Monoparametric family of metrics derived from classical Jensen-Shannon divergence

TL;DR

This paper introduces a new family of metrics derived from the Jensen-Shannon divergence, extending its properties and exploring applications in sequence segmentation and potential quantum extensions.

Contribution

It proves the existence of a monoparametric family of metrics from Jensen-Shannon divergence and explores their applications and extensions.

Findings

Established a family of metrics from Jensen-Shannon divergence

Applied metrics to symbolic sequence segmentation

Discussed potential quantum extensions

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.