Community Detection in Hypergraphs via Mutual Information Maximization

TL;DR

This paper introduces an information-theoretic algorithm for community detection in hypergraphs that maximizes mutual information, performing well on synthetic and real data without needing parameter inference.

Contribution

It presents a novel microcanonical stochastic blockmodel approach for hypergraph community detection that avoids estimating statistical parameters, using simulated annealing for inference.

Findings

Successfully detects communities in sparse hypergraphs

Performs competitively on real hypergraph datasets

Operates without estimating node degrees or connection rates

Abstract

The hypergraph community detection problem seeks to identify groups of related nodes in hypergraph data. We propose an information-theoretic hypergraph community detection algorithm which compresses the observed data in terms of community labels and community-edge intersections. This algorithm can also be viewed as maximum-likelihood inference in a degree-corrected microcanonical stochastic blockmodel. We perform the inference/compression step via simulated annealing. Unlike several recent algorithms based on canonical models, our microcanonical algorithm does not require inference of statistical parameters such as node degrees or pairwise group connection rates. Through synthetic experiments, we find that our algorithm succeeds down to recently-conjectured thresholds for sparse random hypergraphs. We also find competitive performance in cluster recovery tasks on several hypergraph data sets.