Learning Hypergraphs From Signals With Dual Smoothness Prior

TL;DR

This paper introduces HGSL, a framework for learning hypergraph structures from signals using a dual smoothness prior, effectively capturing high-order relationships in data without predefined topologies.

Contribution

The paper proposes a novel hypergraph learning method with a dual smoothness prior, linking node and edge signal smoothness to infer hypergraph structures from observed data.

Findings

HGSL efficiently infers meaningful hypergraph topologies.

The dual smoothness prior improves hypergraph structure learning.

Experiments validate HGSL's effectiveness on synthetic and real datasets.

Abstract

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.