Communications in Mathematical Sciences

Volume 6 (2008)

Number 4

Metrics defined by Bregman Divergences

Pages: 915 – 926

DOI: http://dx.doi.org/10.4310/CMS.2008.v6.n4.a6

Authors

P. Chen

Y. Chen

M. Rao

Abstract

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.

Keywords

Metrics; Bregman divergence; convexity

2010 Mathematics Subject Classification

26D10, 94A15

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