Communications in Mathematical Sciences
Volume 6 (2008)
Metrics defined by Bregman divergences: Part 2
Pages: 927 – 948
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.
Metrics; Bregman divergence; triangle inequality; Kullback-Leibler divergence; Shannon entropy; capacity
2010 Mathematics Subject Classification