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On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

Sony Computer Science Laboratories, Tokyo 141-0022, Japan
Academic Editor: Yong Deng
Entropy 2021, 23(4), 464; https://doi.org/10.3390/e23040464
Received: 12 March 2021 / Revised: 9 April 2021 / Accepted: 9 April 2021 / Published: 14 April 2021
We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson’s information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures. View Full-Text
Keywords: Jensen-Shannon divergence; diversity index; Rényi entropy; information radius; information projection; exponential family; Bregman divergence; Fenchel–Young divergence; Bregman information; q-exponential family; q-divergence; Bhattacharyya distance; centroid; clustering Jensen-Shannon divergence; diversity index; Rényi entropy; information radius; information projection; exponential family; Bregman divergence; Fenchel–Young divergence; Bregman information; q-exponential family; q-divergence; Bhattacharyya distance; centroid; clustering
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MDPI and ACS Style

Nielsen, F. On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius. Entropy 2021, 23, 464. https://doi.org/10.3390/e23040464

AMA Style

Nielsen F. On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius. Entropy. 2021; 23(4):464. https://doi.org/10.3390/e23040464

Chicago/Turabian Style

Nielsen, Frank. 2021. "On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius" Entropy 23, no. 4: 464. https://doi.org/10.3390/e23040464

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