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On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid
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On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid
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Journal Article
On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid
2020
Overview
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.
Publisher
MDPI,MDPI AG
