Hypergraph structure learning, which aims to learn the hypergraph structures from the observed signals to capture the intrinsic high-order relationships among the entities, becomes crucial when a hypergraph topology is not readily available in the datasets. There are two challenges that lie at the heart of this problem: 1) how to handle the huge search space of potential hyperedges, and 2) how to define meaningful criteria to measure the relationship between the signals observed on nodes and the hypergraph structure. In this paper, for the first challenge, we adopt the assumption that the ideal hypergraph structure can be derived from a learnable graph structure that captures the pairwise relations within signals. Further, we propose a hypergraph structure learning framework HGSL with a novel dual smoothness prior that reveals a mapping between the observed node signals and the hypergraph structure, whereby each hyperedge corresponds to a subgraph with both node signal smoothness and edge signal smoothness in the learnable graph structure. Finally, we conduct extensive experiments to evaluate HGSL on both synthetic and real world datasets. Experiments show that HGSL can efficiently infer meaningful hypergraph topologies from observed signals.

翻译：超图结构学习旨在从观测信号中学习超图结构，以捕捉实体间内在的高阶关系。当数据集中缺乏现成的超图拓扑结构时，该技术变得至关重要。该问题面临两大核心挑战：1）如何处理潜在超边的巨大搜索空间；2）如何定义有意义的准则来度量节点观测信号与超图结构之间的关系。针对第一个挑战，本文假设理想超图结构可以从刻画信号内成对关系的可学习图结构中推导得出。在此基础上，我们提出超图结构学习框架HGSL，该框架采用新颖的对偶平滑先验，揭示了观测节点信号与超图结构之间的映射关系——每个超边对应于可学习图结构中兼具节点信号平滑性和边信号平滑性的子图。最后，我们在合成数据集和真实数据集上开展大量实验评估HGSL。实验结果表明，HGSL能够从观测信号中高效推断出有意义的超图拓扑结构。