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