  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 study the
properties of these novel divergences and show how to build parametric families
of symmetric Jensen-Shannon-type 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.
