Geometry Induced by a Generalization of Rényi Divergence
Instituto Federal do Ceará, Campus Maracanaú, Fortaleza 61939-140, Brazil
Computer Engineering School, Campus Sobral, Federal University of Ceará, Sobral 62010-560, Brazil
Department of Teleinformatics Engineering, Federal University of Ceará, Fortaleza 60455-900, Brazil
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editors: Frédéric Barbaresco and Frank Nielsen
Received: 6 September 2016 / Revised: 27 October 2016 / Accepted: 11 November 2016 / Published: 17 November 2016
In this paper, we propose a generalization of Rényi divergence, and then we investigate its induced geometry. This generalization is given in terms of a φ
-function, the same function that is used in the definition of non-parametric φ
-families. The properties of φ
-functions proved to be crucial in the generalization of Rényi divergence. Assuming appropriate conditions, we verify that the generalized Rényi divergence reduces, in a limiting case, to the φ
-divergence. In generalized statistical manifold, the φ
-divergence induces a pair of dual connections
. We show that the family of connections
induced by the generalization of Rényi divergence satisfies the relation
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MDPI and ACS Style
de Souza, D.C.; Vigelis, R.F.; Cavalcante, C.C. Geometry Induced by a Generalization of Rényi Divergence. Entropy 2016, 18, 407.
de Souza DC, Vigelis RF, Cavalcante CC. Geometry Induced by a Generalization of Rényi Divergence. Entropy. 2016; 18(11):407.
de Souza, David C.; Vigelis, Rui F.; Cavalcante, Charles C. 2016. "Geometry Induced by a Generalization of Rényi Divergence." Entropy 18, no. 11: 407.
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