I²HGNN: Iterative Interpretable HyperGraph Neural Network for semi-supervised classification

Learning on hypergraphs has garnered significant attention recently due to their ability to effectively represent complex higher-order interactions among multiple entities compared to conventional graphs. Nevertheless, the majority of existing methods are direct extensions of graph neural networks, and they exhibit noteworthy limitations. Specifically, most of these approaches primarily rely on either the Laplacian matrix with information distortion or heuristic message passing techniques. The former tends to escalate algorithmic complexity, while the latter lacks a solid theoretical foundation. To address these limitations, we propose a novel hypergraph neural network named I²HGNN, which is grounded in an energy minimization function formulated for hypergraphs. Our analysis reveals that propagation layers align well with the message-passing paradigm in the context of hypergraphs. I²HGNN achieves a favorable trade-off between performance and interpretability. Furthermore, it effectively balances the significance of node features and hypergraph topology across a diverse range of datasets. We conducted extensive experiments on 15 datasets, and the results highlight the superior performance of I²HGNN in the task of hypergraph node classification across nearly all benchmarking datasets.