Clustering with Bregman Divergences: an Asymptotic Analysis

Part of Advances in Neural Information Processing Systems 29 (NIPS 2016)

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Chaoyue Liu, Mikhail Belkin


Clustering, in particular $k$-means clustering, is a central topic in data analysis. Clustering with Bregman divergences is a recently proposed generalization of $k$-means clustering which has already been widely used in applications. In this paper we analyze theoretical properties of Bregman clustering when the number of the clusters $k$ is large. We establish quantization rates and describe the limiting distribution of the centers as $k\to \infty$, extending well-known results for $k$-means clustering.