PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering
This addresses the generalization issue in graph neural networks for node classification, which is incremental as it builds on existing methods to handle both homophily and heterophily.
The paper tackles the problem of graph representation learning methods failing to generalize across graphs with varying homophily levels by proposing a two-fold filtering mechanism that extracts homophily in heterophilic graphs and vice versa, resulting in PCNet showing competitive performance on both homophilic and heterophilic graphs.
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.