Itakura–Saito distance

The Itakura–Saito distance (or Itakura–Saito divergence) is a measure of the difference between an original spectrum P ( ω ) and an approximation P ^ ( ω ) of that spectrum. Although it is not a perceptual measure it is intended to reflect perceptual (dis)similarity. It was proposed by Fumitada Itakura and Shuzo Saito in the 1960s while they were with NTT.

The distance is defined as:

The Itakura–Saito distance is a Bregman divergence, but is not a true metric since it is not symmetric and it does not fulfil triangle inequality.

In Non-negative matrix factorization the Itakura-Saito divergence can be used as a measure of the quality of the factorization: this implies a meaningful statistical model of the components and can be solved through an iterative method.