Bregman divergence

A Bregman divergence, or Bregman distance, BF on a space 𝒳d is defined for a strictly convex and differentiable function F:𝒳 as

BF(p,q)=F(p)-F(q)-p-q,F(q), (1)



denotes the inner product, and


the partial derivativesMathworldPlanetmath.

Choosing F(x)=i=1dxi2 yields the squared Euclidean distance Bx2(p,q)=||p-q||2, and choosing F(x)=i=1dxilogxi yields the relative entropyMathworldPlanetmath, called the Kullback-Leibler divergence.

Title Bregman divergence
Canonical name BregmanDivergence
Date of creation 2013-03-22 19:11:38
Last modified on 2013-03-22 19:11:38
Owner FrankTokyo (25936)
Last modified by FrankTokyo (25936)
Numerical id 6
Author FrankTokyo (25936)
Entry type Definition
Classification msc 51K05
Synonym Bregman distance