Graph Convolutional Networks via Adaptive Filter Banks

Xing Gao, Wenrui Dai, Chenglin Li, Junni Zou, Hongkai Xiong, Pascal Frossard

Abstract: Graph convolutional networks have been a powerful tool in representation learning of networked data. However, most architectures of message passing graph convolutional networks (MPGCNs) are limited as they employ a single message passing strategy and typically focus on low-frequency information, especially when graph features or signals are heterogeneous in different dimensions. Then, existing spectral graph convolutional operators lack a proper sharing scheme between filters, which may result in overfitting problems with numerous parameters. In this paper, we present a novel graph convolution operator, termed BankGCN, which extends the capabilities of MPGCNs beyond single `low-pass' features and simplifies spectral methods with a carefully designed sharing scheme between filters. BankGCN decomposes multi-channel signals on arbitrary graphs into subspaces and shares adaptive filters to represent information in each subspace. The filters of all subspaces differ in frequency response and together form a filter bank. The filter bank and the signal decomposition permit to adaptively capture diverse spectral characteristics of graph data for target applications with a compact architecture. We finally show through extensive experiments that BankGCN achieves excellent performance on a collection of benchmark graph datasets.