dimensions.'); - end - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('sigma', 'var') - sigma = 1; - end - if ~exist('eig_impl', 'var') - eig_impl = 'Matlab'; - end - - % Construct neighborhood graph - disp('Constructing neighborhood graph...'); - if size(X, 1) < 4000 - G = L2_distance(X', X'); - % Compute neighbourhood graph - [tmp, ind] = sort(G); - for i=1:size(G, 1) - G(i, ind((2 + k):end, i)) = 0; - end - G = sparse(double(G)); - G = max(G, G'); % Make sure distance matrix is symmetric - else - G = find_nn(X, k); - end - G = G .^ 2; - G = G ./ max(max(G)); - - % Compute weights (W = G) - disp('Computing weight matrices...'); - - % Compute Gaussian kernel (heat kernel-based weights) - G(G ~= 0) = exp(-G(G ~= 0) / (2 * sigma ^ 2)); - - % Construct diagonal weight matrix - D = diag(sum(G, 2)); - - % Compute Laplacian - L = D - G; - L(isnan(L)) = 0; D(isnan(D)) = 0; - L(isinf(L)) = 0; D(isinf(D)) = 0; - - % Compute XDX and XLX and make sure these are symmetric - disp('Computing low-dimensional embedding...'); - DP = X' * D * X; - LP = X' * L * X; - DP = (DP + DP') / 2; - LP = (LP + LP') / 2; - - % Perform eigenanalysis of generalized eigenproblem (as in LEM) - if size(X, 1) > 200 && no_dims < (size(X, 1) / 2) - if strcmp(eig_impl, 'JDQR') - options.Disp = 0; - options.LSolver = 'bicgstab'; - [eigvector, eigvalue] = jdqz(LP, DP, no_dims, 'SA', options); - else - options.disp = 0; - options.issym = 1; - options.isreal = 1; - [eigvector, eigvalue] = eigs(LP, DP, no_dims, 'SA', options); - end - else - [eigvector, eigvalue] = eig(LP, DP); - end - - % Sort eigenvalues in descending order and get smallest eigenvectors - [eigvalue, ind] = sort(diag(eigvalue), 'ascend'); - eigvector = eigvector(:,ind(1:no_dims)); - - % Compute final linear basis and map data - mappedX = X * eigvector; - mapping.M = eigvector; - mapping.mean = mean(X, 1); diff --git a/code/dimReducMethods/ltsa.m b/code/dimReducMethods/ltsa.m deleted file mode 100644 index c5cf73c..0000000 --- a/code/dimReducMethods/ltsa.m +++ /dev/null @@ -1,104 +0,0 @@ -function mappedX = ltsa(X, no_dims, k, eig_impl) -%LTSA Runs the local tangent space alignment algorithm -% -% mappedX = ltsa(X, no_dims, k, eig_impl) -% -% The function runs the local tangent space alignment algorithm on dataset -% X, reducing the data to dimensionality d. The number of neighbors is -% specified by k. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - if ~exist('k', 'var') - k = 12; - end - if ~exist('eig_impl', 'var') - eig_impl = 'Matlab'; - end - - % Compute neighborhood indices - if ischar(k) - warning('Adaptive neighborhood selection often leads to problems in LTSA.'); - end - disp('Find nearest neighbors...'); - n = size(X, 1); - [D, ni] = find_nn(X, k); - - % Compute local information matrix for all datapoints - disp('Compute local information matrices for all datapoints...'); - Bi = cell(1, n); - for i=1:n - % Compute correlation matrix W - Ii = ni(i,:); - Ii = Ii(Ii ~= 0); - kt = numel(Ii); - Xi = X(Ii,:) - repmat(mean(X(Ii,:), 1), [kt 1]); - W = Xi * Xi'; - W = (W + W') / 2; - - % Compute local information by computing d largest eigenvectors of W - [Vi, Si] = schur(W); - [s, Ji] = sort(-diag(Si)); - if length(Ji) < no_dims - no_dims = length(Ji); - warning(['Target dimensionality reduced to ' num2str(no_dims) '...']); - end - Vi = Vi(:,Ji(1:no_dims)); - - % Store eigenvectors in G (Vi is the space with the maximum variance, i.e. a good approximation of the tangent space at point Xi) - % The constant 1/sqrt(kt) serves as a centering matrix - Gi = double([repmat(1 / sqrt(kt), [kt 1]) Vi]); - - % Compute Bi = I - Gi * Gi' - Bi{i} = eye(kt) - Gi * Gi'; - end - - % Construct sparse matrix B (= alignment matrix) - disp('Construct alignment matrix...'); - B = speye(n); - for i=1:n - Ii = ni(i,:); - Ii = Ii(Ii ~= 0); - B(Ii, Ii) = B(Ii, Ii) + Bi{i}; % sum Bi over all points - B(i, i) = B(i, i) - 1; - end - B = (B + B') / 2; % make sure B is symmetric - - % For sparse datasets, we might end up with NaNs in M. We just set them to zero for now... - B(isnan(B)) = 0; - B(isinf(B)) = 0; - - % Perform eigenanalysis of matrix B - disp('Perform eigenanalysis...'); - tol = 0; - if strcmp(eig_impl, 'JDQR') - options.Disp = 0; - options.LSolver = 'bicgstab'; - [mappedX, D] = jdqr(B, no_dims + 1, tol, options); % only need bottom (no_dims + 1) eigenvectors - else - options.disp = 0; - options.isreal = 1; - options.issym = 1; - [mappedX, D] = eigs(B, no_dims + 1, tol, options); % only need bottom (no_dims + 1) eigenvectors - end - - % Sort eigenvalues and eigenvectors - [D, ind] = sort(diag(D), 'ascend'); - mappedX = mappedX(:,ind); - - % Final embedding coordinates - if size(mappedX, 2) < no_dims + 1, no_dims = size(mappedX, 2) - 1; end - mappedX = mappedX(:,2:no_dims + 1); - \ No newline at end of file diff --git a/code/dimReducMethods/mcml.m b/code/dimReducMethods/mcml.m deleted file mode 100644 index e615b41..0000000 --- a/code/dimReducMethods/mcml.m +++ /dev/null @@ -1,72 +0,0 @@ -function mapping = mcml(X, labels, no_dims) -%MCML Performs MCML on the specified dataset -% -% mapping = mcml(X, labels, no_dims) -% -% Performs linear Maximally Collapsing Metric Learning (MCML) on the -% dataset specified through X and labels. The function returns a -% Mahalanobis metrix in M. Distances through the metric are thus given by -% D(x, y) = (x - y) * A * (x - y)'. -% It the does an SVD on A gives you a (low-rank) projection of the data -% into a space where the squared Euclidean distance corresponds to the -% learned Mahalanobis metric in the original space. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Make sure data is zero mean - mapping.mean = mean(X, 1); - X = bsxfun(@minus, X, mapping.mean); - - % Initialize some variables - [n, d] = size(X); - max_iter = 100; - - % Construct matrix with label information - P = zeros(n, n); - [foo, bar, labels] = unique(labels); - for i=1:max(labels) - ind = find(labels == i); - P(ind, ind) = 1; - end - P(1:n+1:end) = 0; - P = bsxfun(@rdivide, P, sum(P, 2)); - P = max(P, realmin); - - % Initialize solution - A = randn(d, d) * .0001; - A = (A + A') + eye(d); - iter = 0; - converged = false; - - % Run iterations - while iter < max_iter && ~converged - - % Perform gradient step - iter = iter + 1; - disp(['Iteration ' num2str(iter) '...']); - [A, f] = minimize(A(:), 'mcml_grad', 5, X, P); - A = reshape(A, [d d]); - if isempty(f) || f(end) - f(1) > -1e-4 - disp('Converged!'); - converged = true; - end - - % Project A back onto the cone of PSD matrices - [vec, val] = eig(A); - val = diag(val); - ind = find(val > 0); - A = real(bsxfun(@times, val(ind)', vec(:,ind)) * vec(:,ind)'); - end - - % Obtain low-dimensional representation - [mapping.M, foo, bar] = svd(A); - mapping.M = mapping.M(:,1:no_dims); diff --git a/code/dimReducMethods/mcml_grad.m b/code/dimReducMethods/mcml_grad.m deleted file mode 100644 index 98d1fec..0000000 --- a/code/dimReducMethods/mcml_grad.m +++ /dev/null @@ -1,49 +0,0 @@ -function [C, dA] = mcml_grad(x, X, P) -%MCML_GRAD Computes MCML cost function and gradient -% -% [C, dA] = mcml_grad(x, X, P) -% -% Computes MCML cost function and gradient. -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - % Decode solution - [n, d] = size(X); - A = reshape(x, [d d]); - - % Compute conditional probabilities for current solution - D = zeros(n, n); - for i=1:n - diffX = bsxfun(@minus, X(i,:), X(i + 1:end,:)); - dist = sum((diffX * A) .