Communications in Mathematical Sciences

Metrics defined by Bregman divergences: Part 2

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

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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.

Article information

Commun. Math. Sci., Volume 6, Number 4 (2008), 927-948.

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 triangle inequality Kullback-Leibler divergence Shannon entropy capacity


Chen, P.; Chen, Y.; Rao, M. Metrics defined by Bregman divergences: Part 2. Commun. Math. Sci. 6 (2008), no. 4, 927--948.

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