GDL

Python code for the paper Online Graph Dictionary Learning.

NEWS: (01/03/2022) An enhanced implementation of GDL can be found in the library Python Optimal Transport. It is now compatible with many backends such as Numpy like the original version but also Pytorch, Tensorflow, JAX, Cuda.

If you find this repository useful for your research please cite GDL using the following bibtex reference:

@InProceedings{pmlr-v139-vincent-cuaz21a,
  title = 	 {Online Graph Dictionary Learning},
  author =       {Vincent-Cuaz, C{\'e}dric and Vayer, Titouan and Flamary, R{\'e}mi and Corneli, Marco and Courty,  Nicolas},
  booktitle = 	 {Proceedings of the 38th International Conference on Machine Learning},
  pages = 	 {10564--10574},
  year = 	 {2021},
  editor = 	 {Meila, Marina and Zhang, Tong},
  volume = 	 {139},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {18--24 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v139/vincent-cuaz21a/vincent-cuaz21a.pdf},
  url = 	 {http://proceedings.mlr.press/v139/vincent-cuaz21a.html},
  abstract = 	 {Dictionary learning is a key tool for representation learning, that explains the data as linear     combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually   belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses    the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes’ pairwise  relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic  algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach  naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov     Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised    embedding of graph datasets and for online graph subspace estimation and tracking.}
}

This repository contains implementations of our methods which led to results detailed in the numerical experiments. Namely vanilla GDL for unlabeled graphs, its extension where we simultaneously learn graphs structure and their nodes relative importance, and its extension to labeled graphs as detailed in the supplementary material of the paper.

Prerequisites

python >= 3.7.7
pot >= 0.6.0 POT Python Optimal Transport library
cython >= 0.29.20
numpy >= 1.18.5
pandas >= 1.0.5
networkx >= 2.4
scikit-learn >= 0.24.0
scikit-learn-extra >= 0.1.0b2
scipy >= 1.5.0
joblib == 0.15.1

Data

Datasets used for unsupervised and supervised classification benchmarks are stored in subrepository data/. Datasets used for online experiments have been omitted for reasons of storage limitation. All these datasets can be found here Benchmark Data Sets for Graph Kernels and directly used in our pipelines.

Code

Experiments with vanilla GDL can be reproduced as follow (for e.g on IMDB-BINARY dataset):

python run_GW_GDL.py --dataset_name "imdb-b" --list_number_atoms [4,8,12,16] --list_shape_atoms [17] --list_l2reg [0.0,0.001,0.01,0.1] --epochs 30 --batch_size 16 --learning_rate 0.01 --mode "ADJ"

or equivalently

python run_GW_GDL.py -ds "imdb-b" -natoms [4,8,12,16] -satoms [17] -reg [0.0,0.001,0.01,0.1] -ep 30 -b 16 -lr 0.01 -mode "ADJ"

Experiments on toy datasets detailed in section 4.1:

  python run_GW_GDL.py -ds "balanced_clustertoy" -natoms [3] -satoms [6] -reg [0.0,0.001] -ep 20 -b 16 -lr 0.01 -mode "ADJ"

  python run_GW_GDL.py -ds "clustertoy2C" -natoms [2] -satoms [12] -reg [0.0] -ep 20 -b 16 -lr 0.01 -mode "ADJ"

Experiments with GDL using Fused Gromov-Wasserstein for labeled graphs:

python run_FGW_GDL.py -ds "mutag" -natoms [4] -satoms [17] -reg [0.0] -alpha [0.25,0.5] -ep 40 -b 16 -lrC 0.01 -lrA 0.01 -mode "ADJ"

Experiments with the proposed extension of GDL where we simultaneously learn atoms structure and their nodes relative importance:

  python run_GW_extendedDL.py -ds "imdb-m" -natoms [12] -satoms [10] -regC [0.0] -ep 40 -b 16 -lrC 0.01 -lrh 0.001 -mode "ADJ"

Online experiments have their dedicated run files with preset parameters: run_streamingTWITCH.py & run_streamingTRIANGLES.py

Authors

References

[1] Rémi Flamary, Nicolas Courty, Alexandre Gramfort, Mokhtar Z. Alaya, Aurélie Boisbunon, Stanislas Chambon, Laetitia Chapel, Adrien Corenflos, Kilian Fatras, Nemo Fournier, Léo Gautheron, Nathalie T.H. Gayraud, Hicham Janati, Alain Rakotomamonjy, Ievgen Redko, Antoine Rolet, Antony Schutz, Vivien Seguy, Danica J. Sutherland, Romain Tavenard, Alexander Tong, Titouan Vayer;, POT Python Optimal Transport library, Journal of Machine Learning Research, 22(78):1−8, 2021.

[2] Kristian Kersting and Nils M. Kriege and Christopher Morris and Petra Mutzel and Marion Neumann, Benchmark Data Sets for Graph Kernels

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GDL

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