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Open AccessArticle

On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid

Sony Computer Science Laboratories, Tokyo 141-0022, Japan
Entropy 2020, 22(2), 221; https://doi.org/10.3390/e22020221
Received: 5 December 2019 / Revised: 14 February 2020 / Accepted: 14 February 2020 / Published: 16 February 2020
The Jensen–Shannon divergence is a renown bounded symmetrization of the Kullback–Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the scalar α -Jensen–Bregman divergences and derive thereof the vector-skew α -Jensen–Shannon divergences. We prove that the vector-skew α -Jensen–Shannon divergences are f-divergences and study the properties of these novel divergences. Finally, we report an iterative algorithm to numerically compute the Jensen–Shannon-type centroids for a set of probability densities belonging to a mixture family: This includes the case of the Jensen–Shannon centroid of a set of categorical distributions or normalized histograms. View Full-Text
Keywords: Bregman divergence; f-divergence; Jensen–Bregman divergence; Jensen diversity; Jensen–Shannon divergence; capacitory discrimination; Jensen–Shannon centroid; mixture family; information geometry; difference of convex (DC) programming Bregman divergence; f-divergence; Jensen–Bregman divergence; Jensen diversity; Jensen–Shannon divergence; capacitory discrimination; Jensen–Shannon centroid; mixture family; information geometry; difference of convex (DC) programming
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Nielsen, F. On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid. Entropy 2020, 22, 221.

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