Addressing Graph Heterogeneity and Heterophily from A Spectral Perspective

Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly hinder the performance of GNNs. Heterogeneity refers to a graph with multiple types of nodes or edges, while heterophily refers to the fact that connected nodes are more likely to have dissimilar attributes or labels. Although there have been few works studying heterogeneous heterophilic graphs, they either only consider the heterophily of specific meta-paths and lack expressiveness, or have high expressiveness but fail to exploit high-order neighbors. In this paper, we propose a Heterogeneous Heterophilic Spectral Graph Neural Network (H2SGNN), which employs two modules: local independent filtering and global hybrid filtering. Local independent filtering adaptively learns node representations under different homophily, while global hybrid filtering exploits high-order neighbors to learn more possible meta-paths. Extensive experiments are conducted on four datasets to validate the effectiveness of the proposed H2SGNN, which achieves superior performance with fewer parameters and memory consumption. The code is available at the GitHub repo: https://github.com/Lukangkang123/H2SGNN/.