Partial Optimality in Cubic Correlation Clustering

TL;DR

This paper develops partial optimality conditions for cubic correlation clustering on complete graphs, providing algorithms to test these conditions and demonstrating their effectiveness through numerical experiments on real datasets.

Contribution

It introduces novel partial optimality conditions for cubic correlation clustering and implements algorithms to verify these conditions in practice.

Findings

Partial optimality conditions can be effectively tested on datasets.

Algorithms improve understanding of solution quality in correlation clustering.

Numerical results demonstrate practical applicability of the methods.

Abstract

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.