Understanding Zipf's law of word frequencies through sample-space collapse in sentence formation

Thurner S, Hanel R, Liu B, & Corominas-Murtra B (2015). Understanding Zipf's law of word frequencies through sample-space collapse in sentence formation. Interface 12 (108): 0330. DOI:10.1098/rsif.2015.0330.

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Abstract

The formation of sentences is a highly structured and history-dependent process. The probability of using a specific word in a sentence strongly depends on the 'history' of word usage earlier in that sentence. We study a simple history-dependent model of text generation assuming that the sample-space of word usage reduces a long sentence formation, on average. We first show that the model explains the approximate Zipf law found in word frequencies as a direct consequence of sample-space reduction. We then empirically quantify the amount of sample-space reduction in the sentences of 10 famous English books, by analysis of corresponding word-transition tables that capture which words can follow any given word in a text. We find a highly nested structure in these transition tables and show that this 'nestedness' is tightly related to the power law exponents of the observed word frequency distributions. With the proposed model, it is possible to understand that the nestedness of a text can be the origin of the actual scaling exponent and that deviations from the exact Zipf law can be understood by variations of the degree of nestedness on a book-by-book basis. On a theoretical level, we are able to show that in the case of weak nesting, Zip's law breaks down in a fast transition. Unlike previous attempts to understand Zipf's law in language the sample-space reducing model is not based on assumptions of multiplicative, preferential or self-organized critical mechanisms behind language formation, but simply uses the empirically quantifiable parameter 'nestedness' to understand the statstics of word frequencies.

Item Type: Article
Uncontrolled Keywords: language formation; random walks on networks; scaling in stochastic processes; word-transition networs
Research Programs: Advanced Systems Analysis (ASA)
Bibliographic Reference: Journal of the Royal Society Interface; 12(108):0330 (July 2015)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:53
Last Modified: 26 Feb 2016 10:06
URI: http://pure.iiasa.ac.at/11401

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