HFGCN: Hybrid Filter Graph Convolutional Network for Heterophilic Graphs

Graph Convolutional Networks (GCNs) are pivotal in analyzing graph data. However, as graph complexity increases, heterophily challenges the traditional GCNs that rely on homophily assumptions. These challenges have elicited various mitigation attempts, which, however, have only achieved partial success. They either inadequately harness the structural intricacies of the data or incorporate irrelevant information, thereby undermining their efficacy in complex heterophilic graphs. To address this, we introduce the Hybrid Filtering Graph Convolutional Network (HFGCN), an innovative framework integrating three specialized filtering mechanisms for spectral domain node aggregation. Inspired by the Power-law transformation, HFGCN employs low-pass filters for homophilic nodes, high-pass filters for heterophilic nodes, and a self-aggregation filter for nodes reliant on their information. An attention mechanism further refines node interaction based on attributes. Our evaluations across seven diverse datasets demonstrate HFGCN’s superior adaptability and performance, surpassing state-of-the-art models in handling both homophilic and heterophilic graphs.