Overlapping and Robust Edge-Colored Clustering in Hypergraphs

TL;DR

This paper extends edge-colored hypergraph clustering to handle overlaps and noise, proposing greedy algorithms and FPT solutions for improved categorical data analysis.

Contribution

It introduces generalized models for overlapping and noise-tolerant hypergraph clustering, along with approximation algorithms and complexity results.

Findings

Greedy algorithms effectively minimize edge mistake objectives.

Bicriteria approximations balance clustering accuracy and budget constraints.

FPT algorithms and hardness results clarify computational complexity.

Abstract

A recent trend in data mining has explored (hyper)graph clustering algorithms for data with categorical relationship types. Such algorithms have applications in the analysis of social, co-authorship, and protein interaction networks, to name a few. Many such applications naturally have some overlap between clusters, a nuance which is missing from current combinatorial models. Additionally, existing models lack a mechanism for handling noise in datasets. We address these concerns by generalizing Edge-Colored Clustering, a recent framework for categorical clustering of hypergraphs. Our generalizations allow for a budgeted number of either (a) overlapping cluster assignments or (b) node deletions. For each new model we present a greedy algorithm which approximately minimizes an edge mistake objective, as well as bicriteria approximations where the second approximation factor is on the budget. Additionally, we address the parameterized complexity of each problem, providing FPT algorithms and hardness results.