On Tsallis extropy with an application to pattern recognition

TL;DR

This paper introduces Tsallis extropy, a new measure of discrimination related to Tsallis entropy, explores its properties and bounds, and demonstrates its application to pattern recognition tasks.

Contribution

The paper proposes Tsallis extropy as a novel measure, analyzes its properties and relationships with entropy, and applies it to improve pattern recognition methods.

Findings

Tsallis extropy is a valid measure with specific properties.

Bounds for Tsallis extropy are established.

Application to pattern recognition shows promising results.

Abstract

Recently, a new measure of information called extropy has been introduced by Lad, Sanfilippo and Agr\`o as the dual version of Shannon entropy. In the literature, Tsallis introduced a measure for a discrete random variable, named Tsallis entropy, as a generalization of Boltzmann-Gibbs statistics. In this work, a new measure of discrimination, called Tsallis extropy, is introduced and some of its properties are then discussed. The relation between Tsallis extropy and entropy is given and some bounds are also presented. Finally, an application of this extropy to pattern recognition is demonstrated.