Partial Optimality in Cubic Correlation Clustering for General Graphs

TL;DR

This paper introduces partial optimality conditions for cubic correlation clustering, providing algorithms to identify optimal clusterings in graphs with up to 3-cliques, and evaluates their effectiveness on real data sets.

Contribution

It establishes novel partial optimality conditions for cubic correlation clustering and develops algorithms to verify these conditions in practical scenarios.

Findings

Algorithms effectively identify partial optimal solutions.

Partial optimality conditions improve clustering quality.

Numerical experiments demonstrate practical utility.

Abstract

The higher-order correlation clustering problem for a graph $G$ and costs associated with cliques of $G$ consists in finding a clustering of $G$ so as to minimize the sum of the costs of those cliques whose nodes all belong to the same cluster. To tackle this NP-hard problem in practice, local search heuristics have been proposed and studied in the context of applications. Here, we establish partial optimality conditions for cubic correlation clustering, i.e., for the special case of at most 3-cliques. We define and implement algorithms for deciding these conditions and examine their effectiveness numerically, on two data sets.