Beyond word frequency: Bursts, lulls, and scaling in the temporal distributions of words

TL;DR

This paper reveals that word recurrence times in language follow a stretched exponential distribution, influenced by semantic type, and introduces a generative model to explain these bursty patterns, extending understanding beyond Zipf's law.

Contribution

It demonstrates that word recurrence times exhibit bursty deviations from Poisson processes, characterized by a stretched exponential distribution, and presents a generative model for this behavior.

Findings

Word recurrence times follow a stretched exponential distribution.

Semantic type influences the extent of burstiness in word usage.

A generative model accurately captures the observed recurrence dynamics.

Abstract

Background: Zipf's discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication. More recent research has also identified scaling regularities in the dynamics underlying the successive occurrences of events, suggesting the possibility of similar findings for language as well. Methodology/Principal Findings: By considering frequent words in USENET discussion groups and in disparate databases where the language has different levels of formality, here we show that the distributions of distances between successive occurrences of the same word display bursty deviations from a Poisson process and are well characterized by a stretched exponential (Weibull) scaling. The extent of this deviation depends strongly on semantic type -- a measure of the logicality of each word -- and less strongly on frequency. We develop a generative model of this behavior that fully determines the dynamics of word usage. Conclusions/Significance: Recurrence patterns of words are well described by a stretched exponential distribution of recurrence times, an empirical scaling that cannot be anticipated from Zipf's law. Because the use of words provides a uniquely precise and powerful lens on human thought and activity, our findings also have implications for other overt manifestations of collective human dynamics.