# Does the Geometry of Word Embeddings Help Document Classification? A Case Study on Persistent Homology Based Representations

arXiv: https://arxiv.org/abs/1705.10900 · HTML: https://mlsanity.com/paper/1705.10900/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2017.

## Built on by (most cited first, 6 of 6)

- [Re-evaluating Word Mover's Distance](https://mlsanity.com/paper/2105.14403/) (2021)
- [Persistence Homology of TEDtalk: Do Sentence Embeddings Have a Topological Shape?](https://mlsanity.com/paper/2103.14131/) (2021)
- [Topological Data Analysis Applications in Natural Language Processing: A Survey](https://mlsanity.com/paper/2411.10298/) (2024)
- [Topological Data Analysis for Word Sense Disambiguation](https://mlsanity.com/paper/2203.00565/) (2022)
- [Exploring Dowker Homology for Sentence Similarity](https://mlsanity.com/paper/2608.22909/) (2026)
- [Optimizing Soft Prompt Tuning via Structural Evolution](https://mlsanity.com/paper/2602.16500/) (2026)

## Abstract (arXiv)

We investigate the pertinence of methods from algebraic topology for text data analysis. These methods enable the development of mathematically-principled isometric-invariant mappings from a set of vectors to a document embedding, which is stable with respect to the geometry of the document in the selected metric space. In this work, we evaluate the utility of these topology-based document representations in traditional NLP tasks, specifically document clustering and sentiment classification. We find that the embeddings do not benefit text analysis. In fact, performance is worse than simple techniques like textittf-idf, indicating that the geometry of the document does not provide enough variability for classification on the basis of topic or sentiment in the chosen datasets.