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We investigate the pertinence of methods from algebraic topology for textdata analysis. These methods enable the development ofmathematically-principled isometric-invariant mappings from a set of vectors toa document embedding, which is stable with respect to the geometry of thedocument in the selected metric space. In this work, we evaluate the utility ofthese topology-based document representations in traditional NLP tasks,specifically document clustering and sentiment classification. We find that theembeddings do not benefit text analysis. In fact, performance is worse thansimple techniques like $\textit{tf-idf}$, indicating that the geometry of thedocument does not provide enough variability for classification on the basis oftopic or sentiment in the chosen datasets.

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