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Entropy 2014, 16(6), 3273-3301;

On Clustering Histograms with k-Means by Using Mixed α-Divergences

Sony Computer Science Laboratories, Inc, Tokyo 141-0022, Japan
Polytechnique, 91128 Palaiseau Cedex, France
NICTA and The Australian National University, Locked Bag 9013, Alexandria NSW 1435, Australia
RIKEN Brain Science Institute, 2-1 Hirosawa Wako City, Saitama 351-0198, Japan
Author to whom correspondence should be addressed.
Received: 15 May 2014 / Revised: 10 June 2014 / Accepted: 13 June 2014 / Published: 17 June 2014
(This article belongs to the Special Issue Information Geometry)
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Clustering sets of histograms has become popular thanks to the success of the generic method of bag-of-X used in text categorization and in visual categorization applications. In this paper, we investigate the use of a parametric family of distortion measures, called the α-divergences, for clustering histograms. Since it usually makes sense to deal with symmetric divergences in information retrieval systems, we symmetrize the α -divergences using the concept of mixed divergences. First, we present a novel extension of k-means clustering to mixed divergences. Second, we extend the k-means++ seeding to mixed α-divergences and report a guaranteed probabilistic bound. Finally, we describe a soft clustering technique for mixed α-divergences. View Full-Text
Keywords: bag-of-X; α-divergence; Jeffreys divergence; centroid; k-means clustering; k-means seeding bag-of-X; α-divergence; Jeffreys divergence; centroid; k-means clustering; k-means seeding

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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Nielsen, F.; Nock, R.; Amari, S.-I. On Clustering Histograms with k-Means by Using Mixed α-Divergences. Entropy 2014, 16, 3273-3301.

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