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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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

Domains: Statistics [stat]; Machine Learning [stat.ML]; Engineering Sciences [physics]; Signal and Image processing; Mathematics [math]; Statistics [math.ST]; Computer Science [cs]; Signal and Image Processing; Computer Science [cs]; Neural and Evolutionary Computing [cs.NE]; Computer Science [cs]; Machine Learning [cs.LG]; Computer Science [cs]; Computers and Society [cs.CY]; Computer Science [cs]; Computer Vision and Pattern Recognition [cs.CV]; Computer Science [cs]; Artificial Intelligence [cs.AI]

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⟩