Entropy and type-token ratio in gigaword corpora

2024-11-15

arXiv.org

AI Summary

This study investigates the quantitative relationship between lexical diversity—measured by word entropy and type-token ratio (TTR)—across large-scale corpora (≈1 billion tokens each) of English, Spanish, and Turkish, spanning books, news, and tweets. Using word-frequency distributions, information-theoretic entropy computation, and power-law fitting, we empirically establish, for the first time across multiple languages and genres at scale, a highly consistent negative functional relationship between word entropy and TTR (R² > 0.99). By integrating Zipf’s law and Heaps’ law, we derive an analytical expression for this relationship in the asymptotic limit of large texts. The resulting function proves cross-linguistically invariant, revealing a universal scaling law governing lexical diversity. This work provides a unified theoretical framework for modeling linguistic diversity and establishes a testable, mathematically grounded metric foundation for quantitative language analysis.

Technology Category

• Natural Language Processing: Lexical Semantics and Morphology
• Knowledge Representation and Reasoning: Knowledge Representation Languages
• Machine Learning: Information Theory

Application Category

• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

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.

Problem

• Measure lexical diversity in languages
• Analyze entropy and type-token ratio
• Examine large text corpora

Innovation

• Lexical diversity metrics analyzed
• Empirical functional relation unveiled
• Analytical expression derived