Entropy and type-token ratio in gigaword corpora

TL;DR

This study explores the relationship between entropy and type-token ratio across diverse large-scale linguistic datasets, revealing a functional link grounded in natural language statistical laws.

Contribution

It introduces an empirical and analytical relation between entropy and type-token ratio in large corpora, supported by data from multiple languages and genres.

Findings

Discovered an empirical functional relation between entropy and type-token ratio.

Derived an analytical expression based on Zipf and Heaps laws.

Validated the relation across multilingual and multi-genre corpora.

Abstract

There are different ways of measuring diversity in complex systems. In particular, in language, lexical diversity is characterized in terms of the type-token ratio and the word entropy. We here investigate both diversity metrics in six massive linguistic datasets in English, Spanish, and Turkish, consisting of books, news articles, and tweets. These gigaword corpora correspond to languages with distinct morphological features and differ in registers and genres, thus constituting a varied testbed for a quantitative approach to lexical diversity. We unveil an empirical functional relation between entropy and type-token ratio of texts of a given corpus and language, which is a consequence of the statistical laws observed in natural language. Further, in the limit of large text lengths we find an analytical expression for this relation relying on both Zipf and Heaps laws that agrees with our empirical findings.