t-Entropy: A New Measure of Uncertainty with Some Applications

TL;DR

This paper introduces t-entropy, a new entropy measure based on the inverse-tan function, demonstrating its theoretical properties and applications in image thresholding, divergence measurement, and data clustering.

Contribution

The paper proposes the t-entropy, a novel entropy measure with proven axiomatic properties and diverse applications in image processing and statistical inference.

Findings

t-entropy satisfies key axiomatic properties of entropy

Effective in multi-level image thresholding

Provides robust estimators with proven statistical properties

Abstract

The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically show that the proposed t-entropy satisfies the prominent axiomatic properties of an entropy measure. We demonstrate an application of the proposed entropy measure for multi-level thresholding of images. We also propose the entropic-loss as a measure of the divergence between two probability distributions, which leads to robust estimators in the context of parametric statistical inference. The consistency and asymptotic breakdown point of the proposed estimator are mathematically analyzed. Finally, we show an application of the t-entropy to feature weighted data clustering.