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:高空结构学习旨在从观测到的信号中学习高空结构,以捕捉各实体之间的内在高度秩序关系,当高空地形无法随时在数据集中找到时,这种结构就变得至关重要。 这个问题的核心有两个挑战:(1) 如何处理潜在高端信号的巨大搜索空间,(2) 如何界定有意义的标准,以衡量在节点和高空结构上观测到的信号之间的关系。 在本文件的第一个挑战中,我们采用以下假设:理想的高空结构可以从一个可学习的图形结构中产生,该结构可以捕捉信号中的对称关系。此外,我们提议一个高空结构学习框架HGSL,该结构在显示所观测到的节点信号和高空结构之间的新的双光度绘图之前,每个高端都与一个有节点信号光和边端信号的子绘图相匹配。最后,我们进行了广泛的实验,以评价合成和真实世界数据集的HGSL。实验表明,HGSL能够有效地从所观测到的信号中推导出有意义的超高空结构。</s>