PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering
Bingheng Li Erlin Pan Zhao Kang
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.