2016/11/28 by Matthew Pietrosanu, Pietrosanu, Matthew
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Applications (stat.AP) #FOS: Computer and information sciences #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1611.09435
openalex publication_date 2016/11/28 · openalex created_date 2016/12/08 · openalex updated_date 2026/07/28
Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first principles and detail a novel application of this method to the field of computational linguistics. Using this method, we search for clusters and other topological features among closely-associated words of the English language. Furthermore, we compare the clustering abilities of persistent homology and the commonly-used Markov clustering algorithm and discuss improvements to basic persistent homology techniques to increase its clustering efficacy.