* diffX, 2); - D(i + 1:end, i) = dist; - D(i, i + 1:end) = dist'; - end - Q = exp(-D); - Q(1:n+1:end) = 0; - Q = bsxfun(@rdivide, Q, sum(Q, 2)); - Q = max(Q, realmin); - - % Compute cost function - C = sum(P(:) .* log(P(:) ./ Q(:))); - - % Compute gradient with respect to A - if nargin > 1 - dA = zeros(d, d); - PQ = P - Q; - for i=1:n - diffX = bsxfun(@minus, X(i,:), X); - dA = dA + bsxfun(@times, PQ(i,:), diffX') * diffX; - end - end - dA = dA(:); - \ No newline at end of file diff --git a/code/dimReducMethods/mds.m b/code/dimReducMethods/mds.m deleted file mode 100644 index e9336b2..0000000 --- a/code/dimReducMethods/mds.m +++ /dev/null @@ -1,28 +0,0 @@ -function mappedX = mds(X, no_dims) -%MDS Run MDS on the data to get a low-dimensional visualization -% -% mappedX = mds(X, no_dims) -% -% Run multidimensional scaling on the dataset X to get a two-dimensional -% visualization. The low-dimensional representation is returned in mappedX. -% It has dimensionality no_dims (default = 2). -% -% - -% This file is part of the Matlab Toolbox for Dimensionality Reduction. -% The toolbox can be obtained from http://homepage.tudelft.nl/19j49 -% You are free to use, change, or redistribute this code in any way you -% want for non-commercial purposes. However, it is appreciated if you -% maintain the name of the original author. -% -% (C) Laurens van der Maaten, Delft University of Technology - - - if ~exist('no_dims', 'var') - no_dims = 2; - end - - % NOTE: Classical scaling is identical to performing PCA, except the - % input data is different. Specifying pairwise similarity data is not - % yet supported by the toolbox. - mappedX = compute_mapping(X, 'PCA', no_dims); \ No newline at end of file diff --git a/code/dimReducMethods/mexCCACollectData.c b/code/dimReducMethods/mexCCACollectData.c deleted file mode 100644 index cb1af60..0000000 --- a/code/dimReducMethods/mexCCACollectData.c +++ /dev/null @@ -1,281 +0,0 @@ -/* - * - * mexCCACollectdata.c - * prepare data for cca.m to form SDP - * - * by feisha@cis.upenn.edu - */ - - #include "mex.h" - #include "matrix.h" -#include -#include -#include -#include - - /* the computation engine */ -void collectdata(double *x, double *y, int* edgerow, int *edgecol, int *relative, -int *nv, int *vidx, int D, int d, int n, int ks, double *a, double *b, double *g); - -/* auxiliary functions */ -void sanity_check(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]); - -/* the gateway */ -void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) -{ - int n, ks=1, D, d; - double *x, *y, *a, *b, *g; - int *neighbors; - - /* sanity_check(nlhs, plhs, nrhs, prhs); */ - - n = mxGetN(prhs[0]); - D = mxGetM(prhs[0]); - d = mxGetM(prhs[1]); - /*printf("%d data points, reducing from dimension %d ---> dimension %d, using \ -%d nearest neighbors\n", n, D, d, ks); */ - - plhs[0] = mxCreateDoubleMatrix(d*d, d*d, mxREAL); - plhs[1] = mxCreateDoubleMatrix(d*d, n, mxREAL); - plhs[2] = mxCreateDoubleMatrix(n,1, mxREAL); - - collectdata( (double*)mxGetData(prhs[0]), - (double*)mxGetData(prhs[1]), - (int*)mxGetData(prhs[2]), - (int*)mxGetData(prhs[3]), - (int*)mxGetData(prhs[4]), - (int*)mxGetData(prhs[5]), - (int*)mxGetData(prhs[6]), - D, d, n, ks, - (double*)mxGetData(plhs[0]), - (double*)mxGetData(plhs[1]), - (double*)mxGetData(plhs[2])); - return; -} - - -/* check input arguments */ -void sanity_check(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) -{ - int n1, n2, n3; - /* Check for proper number of input and output arguments. */ - if (nrhs != 4) { - mexErrMsgTxt("Four input argument required."); - } - if (nlhs != 3) { - mexErrMsgTxt("Three output arguments required."); - } - - /* Check data type of input argument. */ - /*if (!(mxIsDouble(prhs[0])) || !(mxIsDouble(prhs[1])) || !(mxIsDouble(prhs[2]))) { - mexErrMsgTxt("Input array must be of type double."); - }*/ - - /* Check dimensions */ - if(mxGetNumberOfDimensions(prhs[0])!