On a generalization of the Jensen-Shannon divergence

The Jensen-Shannon divergence is a renown bounded symmetrization of the Kullback-Leibler divergence which does not require probability densities to have coinciding support. In this paper, we introduce a vector-skew generalization of the $\alpha$-Jensen-Bregman divergences and derive thereof the vector-skew $\alpha$-Jensen-Shannon divergences. We study the properties of these novel divergences and show how to build parametric families of symmetric Jensen-Shannon-type divergences. Finally, we report an algorithm to compute these Jensen-Shannon-type centroids for a set of probability densities belonging to a mixture family.