In this paper, we consider the task of clustering multivariate normal distributions with respect to the relative entropy into\r 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,\r 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\r 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\r in statistics.
CITATION STYLE
Nielsen, F., & Nock, R. (2009). Emerging Trends in Visual Computing. Emerging Trends in Visual Computing (Vol. 5416, pp. 164–174). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-00826-9
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