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Selected Papers from the 5th conference on Geometric Science of Information

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (17 December 2021) | Viewed by 8783

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Sony Computer Science Laboratories, Takanawa Muse Bldg., 3-14-13, Higashigotanda, Shinagawa-ku, Tokyo 141-0022, Japan
Interests: information geometry; machine learning; imaging
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Special Issue Information

Dear Colleagues,

This Special Issue will collect a limited number of selected invited and contributed talks presented during the conference GSI'21 on Geometric Science of Information, which will be held in Sorbonne University, Paris, France, in July 2021. The conference website can be found at https://www.see.asso.fr/en/GSI2021

Prof. Frédéric Barbaresco
Prof. Dr. Frank Nielsen
Guest Editors

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Published Papers (1 paper)

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28 pages, 1106 KiB  
Article
On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius
by Frank Nielsen
Entropy 2021, 23(4), 464; https://0-doi-org.brum.beds.ac.uk/10.3390/e23040464 - 14 Apr 2021
Cited by 17 | Viewed by 7871
Abstract
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 [...] Read more.
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. Full article
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