Clustering with a faulty oracle

Clustering, i.e., finding groups in the data, is a problem that permeates multiple fields of science and engineering. Recently, the problem of clustering with a noisy oracle has drawn attention due to various applications including crowdsourced entity resolution [33] , and predicting signs of interactions in large-scale online social networks [20, 21] . Here, we consider the following fundamental model for two clusters as proposed by Mitzenmacher and Tsourakakis [28] , and Mazumdar and Saha [25] ; there exist n items, belonging to two unknown groups. We are allowed to query any pair of nodes whether they belong to the same cluster or not, but the answer to the query is corrupted with some probability 0 < q < 1 2 . Let 1 > δ = 1 -2q > 0 be the bias. In this work, we provide a polynomial time algorithm that recovers all signs correctly with high probability in the presence of noise with O( ) queries. This is the best known result for this problem for all but tiny δ , improving on the current state-of-the-art due to Mazumdar and Saha [25] .