Xin‐Jian Xu

Murong Yang, Xin-Jian Xu

The growing interest in hypergraph neural networks (HGNNs) is driven by their capacity to capture the complex relationships and patterns within hypergraph structured data across various domains, including computer vision, complex networks, and natural language processing. This paper comprehensively reviews recent advances in HGNNs and presents a taxonomy of mainstream models based on their architectures: hypergraph convolutional networks (HGCNs), hypergraph attention networks (HGATs), hypergraph autoencoders (HGAEs), hypergraph recurrent networks (HGRNs), and deep hypergraph generative models (DHGGMs). For each category, we delve into its practical applications, mathematical mechanisms, literature contributions, and open problems. Finally, we discuss some common challenges and promising research directions.This paper aspires to be a helpful resource that provides guidance for future research and applications of HGNNs.

Murong Yang, Shihui Ying, Xin-Jian Xu et al.

Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in high-dimensional Euclidean spaces. In this paper, we introduce a novel approach that begins to generate hypergraphs by leveraging sparse representation learning from data points. Based on the generated hypergraph, we propose an optimization function with orthogonality constraints for multi-view hypergraph spectral clustering, which incorporates spectral clustering for each view and ensures consistency across different views. In Euclidean space, solving the orthogonality-constrained optimization problem may yield local maxima and approximation errors. Innovately, we transform this problem into an unconstrained form on the Grassmannian manifold. Finally, we devise an alternating iterative Riemannian optimization algorithm to solve the problem. To validate the effectiveness of the proposed algorithm, we test it on four real-world multi-view datasets and compare its performance with seven state-of-the-art multi-view clustering algorithms. The experimental results demonstrate that our method outperforms the baselines in terms of clustering performance due to its superior low-dimensional and resilient feature representation.