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Clustering with Bregman Divergences: an Asymptotic Analysis

Chaoyue Liu · Mikhail Belkin

Area 5+6+7+8 #95

Keywords: [ Learning Theory ] [ Clustering ]

Abstract: 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.

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