A2GCN: Graph Convolutional Networks with Adaptive Frequency and Arbitrary Order

Abstract

Graph Neural Networks (GNNs) gain remarkable success in various graph learning tasks under homophily graph assumption. This assumption is extremely fragile since real-world graphs with heterophily are ubiquitous. Under this circumstance, existing GNNs attempt to design or learn graph spectral filters for observed graphs. The representation ability of them, however, is limited due to: (1) Constant frequency response is incapable of simulating complicated filters that real-world applications require. (2) Fixed polynomial order fails to effectively uncover the node label patterns concealing different order neighborhoods. To this end, we propose a novel Graph Convolutional Networks with Adaptive Frequency and Arbitrary Order (A2GCN) to learn various graph spectral filters suitable for distinct networks. Specifically, a simple but elegant filter with adaptive frequency response is designed to span across multiple layers for capturing different frequency components hiding in varying orders, producing A2GCN filter bases. Afterward, the coefficients of the A2GCN basis for each node are learned to achieve A2GCN filters with arbitrary polynomial order. The resulting A2GCN filters possess flexible frequency response that can automatically adapt to the node label pattern, as such, it empowers A2GCN with stronger expressiveness and naturally alleviates the over-smoothing problem. Theoretical analysis is provided to show the superiority of the proposed A2GCN. Additionally, extensive experiments on both node-level and graph-level tasks validate that the proposed A2GCN accomplishes highly competitive performance and improves classification accuracy. Codes are available at https://github.com/AIG22/A2GCN.