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

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.