Clustering with Same-Cluster Queries

We propose a framework for Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to interact with a domain expert, asking whether two given instances belong to the same cluster or not. We study the query and computational complexity of clustering in this framework. We consider a setting where the expert conforms to a center-based clustering with a notion of margin. We show that there is a trade off between computational complexity and query complexity; We prove that for the case of k-means clustering (i.e., when the expert conforms to a solution of k-means), having access to relatively few such queries allows efficient solutions to otherwise NP hard problems.