Communications in Mathematical Sciences

Metrics defined by Bregman divergences: Part 2

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

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Abstract

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

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

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.cms/1229619677

Mathematical Reviews number (MathSciNet)
MR2511700

Zentralblatt MATH identifier
1163.26320

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

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

Citation

Chen, P.; Chen, Y.; Rao, M. Metrics defined by Bregman divergences: Part 2. Commun. Math. Sci. 6 (2008), no. 4, 927--948. https://projecteuclid.org/euclid.cms/1229619677


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