Metrics defined by Bregman divergences. (English) Zbl 1163.26320

Chen, Pengwen; Chen, Yunmei; Rao, Murali

Commun. Math. Sci. 6, No. 4, 915-926 (2008).

Summary: 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.

MSC:

26D10	Inequalities involving derivatives and differential and integral operators
94A15	Information theory (general)

Keywords:

Bregman divergence; convexity subject classifications