Comparison of modularity-based approaches for nodes clustering in hypergraphs

TL;DR

This paper compares various modularity-based methods for clustering nodes in hypergraphs, providing a unified framework, analyzing their performance, and clarifying their advantages and limitations to improve understanding of hypergraph community detection.

Contribution

It offers the first comprehensive comparison of hypergraph modularity methods, clarifying their differences, performance, and suitability for binary hypergraph node clustering.

Findings

Different methods vary in clustering accuracy and runtime

Some methods better recover true communities under certain conditions

The study highlights strengths and weaknesses of each approach

Abstract

Statistical analysis and node clustering in hypergraphs constitute an emerging topic suffering from a lack of standardization. In contrast to the case of graphs, the concept of nodes' community in hypergraphs is not unique and encompasses various distinct situations. In this work, we conducted a comparative analysis of the performance of modularity-based methods for clustering nodes in binary hypergraphs. To address this, we begin by presenting, within a unified framework, the various hypergraph modularity criteria proposed in the literature, emphasizing their differences and respective focuses. Subsequently, we provide an overview of the state-of-the-art codes available to maximize hypergraph modularities for detecting node communities in binary hypergraphs. Through exploration of various simulation settings with controlled ground truth clustering, we offer a comparison of these methods using different quality measures, including true clustering recovery, running time, (local) maximization of the objective, and the number of clusters detected. Our contribution marks the first attempt to clarify the advantages and drawbacks of these newly available methods. This effort lays the foundation for a better understanding of the primary objectives of modularity-based node clustering methods for binary hypergraphs.