Hypergraph Mining via Proximity Matrix

TL;DR

This paper introduces a continuous-valued proximity matrix for hypergraphs, improving the accuracy of hypergraph analysis tasks like link prediction, vital nodes identification, and community detection.

Contribution

It proposes a novel proximity matrix based on resource allocation, enhancing hypergraph mining beyond traditional binary incidence matrices.

Findings

Proposed proximity matrix outperforms benchmarks in link prediction.

Enhanced identification of vital nodes in hypergraphs.

Improved community detection accuracy on real-world hypergraphs.

Abstract

Hypergraphs serve as an effective tool widely adopted to characterize higher-order interactions in complex systems. The most intuitive and commonly used mathematical instrument for representing a hypergraph is the incidence matrix, in which each entry is binary, indicating whether the corresponding node belongs to the corresponding hyperedge. Although the incidence matrix has become a foundational tool for hypergraph analysis and mining, we argue that its binary nature is insufficient to accurately capture the complexity of node-hyperedge relationships arising from the fact that different hyperedges can contain vastly different numbers of nodes. Accordingly, based on the resource allocation process on hypergraphs, we propose a continuous-valued matrix to quantify the proximity between nodes and hyperedges. To verify the effectiveness of the proposed proximity matrix, we investigate three important tasks in hypergraph mining: link prediction, vital nodes identification, and community detection. Experimental results on numerous real-world hypergraphs show that simply designed algorithms centered on the proximity matrix significantly outperform benchmark algorithms across these three tasks.