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RSS FeedsEntropy, Vol. 22, Pages 221: On a Generalization of the Jensen-Shannon Divergence and the Jensen-Shannon Centroid (Entropy)

 
 

16 february 2020 16:02:35

 
Entropy, Vol. 22, Pages 221: On a Generalization of the Jensen-Shannon Divergence and the Jensen-Shannon Centroid (Entropy)
 


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 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.


 
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