Johanna Immonen | Amauri H. Souza | Vikas Garg

This is the official repo for the paper Going beyond persistent homology using persistent homology (NeurIPS 2023).

In our work, we study the expressive power of PH on attributed (or colored) graphs. In particular, we establish lower and upper bounds for the expressivity of 0-dimensional persistence diagrams obtained from vertex- and edge-level filtration functions. Based on our insights, we present RePHINE (short for ''Refining PH by Incorporating Node-color into Edge-based filtration''), a simple method that exploits a subtle interplay between vertex- and edge-level persistence information to improve the expressivity of color-based PH. We show the effectiveness of RePHINE on three synthetic and six real datasets.

If you use conda as package manager you can use to create a virtual environment:

  conda create -n rephine 
  conda activate rephine

or if use venv

  python -m venv env 
  source env/bin/activate         #If you use Linux or Mac
  .\venv\Scripts\Activate.ps1     #If you use Windows

you can install dependencies in requirements.txt

  pip install -r requirements.txt

If you prefer to install manually

  pip install torch-scatter torch-sparse torch-cluster torch-spline-conv torch-geometric
  pip install ogb
  pip install dgl
  pip install networkx
  pip install h5py

After that, you have to install the necessary dependencies that computes persistence diagrams

  cd torch_ph
  python setup_rephine.py install 
  python setup_std_ph.py install

For the experiments with synthetic data, we first create the datasets:

python datasets/create_data.py --dataset cub08 --num_alien_nodes 1
python datasets/create_data.py --dataset cub10 --num_alien_nodes 2
python datasets/create_data.py --dataset cub12 --num_alien_nodes 3

and then run the scripts for rephine, standard (PH), and GCN:

python main_toy.py --setting cub10-2  --seed 8 --model rephine --reduce_tuples --no-dim1
python main_toy.py --setting cub10-2  --seed 8 --model standard --no-dim1
python main_toy.py --setting cub10-2  --seed 8 --model gcn 

For the main experiments, we run the main.py with the arguments in cli_main.py. For instance, to run RePHINE and Standard on NCI109 combined with a GCN model, we run:

python main.py --dataset NCI109  --diagram_type rephine --gnn gcn   
python main.py --dataset NCI109  --diagram_type standard --gnn gcn   

We first need to generate data using the file datasets/generate_data_perslay.py. Then, to run RePHINE+Linear, we choose --gnn linear and run

python main.py --dataset NCI109  --diagram_type rephine --gnn linear   

To run the PersLay model, we use the file main_perslay.py, e.g.,

python main_perslay.py --dataset NCI109    

@inproceedings{rephine,
  title={Going beyond persistent homology using persistent homology},
  author={Johanna Immonen and Amauri H. Souza and Vikas Garg},
  booktitle={Advances in Neural Information Processing Systems (NeurIPS)},
  year={2023}
}

Some of the routines in this repo were modified from TOGL and PersLay.