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 @math , 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.
Topological data analysis has been used for various tasks such as 3D shapes classification @cite_6 or protein structure analysis @cite_1 . However, such techniques have not been used in NLP, primarily because the theory is inaccessible and suitable applications are scarce. offers an introduction to using persistent homology in NLP, by creating representations of nursery-rhymes and novels, as well as highlights structural differences between child and adolescent writing. However, these techniques have not been applied to core NLP tasks.
@cite_1 @cite_6
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Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive condence sets for persistence diagrams and condence bands for persistence landscapes. Persistent homology is a vital tool for topological data analysis. Previous work has developed some statistical estimators for characteristics of collections of persistence diagrams. However, tools that provide statistical inference for observations that are persistence diagrams are limited. Specifically, there is a need for tests that can assess the strength of evidence against a claim that two samples arise from the same population or process. We propose the use of randomization-style null hypothesis significance tests (NHST) for these situations. The test is based on a loss function that comprises pairwise distances between the elements of each sample and all the elements in the other sample. We use this method to analyze a range of simulated and experimental data. Through these examples we experimentally explore the power of the p-values. Our results show that the randomization-style NHST based on pairwise distances can distinguish between samples from different processes, which suggests that its use for hypothesis tests upon persistence diagrams is reasonable. We demonstrate its application on a real dataset of fMRI data of patients with ADHD.