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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Clustering Multivariate Normal Distributions
verfasst von : Frank Nielsen, Richard Nock
Erschienen in: Emerging Trends in Visual Computing
Verlag: Springer Berlin Heidelberg
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In this paper, we consider the task of clustering multivariate normal distributions with respect to the relative entropy into a prescribed number,
k
, of clusters using a generalization of Lloyd’s
k
-means algorithm [1]. We revisit this information-theoretic clustering problem under the auspices of mixed-type Bregman divergences, and show that the approach of Davis and Dhillon [2] (NIPS*06) can also be derived directly, by applying the Bregman
k
-means algorithm, once the proper vector/matrix Legendre transformations are defined. We further explain the dualistic structure of the sided
k
-means clustering, and present a novel
k
-means algorithm for clustering with respect to the symmetrical relative entropy, the
J
-divergence.Our approach extends to differential entropic clustering of arbitrary members of the same exponential families in statistics.