Nonextensive Generalizations of the Jensen-Shannon Divergence

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dc.creatorMartins, Andre
dc.creatorAguiar, Pedro
dc.creatorFigueiredo, Mario
dc.date2008-04-10
dc.date.accessioned2026-07-07T09:31:32Z
dc.date.available2026-07-07T09:31:32Z
dc.descriptionConvexity is a key concept in information theory, namely via the many implications of Jensen's inequality, such as the non-negativity of the Kullback-Leibler divergence (KLD). Jensen's inequality also underlies the concept of Jensen-Shannon divergence (JSD), which is a symmetrized and smoothed version of the KLD. This paper introduces new JSD-type divergences, by extending its two building blocks: convexity and Shannon's entropy. In particular, a new concept of q-convexity is introduced and shown to satisfy a Jensen's q-inequality. Based on this Jensen's q-inequality, the Jensen-Tsallis q-difference is built, which is a nonextensive generalization of the JSD, based on Tsallis entropies. Finally, the Jensen-Tsallis q-difference is charaterized in terms of convexity and extrema.
dc.descriptionSubmitted to the IEEE Transactions on Information Theory
dc.identifierhttps://arxiv.org/abs/0804.1653
dc.identifierhttp://arxiv.org/abs/0804.1653
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158490
dc.subjectInformation Theory
dc.subjectStatistics Theory
dc.subject94A17; 94A15
dc.titleNonextensive Generalizations of the Jensen-Shannon Divergence
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