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December 2008 Metrics defined by Bregman Divergences
P. Chen, Y. Chen, M. Rao
Commun. Math. Sci. 6(4): 915-926 (December 2008).


Bregman divergences are generalizations of the well known Kullback-Leibler divergence. They are based on convex functions and have recently received great attention. We present a class of “squared root metrics” based on Bregman divergences. They can be regarded as natural generalization of Euclidean distance. We provide necessary and sufficient conditions for a convex function so that the square root of its associated average Bregman divergence is a metric.


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P. Chen. Y. Chen. M. Rao. "Metrics defined by Bregman Divergences." Commun. Math. Sci. 6 (4) 915 - 926, December 2008.


Published: December 2008
First available in Project Euclid: 18 December 2008

zbMATH: 1163.26320
MathSciNet: MR2511699

Primary: 26D10 , 94A15

Keywords: Bregman divergence , convexity , Metrics

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 4 • December 2008
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