Correlation Clustering with Asymmetric Classification Errors

In the Correlation Clustering problem, we are given a weighted graph G with its edges labeled as "similar" or "dissimilar" by a binary classifier. The goal is to produce a clustering that minimizes the weight of "disagreements": the sum of the weights of "similar" edges across clusters and "dissimilar" edges within clusters. We study the correlation clustering problem under the following assumption: Every "similar" edge e has weight we∈[α w, w] and every "dissimilar" edge e has weight we≥ α w (where α≤ 1 and w>0 is a scaling parameter). We give a (3 + 2 loge (1/α)) approximation algorithm for this problem. This assumption captures well the scenario when classification errors are asymmetric. Additionally, we show an asymptotically matching Linear Programming integrality gap of Omega(log 1/α).