HyperCOT: Hypergraph Co-Optimal Transport

This repository contains code related to the paper Hypergraph Co-Optimal Transport: Metric and Categorical Properties by Samir Chowdhury, Tom Needham, Ethan Semrad, Bei Wang, and Youjia Zhou.

To get started, we suggest creating a new conda environment. From the terminal window, type in:

conda create -n HyperCOT python=3.9
conda activate HyperCOT

Next, please install the dependencies from the provided requirements.txt file.

pip install -r requirements.txt

The main dependencies for our package are:

• Python Optimal Transport (https://pythonot.github.io/)
• HyperNetX (https://github.com/pnnl/HyperNetX)

Additionally, we utilize code from:

• Redko, Vayer, Flamary, Courty (2020), CO-Optimal Transport
  • https://github.com/PythonOT/COOT
• Zhou, Rathore, Purvine, Wang (2021), Topological Simplifications of Hypergraphs
  • https://github.com/tdavislab/Hypergraph-Vis
• Do, Yoon, Hooi, Shin (2020), Structural Patterns and Generative Models of Real-world Hypergraphs
  • https://github.com/manhtuando97/KDD-20-Hypergraph

Included in this repo:

• code to compute HyperCOT distances
• demo notebook to perform multiscale matching (requires plotly) as below:

Getting started

• Try running the run_simulated.ipynb notebook. Here we load a dataset of 40 simulated hypergraphs and show how to compute HyperCOT distances for a pair of hypergraphs. Although we do not go through the full computation in the notebook, computing all the pairwise distances should yield a matrix as follows (plotted using seaborn):

Extra

To generate hypergraphs of the form in the header, please visit https://github.com/tdavislab/Hypergraph-Vis.