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arXiv · 0804.1653

Nonextensive Generalizations of the Jensen-Shannon Divergence

Andre Martins·Pedro Aguiar·Mario Figueiredo
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Abstract

Convexity 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.

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Andre Martins, Pedro Aguiar, Mario Figueiredo. 2008-04-10. Nonextensive Generalizations of the Jensen-Shannon Divergence. https://arxiv.org/abs/0804.1653

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