Correlation Clustering with Noisy Partial Information

TL;DR

This paper introduces a semi-random model for correlation clustering on arbitrary graphs and provides two approximation algorithms with guarantees on solution quality and accuracy.

Contribution

It proposes a new semi-random model for correlation clustering and develops two approximation algorithms with provable performance guarantees.

Findings

First algorithm achieves near-optimal cost with high probability.

Second algorithm recovers the true clustering with arbitrarily small error.

Algorithms work under semi-random noise assumptions.

Abstract

In this paper, we propose and study a semi-random model for the Correlation Clustering problem on arbitrary graphs G. We give two approximation algorithms for Correlation Clustering instances from this model. The first algorithm finds a solution of value $(1+ \delta) optcost + O_{\delta}(n\log^3 n)$ with high probability, where $optcost$ is the value of the optimal solution (for every $\delta > 0$). The second algorithm finds the ground truth clustering with an arbitrarily small classification error $\eta$ (under some additional assumptions on the instance).