2019/12/19 by Frank Nielsen · 2 citations
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #Bounded function #Categorical variable #Centroid #Divergence (linguistics) #Generalization #Matching (statistics) #Mathematical Inequalities and Applications #Multi-Criteria Decision Making #Statistical Mechanics and Entropy #Symmetrization #cs.IT #math.IT #math.ST #stat.TH
paper · pdf · doi:10.3390/e22020221
published as Entropy 2020, 22(2), 221 · 19 pages, 3 figures
openalex created_date 2019/12/05 · arxiv created 2019/12/19 · openalex publication_date 2020/02/16 · arxiv updated 2020/10/01 · openalex updated_date 2026/08/05
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 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.