Multi-Channel Graph Convolutions

Andreas Roth, Thomas Liebig

Keywords: graph convolution, spectral graph convolution, message-passing neural network

TL;DR: We introduce the convolution for multi-channel signals to graphs using the convolution theorem.

Abstract:

Defining the convolution on graphs has led to much progress in graph machine learning, particularly through approximations based on polynomials and, ultimately, message-passing neural networks (MPNNs). However, this convolution is defined for single-channel graph signals, i.e., a single feature is given at each node, and a single new feature is assigned to each node. As multiple initial node features are provided for many challenging tasks and convolutions are generally defined for these multi-channel signals, we introduce multi-channel graph convolutions (MCGCs) by obtaining their form using the graph Fourier transform. MCGCs highlight the critical importance of utilizing multiple edge relations to amplify different signals for each feature channel. We further introduce localized multi-channel MPNNs and the multi-channel graph isomorphism network (MC-GINs), with which we can provably obtain linear mappings that are injective on multisets. Our experiments confirm the greatly improved capabilities of MCGCs and MC-GINs.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 9759