Unsupervised hyperlink prediction based on hypergraph random walk

Abstract Conventional link prediction methods mainly aim to estimate pairwise relationships between nodes in graph structures, typically addressing single-type interactions. However, real-world complex systems often exhibit high-order group relationships that extend beyond binary interactions. For instance, a research paper is often co-authored by multiple researchers. To address the loss of high-order structural information in traditional graph models for representing multivariate interactions, we propose HP2PH, a novel hyperlink prediction method based on 2-head preferential hypergraph weighted random walk with restart. Firstly, considering the uncertainty of hyperedge cardinalities in non-uniform hypergraphs, we introduce a preferential hypergraph weighted random walk with restart strategy, called P-HWRWR. This strategy fully exploits the high-order topological properties of hypergraphs, and jointly optimizes the random walking sub-paths from node to hyperedge and from hyperedge to node by assigning weights to both the hyperedges and nodes encountered by the random walker. Subsequently, an unsupervised hyperlink prediction method based on the two-head preferential hypergraph weighted random walk with restart is proposed. This approach searches for potential member nodes within new hyperedges from different directions, ensuring efficient predicting multivariate interactions with relatively low time complexity. Finally, through extensive experimental verification and analysis on 10 non-uniform hypergraph datasets and 5 uniform hypergraph datasets, it is demonstrated that HP2PH achieves improvements of 0.8% to 137.2% in the AFS metric and 0.8% to 412.1% in the HPA metric on non-uniform datasets and achieves improvement of 94.4% to 202.5% in the AFS metric on uniform hypergraph datasets compared baselines. These experiments substantiate the superiority and operational viability of the developed method when predicting hyperlinks.