Abstract

Despite the ubiquity of clustering as a tool in unsupervised learning, there is not yet a consensus on a formal theory, and the vast majority of work in this direction has focused on unsupervised clustering. We study a recently proposed framework for supervised clustering where there is access to a teacher. We give an improved generic algorithm to cluster any concept class in that model. Our algorithm is query-efficient in the sense that it involves only a small amount of interaction with the teacher. We also present and study two natural generalizations of the model. The model assumes that the teacher response to the algorithm is perfect. We eliminate this limitation by proposing a noisy model and give an algorithm for clustering the class of intervals in this noisy model. We also propose a dynamic model where the teacher sees a random subset of the points. Finally, for datasets satisfying a spectrum of weak to strong properties, we give query bounds, and show that a class of clustering functions containing Single-Linkage will find the target clustering under the strongest property.