Communications in Mathematical Sciences

Metrics defined by Bregman Divergences

P. Chen, Y. Chen, and M. Rao

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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.

Article information

Commun. Math. Sci., Volume 6, Number 4 (2008), 915-926.

First available in Project Euclid: 18 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26D10: Inequalities involving derivatives and differential and integral operators 94A15: Information theory, general [See also 62B10, 81P94]

Metrics Bregman divergence convexity


Chen, P.; Chen, Y.; Rao, M. Metrics defined by Bregman Divergences. Commun. Math. Sci. 6 (2008), no. 4, 915--926.

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