Variation of Zipf's exponent in one hundred live languages: A study of the Holy Bible translations

Mehri, Ali; Jamaati, Maryam

doi:10.1016/j.physleta.2017.05.061

Cited by 35 publications

(32 citation statements)

References 43 publications

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“…However, first, each of these metrics measures only one of the aspects of TM performance. It is known that the distribution of words, at least in European languages, satisfies the so-called Zipf law (a power-law distribution), which is characteristic of complex systems, i.e., of systems with non-Markov processes [ 25 , 26 ]. It is known that the most effective way to investigate the behavior of complex systems is application of mathematical formalism borrowed from the theory of non-additive systems [ 26 ].…”

Section: Introductionmentioning

confidence: 99%

Estimating Topic Modeling Performance with Sharma–Mittal Entropy

Koltcov

Ignatenko

Koltsova

2019

Entropy

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Topic modeling is a popular approach for clustering text documents. However, current tools have a number of unsolved problems such as instability and a lack of criteria for selecting the values of model parameters. In this work, we propose a method to solve partially the problems of optimizing model parameters, simultaneously accounting for semantic stability. Our method is inspired by the concepts from statistical physics and is based on Sharma–Mittal entropy. We test our approach on two models: probabilistic Latent Semantic Analysis (pLSA) and Latent Dirichlet Allocation (LDA) with Gibbs sampling, and on two datasets in different languages. We compare our approach against a number of standard metrics, each of which is able to account for just one of the parameters of our interest. We demonstrate that Sharma–Mittal entropy is a convenient tool for selecting both the number of topics and the values of hyper-parameters, simultaneously controlling for semantic stability, which none of the existing metrics can do. Furthermore, we show that concepts from statistical physics can be used to contribute to theory construction for machine learning, a rapidly-developing sphere that currently lacks a consistent theoretical ground.

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Section: Introductionmentioning

confidence: 99%

Estimating Topic Modeling Performance with Sharma–Mittal Entropy

Koltcov

Ignatenko

Koltsova

2019

Entropy

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“…Human languages have been known to demonstrate similar probabilistic distributions. Specifically, the frequency of occurrence of the words from a piece of text mostly follow a power-law distribution obeying the Zipf-Mandelbrot law [ 20 ]. Interestingly, this trend remains conserved and consistent across all known human languages and has been used to assign language-like property or lack thereof to other analogous datasets as diverse as inscriptions from ancient civilizations such as the Indus valley script [ 21 ], animal vocalizations like dolphin whistles [ 22 ] and bird songs [ 23 ], behavioral displays and sequences pertaining to courtship like the “push-up” displays of lizards [ 24 ] and even genetic distribution in an organism [ 25 ].…”

Section: Introductionmentioning

confidence: 99%

Power-laws in dog behavior may pave the way to predictive models: A pattern analysis study

Banerjee

Das

Dey

et al. 2021

Heliyon

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This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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“…For instance, Moreno-Sánchez et al [13] analyzed different mathematical alternatives to Zipf's law, using all English texts (tens of thousands) available from the Project Gutenberg digital library. In a sort of complementary study, Mehri and Jamaati [31] considered just one text (the Bible) but in its translation to one hundred distinct languages.…”

Section: Introductionmentioning

confidence: 99%

Lognormals, Power Laws and Double Power Laws in the Distribution of Frequencies of Harmonic Codewords from Classical Music

Serra-Peralta¹,

Serrà²,

Corral³

2021

Preprint

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Zipf's law is a paradigm describing the importance of different elements in communication systems, especially in linguistics. Despite the complexity of the hierarchical structure of language, music has in some sense an even more complex structure, due to its multidimensional character (melody, harmony, rhythm, timbre...). Thus, the relevance of Zipf's law in music is still an open question. Using discrete codewords representing harmonic content obtained from a large-scale analysis of classical composers, we show that a nearly universal Zipf-like law holds at a qualitative level. However, in an in-depth quantitative analysis, where we introduce the double power-law distribution as a new player in the classical debate between the superiority of Zipf's (power) law and that of the lognormal distribution, we conclude not only that universality does not hold, but that there is not a unique probability distribution that best describes the usage of the different codewords by each composer.

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Variation of Zipf's exponent in one hundred live languages: A study of the Holy Bible translations

Cited by 35 publications

References 43 publications

Estimating Topic Modeling Performance with Sharma–Mittal Entropy

Estimating Topic Modeling Performance with Sharma–Mittal Entropy

Power-laws in dog behavior may pave the way to predictive models: A pattern analysis study

Lognormals, Power Laws and Double Power Laws in the Distribution of Frequencies of Harmonic Codewords from Classical Music

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