Persistent homology for high-dimensional data based on spectral methods

Repository accompanying the paper

Persistent homology for high-dimensional data based on spectral methods NeurIPS 2024 (openreview)
Sebastian Damrich, Philipp Berens, Dmitry Kobak

@article{damrich2024persistent, title={Persistent homology for high-dimensional data based on spectral methods}, author={Damrich, Sebastian and Berens, Philipp and Kobak, Dmitry}, journal={Advances in Neural Information Processing Systems}, volume={38}, year={2024} }

Usage

Compute the persistent homology of a toy dataset with compute_ph.py, of toy datasets with outliers with compute_ph_outliers.py and that of a single-cell dataset with compute_ph_real_data.py. For the cycle matching experiments run the script compute_matchings.py Changing the dataset in the top of the script allows to compute the persistent homology of different datasets. cd scripts python compute_ph.py

Create the figures of the paper with the various fig_*.ipynb notebooks. The notebooks create the following figures: - Figure 1: fig_1.ipynb - Figure 2: fig_ph.ipynb - Figure 3: fig_vary_dim_mds.ipynb - Figure 4: fig_spectral_intuition.ipynb - Figure 5: fig_spectral.ipynb - Figure 6: fig_circle.ipynb - Figure 7: fig_datasets.ipynb - Figure 8: fig_dims.ipynb - Figure 9, 10: fig_real_data.ipynb - Figure S1: fig_dims.ipynb - Figure S2: fig_pca.ipynb - Figure S3: fig_wide_gap.ipynb - Figure S4, S5: fig_cycle_matching.ipynb - Figure S7, S8: fig_spectral.ipynb - Figure S9: fig_real_data.ipynb - Figure S10, S11: fig_circle.ipynb - Figure S12, S13: fig_toy_datasets.ipynb - Figure S14: fig_sc_datasets.ipynb - Figure S15: fig_sensitivity.ipynb - Figure S16: fig_outliers.ipynb - Figure S17, S18: fig_high_dim_UMAP.ipynb - Figure S19: fig_real_data.ipynb - Figure S20: fig_circle.ipynb - Figure S21: fig_datasets.ipynb - Figure S22: fig_circle.ipynb - Figures S23-S30, S33: fig_all_methods_on_toy.ipynb - Figure S31, S32: fig_torus_high_n.ipynb - Figure S29: fig_real_data.ipynb

Installation

Clone the repository git clone https://github.com/berenslab/eff-ph.git

Create a conda python environment cd eff-ph conda env create -f environment.yml

Install the utils: cd ../eff-ph python setup.py install

Clone the repository ripser and compile it: cd .. git clone -b representative-cycles https://github.com/Ripser/ripser.git cd risper make

Clone the repository interval-matching for the cycle matching experiments and compile the two C++ files: cd .. git clone https://github.com/inesgare/interval-matching.git cd modified ripser/ripser-image-persistence-simple make cd ../ripser-tight-representative-cycles make cd ../..

Clone the repository vis_utils git clone https://github.com/sdamrich/vis_utils.git --branch eff-ph-arxiv-v1 --single-branch

Create the conda R environment (for loading some single-cell datasets) cd vis_utils conda create -f r_env.yml

Install vis_utils conda activate eff-ph python setup.py install