## Communications in Mathematical Sciences

### Metrics defined by Bregman divergences: Part 2

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

#### 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