PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering

TL;DR

This paper introduces PC-Conv, a novel graph convolution method that unifies homophily and heterophily learning by employing a two-fold filtering mechanism based on the Poisson-Charlier polynomial approximation.

Contribution

It proposes a two-fold filtering mechanism and a new graph convolution PC-Conv that effectively captures both homophily and heterophily in graphs, improving generalization across diverse graph types.

Findings

PCNet achieves competitive results on homophilic and heterophilic graphs.

The method extends the graph heat equation for heterophilic aggregation.

PC-Conv outperforms state-of-the-art GNNs in node classification.

Abstract

Recently, many carefully crafted graph representation learning methods have achieved impressive performance on either strong heterophilic or homophilic graphs, but not both. Therefore, they are incapable of generalizing well across real-world graphs with different levels of homophily. This is attributed to their neglect of homophily in heterophilic graphs, and vice versa. In this paper, we propose a two-fold filtering mechanism to extract homophily in heterophilic graphs and vice versa. In particular, we extend the graph heat equation to perform heterophilic aggregation of global information from a long distance. The resultant filter can be exactly approximated by the Possion-Charlier (PC) polynomials. To further exploit information at multiple orders, we introduce a powerful graph convolution PC-Conv and its instantiation PCNet for the node classification task. Compared with state-of-the-art GNNs, PCNet shows competitive performance on well-known homophilic and heterophilic graphs. Our implementation is available at https://github.com/uestclbh/PC-Conv.