Journal
ENTROPY
Volume 22, Issue 2, Pages -Publisher
MDPI
DOI: 10.3390/e22020221
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
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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 alpha-Jensen-Bregman divergences and derive thereof the vector-skew alpha-Jensen-Shannon divergences. We prove that the vector-skew alpha-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.
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