Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 6, Number 4 (2008), 915-926.
Metrics defined by Bregman Divergences
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.
Commun. Math. Sci., Volume 6, Number 4 (2008), 915-926.
First available in Project Euclid: 18 December 2008
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Chen, P.; Chen, Y.; Rao, M. Metrics defined by Bregman Divergences. Commun. Math. Sci. 6 (2008), no. 4, 915--926. https://projecteuclid.org/euclid.cms/1229619676