Finding Bipartite Components in Hypergraphs

TL;DR

This paper introduces a new heat diffusion-based algorithm for detecting bipartite components in hypergraphs, demonstrating superior performance over previous methods through theoretical analysis and extensive experiments.

Contribution

The paper presents a novel polynomial-time algorithm leveraging heat diffusion in hypergraphs to find bipartite components, with proven theoretical guarantees.

Findings

Algorithm outperforms previous methods on synthetic datasets

Consistent improvements observed on real-world datasets

Theoretical performance guarantees established

Abstract

Hypergraphs are important objects to model ternary or higher-order relations of objects, and have a number of applications in analysing many complex datasets occurring in practice. In this work we study a new heat diffusion process in hypergraphs, and employ this process to design a polynomial-time algorithm that approximately finds bipartite components in a hypergraph. We theoretically prove the performance of our proposed algorithm, and compare it against the previous state-of-the-art through extensive experimental analysis on both synthetic and real-world datasets. We find that our new algorithm consistently and significantly outperforms the previous state-of-the-art across a wide range of hypergraphs.