Co-Representation Neural Hypergraph Diffusion for Edge-Dependent Node Classification

Abstract: Hypergraphs are widely employed to represent complex higher-order relations in real-world applications. Most hypergraph learning research focuses on node-level or edge-level tasks. A practically relevant but more challenging task, edge-dependent node classification (ENC), is only recently proposed. In ENC, a node can have different labels across different hyperedges, which requires the modeling of node-edge pairs instead of single nodes or hyperedges. Existing solutions for this task are based on message passing and model interactions in within-edge and within-node structures as multi-input single-output functions. This brings three limitations: (1) non-adaptive representation size, (2) non-adaptive messages, and (3) insufficient direct interactions among nodes or edges. To tackle these limitations, we propose CoNHD, a new ENC solution that models both within-edge and within-node interactions as multi-input multi-output functions. Specifically, we represent these interactions as a hypergraph diffusion process on node-edge co-representations. We further develop a neural implementation for this diffusion process, which can adapt to a specific ENC dataset. Extensive experiments demonstrate the effectiveness and efficiency of the proposed CoNHD method.