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Abstract This paper proposes an application of distorted entropy as well-known tools for non-additive expected utility theory in word ranking. Our algorithms for two books "Statistical Inference" by Casella and Berger and "The Origin of Species" by Charles Darwin show that our method on the distorted entropy improves the corresponding ones in the literature. Highlights • An algorithm for word ranking based on distorted entropy is discussed. • This paper proposes an application of distorted probabilities in word ranking. • Our results improve the corresponding ones in the literature. • Our method is new and is applicable to any distorted entropy. [ABSTRACT FROM AUTHOR]

Long-range correlations between the elements of natural languages enable them to convey very complex information. Complex structure of human language, as a manifestation of natural languages, motivates us to apply nonextensive statistical mechanics in text mining. Tsallis entropy appropriately ranks the terms’ relevance to document subject, taking advantage of their spatial correlation length. We apply this statistical concept as a new powerful word ranking metric in order to extract keywords of a single document. We carry out an experimental evaluation, which shows capability of the presented method in keyword extraction. We find that, Tsallis entropy has reliable word ranking performance, at the same level of the best previous ranking methods. [ABSTRACT FROM AUTHOR]

Spatial distribution of cone and rod photoreceptors in human eye retina, are studied by using non-extensive statistics. We show that photoreceptors’ packing density obeys q -exponential and q -Gaussian distributions. Cones retinal distribution has higher non-extensivity in young subjects in comparison with old ones. Absolute value of q -parameter for spatial distribution of both types of photocells gets higher values along horizontal meridian. We also calculate Shannon's additive entropy and Tsallis’ non-additive entropy for cone photocells distribution in retina, and compare their results. Information entropy, especially Tsallis entropy, is capable to discriminate between young and old subjects, properly. Our results confirm the ability of non-extensive statistics to unveil retinal eye problems caused by abnormal photoreceptors distribution. [ABSTRACT FROM AUTHOR]

Ranking the words in human written texts, according to their relevance to text context, plays a crucial role in many text mining tasks. Highly relevant words concentrate in some limited areas, while the irrelevant ones have nearly random spatial distribution throughout the text. But in the randomly shuffled version of the text, all word types are distributed at random. The difference between spatial distribution of words in the original version of a text and its shuffled version seems a proper criterion for word relevance ranking. In this procedure, spatial distribution of each word type in the document is defined by box counting method. Then we apply Jensen–Shannon divergence to measure the difference between probability distributions of each word in the original text and its shuffled version. This metric properly distinguishes relevant words from irrelevants without requiring any previous knowledge about text structure. [ABSTRACT FROM AUTHOR]

Abstract: Entropy as a measure of complexity in the systems has been applied for ranking the words in the human written texts. We introduce a novel approach to evaluate accuracy for retrieved indices. We also have an illustrative comparison between proposed entropic metrics and some other methods in extracting the keywords. It seems that, some of the discussed metrics apply similar features for word ranking in the text. This work recommend the entropy as a systematic measure in text mining. [Copyright &y& Elsevier]

Non-extensive statistical mechanics appears as a powerful way to describe complex systems. Tsallis entropy, the main core of this theory has been remained as an unproven assumption. Many people have tried to derive the Tsallis entropy axiomatically. Here we follow the work of Wang (EPJB, 2002) and use the incomplete information theory to retrieve the Tsallis entropy. We change the incomplete information axioms to consider the escort probability and obtain a correct form of Tsallis entropy in comparison with Wang's work. [ABSTRACT FROM AUTHOR]