Multi-Scale Graph Convolutional Network With Spectral Graph Wavelet Frame

Abstract

Graph neural networks have achieved impressive progress in solving large and complex graph-structured problems. However, existing methods cannot sufficiently explore the advantages of multi-scale information by enlarging the receptive fields through stacking deep layers or multiplying exponentiated graph Laplacian. They are restricted by the discrete scales rigidly dependent on node-hops or suffer from the over-smoothing issue incurred by long-range low-pass filtering. In this paper, we propose a multi-scale graph convolutional network based on the spectral graph wavelet frame to improve multi-scale representation learning. The proposed network flexibly leverages multi-scale neighboring information with continuous scaling to enhance the discrimination ability of the learned multi-scale representations and offer stable feature extraction ensured by frame bounds in theory. The multi-scale spectral convolutional layer is constructed with a low-pass filter and a sequence of dilated band-pass filters to achieve well-established localization in both vertex and frequency domains. The graph convolutional filters can be realized based on spectral graph wavelet kernel functions analytically formulated using parameterized band-limited filters or adaptively learned from training data. Furthermore, fast approximations of exact spectral filtering are developed for memory efficient operations on sparse tensors with guaranteed prediction accuracy and numerical stability. The proposed network is shown to achieve state-of-the-art performance in extensive experiments on citation networks, bioinformatics graphs, and social networks.