How to tell when a clustering is (approximately) correct using convex relaxations

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Marina Meila


We introduce the Sublevel Set (SS) method, a generic method to obtain sufficient guarantees of near-optimality and uniqueness (up to small perturbations) for a clustering. This method can be instantiated for a variety of clustering loss functions for which convex relaxations exist. Obtaining the guarantees in practice amounts to solving a convex optimization. We demonstrate the applicability of this method by obtaining distribution free guarantees for K-means clustering on realistic data sets.