Semi-Supervised Max-Sum Clustering

We study max-sum clustering in a semi-supervised setting. Our objective function maximizes the pairwise within-cluster similarity with respect to some null hypothesis regarding the similarity. This is a natural objective that does not require any additional parameters, and is a generalization of the well-known modularity objective function. We show that for such an objective function in a semi-supervised setting we can compute an additive approximation of the optimal solution in the general case, and a constant-factor approximation when the optimal objective value is large. The supervision that we consider is in the form of cluster assignment queries and same-cluster queries; we also study the setting where the query responses are noisy. Our algorithm also generalizes to the min-sum objective function, for which we can achieve similar performance guarantees. We present computational experiments to show that our framework is effective for clustering text data - we are able to find clusterings that are close to the queried clustering and have a good objective value.