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Coresets are efficient representations of data sets such that models trainedon the coreset are provably competitive with models trained on the originaldata set. As such, they have been successfully used to scale up clusteringmodels such as K-Means and Gaussian mixture models to massive data sets.However, until now, the algorithms and the corresponding theory were usuallyspecific to each clustering problem.  We propose a single, practical algorithm to construct strong coresets for alarge class of hard and soft clustering problems based on Bregman divergences.This class includes hard clustering with popular distortion measures such asthe Squared Euclidean distance, the Mahalanobis distance, KL-divergence andItakura-Saito distance. The corresponding soft clustering problems are directlyrelated to popular mixture models due to a dual relationship between Bregmandivergences and Exponential family distributions. Our theoretical resultsfurther imply a randomized polynomial-time approximation scheme for hardclustering. We demonstrate the practicality of the proposed algorithm in anempirical evaluation.

Strong Coresets for Hard and Soft Bregman Clustering with Applications to Exponential Family Mixtures