Hypergraph Clustering Based on PageRank

TL;DR

This paper introduces two novel hypergraph clustering algorithms based on personalized PageRank, providing theoretical guarantees and outperforming existing methods in quality and efficiency.

Contribution

First practical hypergraph clustering algorithms using personalized PageRank with proven conductance guarantees and superior performance.

Findings

Algorithms outperform existing methods in solution quality

Algorithms are faster in running time

Theoretical guarantees on conductance are established

Abstract

A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on personalized PageRank on hypergraphs. The first one is local in the sense that its goal is to find a tightly connected vertex set with a bounded volume including a specified vertex. The second one is global in the sense that its goal is to find a tightly connected vertex set. For both algorithms, we discuss theoretical guarantees on the conductance of the output vertex set. Also, we experimentally demonstrate that our clustering algorithms outperform existing methods in terms of both the solution quality and running time. To the best of our knowledge, ours are the first practical algorithms for hypergraphs with theoretical guarantees on the conductance of the output set.