Clustering in graphs and hypergraphs with categorical edge labels

TL;DR

This paper introduces a new computational framework for clustering hypergraphs with categorical edge labels, enabling analysis of complex, higher-order interactions in network data with efficient algorithms and theoretical guarantees.

Contribution

It develops a novel combinatorial objective for hypergraph clustering with categorical labels, along with polynomial-time and approximation algorithms, extending correlation clustering to hypergraphs.

Findings

Efficient polynomial-time algorithm for two-label hypergraph clustering.

Approximation algorithms with theoretical guarantees for multiple labels.

Successful application to community detection, temporal data clustering, and exploratory analysis.

Abstract

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called "higher-order interactions" that involve more than two nodes at a time. However, we have fewer rigorous methods that can provide insight from such representations. Here, we develop a computational framework for the problem of clustering hypergraphs with categorical edge labels --- or different interaction types --- where clusters corresponds to groups of nodes that frequently participate in the same type of interaction. Our methodology is based on a combinatorial objective function that is related to correlation clustering on graphs but enables the design of much more efficient algorithms that also seamlessly generalize to hypergraphs. When there are only two label types, our objective can be optimized in polynomial time, using an algorithm based on minimum cuts. Minimizing our objective becomes NP-hard with more than two label types, but we develop fast approximation algorithms based on linear programming relaxations that have theoretical cluster quality guarantees. We demonstrate the efficacy of our algorithms and the scope of the model through problems in edge-label community detection, clustering with temporal data, and exploratory data analysis.