When Spectral Domain Meets Spatial Domain in Graph Neural Networks
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.
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]
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