A Novel Distance Matric: Generalized Relative Entropy

TL;DR

This paper introduces a new generalized relative entropy that addresses limitations of traditional relative entropy, proving it to be a finite distance metric with a finite range, applicable across various research domains.

Contribution

The paper proposes a novel generalized relative entropy with proven properties, including being a finite distance metric, improving upon traditional measures.

Findings

The generalized relative entropy has a finite range.

It is proven to be a finite distance metric.

The structure and properties of the new entropy are established.

Abstract

Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We presented the structure of generalized relative entropy after the discussion of defects in relative entropy. Moreover, some properties of the provided generalized relative entropy is presented and proved. The provided generalized relative entropy is proved to have a finite range and is a finite distance metric.