Itakura-Saito divergence

The Itakura-Saito divergence is one of the many measures used to measure the similarity between an object x and a reference y.

It is defined as d(x|y)= x/y - log(x/y) - 1. Only if x = y the divergence is zero.

It is called a divergence and not a distance, technically speaking, because it is not symmetric: d(x|y) is not the same as d(y|x).

One of the advantages of the Itakura-Saito divergence is its scale invariance which means that d(λx|λy)=d(x|y), for any number λ. This makes it a very suitable measure for the comparison of audio spectra.