The quality of an image affects its utility and image quality assessment has been a hot research topic for many years. One widely used measure for image quality assessment is Shannon entropy, which has a well-established information-theoretic basis. The value of this entropy can be interpreted as the amount of information. However, Shannon entropy is badly adapted to information measurement in ...

In this paper, we derive the exact analytical expressions for the Shannon entropy of generalized orderstatistics from Pareto-type and related distributions.

We provide a method that approximates the Bayes error rate and the Shannon entropy with high probability. The Bayes error rate approximation makes possible to build a classifier that polynomially approaches Bayes error rate. The Shannon entropy approximation provides provable performance guarantees for learning trees and Bayesian networks from continuous variables. Our results rely on some reas...

Probability representation entropy (tomographic entropy) of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed. Relation of the tomographic entropy to Shannon entropy and von Neumann entropy is elucidated.

In the past few years, several entropy-based tests have been proposed for testing either single SNP association or gene-gene interaction. These tests are mainly based on Shannon entropy and have higher statistical power when compared to standard χ2 tests. In this paper, we extend some of these tests using a more generalized entropy definition, Rényi entropy, where Shannon entropy is a special c...

An analytical relationship between the densities of the Shannon entropy and Fisher information for atomic and molecular systems has been established in this work. Two equivalent forms of the Fisher information density are introduced as well. It is found that for electron densities of atoms and molecules the Shannon entropy density is intrinsically related to the electron density and the two for...

We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs [1] and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical systems, we retrieve the equality between the Kolmogorov complexity rate and the Shannon entropy rate derived by A.A. Brudno [2]. On the other hand, using the quantu...

Recurrence plots were introduced to quantify the recurrence properties of chaotic dynamics. Hereafter, the recurrence quantification analysis was introduced to transform graphical interpretations into statistical analysis. In this spirit, a new definition for the Shannon entropy was recently introduced in order to have a measure correlated with the largest Lyapunov exponent. Recurrence plots an...

Abstract The long-standing problem of Shannon entropy estimation in data streams (assuming the strict Turnstile model) is now an easy task by using the technique proposed in this paper. Essentially speaking, in order to estimate the Shannon entropy with a guaranteed ν-additive accuracy, it suffices to estimate the αth frequency moment, where α = 1−∆, with a guaranteed ǫ-multiplicative accuracy,...