[Paper Review] An Introduction to a New Text Classification and Visualization for Natural Language Processing Using Topological Data Analysis

Naiereh Elyasi, Mehdi Hosseini Moghadam|arXiv (Cornell University)|Jun 3, 2019

Topological and Geometric Data Analysis27 references4 citations

TL;DR

This paper introduces a novel text classification and visualization approach for natural language processing using topological data analysis (TDA), specifically persistent homology and Mapper, to distinguish Persian poems by Ferdowsi and Hafez. It demonstrates that TDA can effectively capture high-level structural patterns in poetic texts, achieving accurate classification and meaningful visualizations without relying on traditional NLP pipelines.

ABSTRACT

Topological Data Analysis (TDA) is a novel new and fast growing field of data science providing a set of new topological and geometric tools to derive relevant features out of complex high-dimensional data. In this paper we apply two of best methods in topological data analysis, "Persistent Homology" and "Mapper", in order to classify persian poems which has been composed by two of the best Iranian poets namely "Ferdowsi" and "Hafez". This article has two main parts, in the first part we explain the mathematics behind these two methods which is easy to understand for general audience and in the second part we describe our models and the results of applying TDA tools to NLP.

Motivation & Objective

• To investigate the applicability of topological data analysis (TDA) in natural language processing for text classification.
• To develop a method that leverages topological features to distinguish between poetic styles of two prominent Persian poets, Ferdowsi and Hafez.
• To provide an accessible introduction to persistent homology and Mapper for non-specialists in algebraic topology.
• To demonstrate that topological features can capture semantic and stylistic patterns in text data without traditional NLP preprocessing.
• To visualize high-dimensional text data in a way that preserves structural relationships and enables interpretability.

Proposed method

• The authors apply persistent homology to extract topological features from text embeddings, capturing the shape of data across multiple scales.
• Mapper is used to construct a topological summary of the data by clustering and connecting regions of high density in the feature space.
• Texts are first embedded into a vector space using standard NLP techniques, then processed through TDA pipelines.
• The resulting persistence diagrams and mapper graphs are used as input for classification models.
• The method relies on the geometric and topological structure of data rather than linguistic or syntactic features.
• The approach is designed to be interpretable, with visual outputs reflecting the underlying data topology.

Experimental results

Research questions

• RQ1 Can topological data analysis effectively classify Persian poetry based on stylistic differences between Ferdowsi and Hafez?
• RQ2 How do persistent homology and Mapper capture meaningful structural patterns in high-dimensional text data?
• RQ3 To what extent can TDA-based features outperform or complement traditional NLP methods in text classification tasks?
• RQ4 Can topological visualization reveal interpretable clusters or patterns in poetic texts?
• RQ5 Is the TDA pipeline accessible and understandable for non-experts in algebraic topology?

Key findings

• The TDA-based approach successfully classified Persian poems by Ferdowsi and Hafez using topological features derived from text embeddings.
• Persistent homology captured stable topological invariants that reflected stylistic differences between the two poets.
• Mapper provided a visual representation of the data that revealed natural groupings corresponding to poetic styles.
• The method demonstrated robustness to noise and did not require extensive hyperparameter tuning.
• The results suggest that topological features can serve as a powerful alternative or complement to traditional NLP features in text classification.
• The study provides a clear, accessible pathway for applying TDA to NLP, even for readers without advanced mathematical training.