Monoparametric family of metrics derived from classical Jensen–Shannon divergence

Abstract

Jensen–Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic properties of a distance, it also satisfies the triangle inequality. In this work we extend this last result to prove that in fact it is possible to derive a monoparametric family of metrics from the classical Jensen–Shannon divergence. Motivated by our results, an application into the field of symbolic sequences segmentation is explored. Additionally, we analyze the possibility to extend this result into the quantum realm.