Summary and Distance between Sets of Texts based on Topological Data Analysis

TL;DR

This paper introduces a novel method combining topological data analysis and deep learning word embeddings to summarize and compare literary texts, revealing topological features of different authors and styles.

Contribution

It presents the first integration of persistent homology, persistent entropy, and bottleneck distance with word embeddings for literary text analysis.

Findings

Successfully characterized texts of three Spanish Golden Age poets.

Provided a new topological approach to compare literary styles.

Demonstrated the effectiveness of TDA tools in literary analysis.

Abstract

In this paper, we use topological data analysis (TDA) tools such as persistent homology, persistent entropy and bottleneck distance, to provide a {\it TDA-based summary} of any given set of texts and a general method for computing a distance between any two literary styles, authors or periods. To this aim, deep-learning word-embedding techniques are combined with these tools in order to study the topological properties of texts embedded in a metric space. As a case of study, we use the written texts of three poets of the Spanish Golden Age: Francisco de Quevedo, Luis de G\'ongora and Lope de Vega. As far as we know, this is the first time that word embedding, bottleneck distance, persistent homology and persistent entropy are used together to characterize texts and to compare different literary styles.