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December 2008 Metrics defined by Bregman divergences: Part 2
P. Chen, Y. Chen, M. Rao
Commun. Math. Sci. 6(4): 927-948 (December 2008).


Bregman divergences have played an important role in many research areas. Divergence is a measure of dissimilarity and by itself is not a metric. If a function of the divergence is a metric, then it becomes much more powerful. In Part 1 we have given necessary and sufficient conditions on the convex function in order that the square root of the averaged associated divergence is a metric. In this paper we provide a min-max approach to getting a metric from Bregman divergence. We show that the “capacity” to the power 1/e is a metric.


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P. Chen. Y. Chen. M. Rao. "Metrics defined by Bregman divergences: Part 2." Commun. Math. Sci. 6 (4) 927 - 948, December 2008.


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

zbMATH: 1163.26320
MathSciNet: MR2511700

Primary: 26D10 , 94A15

Keywords: Bregman divergence , capacity , Kullback-Leibler divergence , Metrics , Shannon entropy , triangle inequality

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 4 • December 2008
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