=2 || mxGetNumberOfDimensions(prhs[1])!=2 || mxGetNumberOfDimensions(prhs[2])!=2) { - mexErrMsgTxt("Input arrays must be two-dimension arrays"); - } - - /* matching dimensions */ - n1 = mxGetN(prhs[0]); - n2 = mxGetN(prhs[1]); - n3 = mxGetN(prhs[2]); - if (n1 != n2 || n1 !=n3) { - mexErrMsgTxt("Input arrays must have same number of columns!"); - } - return; -} - -/* computing */ -double vecdot(double* v1, int n) { /* v1'*v2 */ - double x = 0; - int i; - for(i = 0; i < n; i++) { - x += v1[i]*v1[i]; - } - return x; -} -void vecsub(double* v1,double* v2, double* v3, int n) { /* v3=v1-v2 */ - int incx=1; - double none = -1; - /* dcopy_(&n, v1, &incx,v3, &incx); - daxpy_(&n, &none, v2, &incx, v3, &incx);*/ - int i; - for(i=0;i= nn_start) { - for(nn=nn_start; nn<=nn_end; nn++) { - j = edgesrow[nn]; - - /* compute diffx and diffy */ - vecsub(x+i*D, x+j*D, diffx, D); - gij = vecdot(diffx, D); - - vecsub(y+i*d, y+j*d, diffy, d); - vecout(diffy, yij, d); - - /* update A, b */ - updateA(tempA, yij, 1.0*nv[iEdge],d*d); - for(itemp=0; itemp < nv[iEdge]; itemp++) { - ii = vidx[iVertex]-1; - updateB(b+ii*d*d, gij, yij, d*d); - g[ii] = g[ii]+gij*gij; - iVertex++; - } - - iEdge++; - } - } - } - printf("Iedge :%d, ivertex: %d\n", iEdge, iVertex); - } else { - /* reproducing the code above to some degree so that we don't have to - do if statement inside cache-intensive loop */ - for(i=0; i = nn_start) { - for(nn=nn_start; nn<=nn_end; nn++) { - j = edgesrow[nn]; - - /* compute diffx and diffy */ - vecsub(x+i*D, x+j*D, diffx, D); - gij = vecdot(diffx, D); - - vecsub(y+i*d, y+j*d, diffy, d); - vecout(diffy, yij, 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z0QWh3@tZr2=8t!&IJ{oP;ngng3;5!tNcvR#DRqlElJ}UbiTD(8kD)n_F41}r(`u>K>+V!EA{DF1Bz;m4cg -#include -#include -#include - - /* the computation engine */ -void collectdata(double *y, int* edgerow, int *edgecol, double *edgesdist, int *relative, int d, int n, int ks, double *a, double *b, double *g); - -/* auxiliary functions */ -void sanity_check(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]); - -/* the gateway */ -void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) -{ - int n, ks=1, d; - double *x, *y, *a, *b, *g; - int *neighbors; - - /* sanity_check(nlhs, plhs, nrhs, prhs); */ - - - d = mxGetM(prhs[0]); - n = mxGetN(prhs[0]); - /*printf("%d data points, reducing from dimension %d ---> dimension %d, using \ -%d nearest neighbors\n", n, D, d, ks); */ - plhs[0] = mxCreateDoubleMatrix(d*d, d*d, mxREAL); - plhs[1] = mxCreateDoubleMatrix(d*d, n, mxREAL); - plhs[2] = mxCreateDoubleMatrix(n,1, mxREAL); - - collectdata( (double*)mxGetData(prhs[0]), - (int*)mxGetData(prhs[1]), - (int*)mxGetData(prhs[2]), - (double*)mxGetData(prhs[3]), - (int*)mxGetData(prhs[4]), - d, n, ks, - (double*)mxGetData(plhs[0]), - (double*)mxGetData(plhs[1]), - (double*)mxGetData(plhs[2])); - return; -} - - - - -/* computing */ -double vecdot(double* v1, int n) { /* v1'*v2 */ - double x = 0; - int i; - for(i = 0; i < n; i++) { - x += v1[i]*v1[i]; - } - return x; -} -void vecsub(double* v1,double* v2, double* v3, int n) { /* v3=v1-v2 */ - int incx=1; - double none = -1; - int i; - /* dcopy_(&n, v1, &incx,v3, &incx); - daxpy_(&n, &none, v2, &incx, v3, &incx);*/ - for(i=0;i nn_start) { - for(nn=nn_start; nn<=nn_end; nn++) { - j = edgesrow[nn]; - - /* compute diffx and diffy */ - /* vecsub(x+i*D, x+j*D, diffx, D);*/ - gij = edgesdist[nn]; - - vecsub(y+i*d, y+j*d, diffy, d); - vecout(diffy, yij, d); - - /* update A, b */ - updateA(tempA, yij, 1.0,d*d); - - updateB(b+i*d*d, gij, yij, d*d); - g[i] = g[i]+gij*gij; - } - } - } - } else { - /* reproducing the code 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