The analysis of topological structure in data using persistent homology: applications to lexical word association networks

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.