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Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

Michaël Defferrard, Xavier Bresson, Pierre Vandergheynst,
Conference on Neural Information Processing Systems (NIPS), 2016.

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

@inproceedings{cnn_graph,
  title = {Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering},
  author = {Defferrard, Micha\"el and Bresson, Xavier and Vandergheynst, Pierre},
  booktitle = {Advances in Neural Information Processing Systems (NIPS)},
  year = {2016},
  archiveprefix = {arXiv},
  eprint = {1606.09375},
  url = {https://arxiv.org/abs/1606.09375},
}

Resources

PDF available at arXiv, NIPS, EPFL.

Related: poster, slides, video, code.

Compilation

Compile the latex source into a PDF with make. Run make clean to remove temporary files and make arxiv.zip to prepare an archive to be uploaded on arXiv.

Figures

All the figures are in the figures folder. PDFs can be generated with make figures.

Peer-review

The paper got a metareview based on six reviews, on which our rebuttal is based. The reviews are also at NIPS.

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Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

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