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When Spectral Domain Meets Spatial Domain in Graph Neural Networks

Balcilar Muhammet 1 Renton Guillaume 1 Héroux Pierre 1 Gaüzère Benoit 1 Adam Sébastien 1 Paul Honeine 1 
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LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
Abstract : Convolutional Graph Neural Networks (Con-vGNNs) are designed either in the spectral domain or in the spatial domain. In this paper, we provide a theoretical framework to analyze these neural networks, by deriving some equivalence of the graph convolution processes, regardless if they are designed in the spatial or the spectral domain. We demonstrate the relevance of the proposed framework by providing a spectral analysis of the most popular ConvGNNs (ChebNet, CayleyNet, GCN and Graph Attention Networks), which allows to explain their performance and shows their limits.
Keywords : Convolutional neural networks graph neural networks graph data deep learning ChebNet CayleyNet graph convolution networks graph attention networks spatial domain spectral domain spectral analysis eigenanalysis
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Conference papers
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https://hal-normandie-univ.archives-ouvertes.fr/hal-03088374
Contributor : Paul Honeine Connect in order to contact the contributor
Submitted on : Saturday, December 26, 2020 - 10:57:12 AM
Last modification on : Wednesday, March 2, 2022 - 10:10:12 AM
Long-term archiving on: : Monday, March 29, 2021 - 4:42:50 PM

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  • HAL Id : hal-03088374, version 1

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Balcilar Muhammet, Renton Guillaume, Héroux Pierre, Gaüzère Benoit, Adam Sébastien, et al.. When Spectral Domain Meets Spatial Domain in Graph Neural Networks. Thirty-seventh International Conference on Machine Learning (ICML 2020) - Workshop on Graph Representation Learning and Beyond (GRL+ 2020), Jul 2020, Vienna, Austria. ⟨hal-03088374⟩

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