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Nielsen, Frank
Entropy, 02/2020, Letnik: 22, Številka: 2Journal Article
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 -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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