Jafar Jafarov : Correlation Clustering with Local and Global Objectives

Posted by Karoline Dubin , part of the Computer Science Theory Seminar.

At

March 30, 2022, 3 p.m.

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Abstract

In the Correlation Clustering problem, we are given a graph with its edges labeled as "similar" and "dissimilar" by a noisy binary classifier, and the goal is to produce a clustering of the vertex set which matches with the edge labels as much as possible. Correlation Clustering has been mainly studied under two models where the input graph is (i) complete and unweighted, and (ii) arbitrary and weighted. In this talk, we introduce a new model of Correlation Clustering that better captures real life instances. In this model the input graph is complete with bounded edge weights. We give an approximation algorithm and give a matching integrality gap instance. We examine the model under a $\ell_p$ objective which is a generalization of the standard Correlation Clustering objective, MinDisagree. We give an approximation algorithm and show an almost matching integrality gap for this objective.