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# Correlation Clustering with Noisy Partial Information

; Proceedings of The 28th Conference on Learning Theory, PMLR 40:1321-1342, 2015.

#### 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+ δ)\mathrmopt-cost + O_δ(n\log^3 n) with high probability, where \mathrmopt-cost is the value of the optimal solution (for every δ> 0). The second algorithm finds the ground truth clustering with an arbitrarily small classification error η(under some additional assumptions on the instance).