Communications in Mathematical Sciences
Volume 6 (2008)
Metrics defined by Bregman Divergences
Pages: 915 – 926
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.
Metrics; Bregman divergence; convexity
2010 Mathematics Subject Classification