This memo contains proofs that the Shannon entropy is the limiting case of both the Renyi entropy and the Tsallis entropy, or information. These results are also confirmed experimentally. We conclude with some general observations on the utility of entropy measures. A brief summary of the origins of the concept of physical entropy are provided in an appendix.

An axiomatization of the concept of entropy of a discrete Choquet capacity is given. It is based on three axioms: the symmetry property, a boundary condition for which the entropy reduces to the classical Shannon entropy, and a generalized version of the well-known recursivity property. This entropy, recently introduced to extend the Shannon entropy to nonadditive measures, fulfills several pro...

Shannon entropy used in standard top-down decision trees does not guarantee the best generalization. Split criteria based on generalized entropies offer different compromise between purity of nodes and overall information gain. Modified C4.5 decision trees based on Tsallis and Renyi entropies have been tested on several high-dimensional microarray datasets with interesting results. This approac...

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect ...

Image Segmentation plays an important role in medical field that enable professionals to detect their patient’s problems and help them to get proper diagnosed. In this article, an entropy based approach for image segmentation is discussed to highlight tumor in MRI images. Magnetic Resonance Imaging (MRI) is an imaging, in which pixel values are based on radiation absorption. In the proposed app...

Hyperspectral band image selection is a fundamental problem for hyperspectral remote sensing data processing. Accepting its importance, several information-based band selection methods have been proposed, which apply Shannon entropy to measure image information. However, the Shannon entropy is not accurate in measuring image information since it neglects the spatial distribution of pixels and i...

A relation between Shannon entropy and Kerridge inaccuracy, which is known as Shannon inequality, is well known in information theory. In this communication, first we generalized Shannon inequality and then given its application in coding theory.

It was mentioned by Kolmogorov (1968, IEEE Trans. Inform. Theory 14, 662 664) that the properties of algorithmic complexity and Shannon entropy are similar. We investigate one aspect of this similarity. Namely, we are interested in linear inequalities that are valid for Shannon entropy and for Kolmogorov complexity. It turns out that (1) all linear inequalities that are valid for Kolmogorov com...

Methods for efficiently estimating Shannon entropy of data streams have important applications in learning, data mining, and network anomaly detections (e.g., the DDoS attacks). For nonnegative data streams, the method of Compressed Counting (CC) [11, 13] based on maximally-skewed stable random projections can provide accurate estimates of the Shannon entropy using small storage. However, CC is...