2019/04/24 by Jeff Murugan, Murugan, Jeff, Duncan Robertson +1 · 4 citations
Computer Science · Medicine · #Clusterin in disease pathology #FOS: Physical sciences #High Energy Astrophysical Phenomena (astro-ph.HE) #High Energy Physics - Theory (hep-th) #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1904.11044
openalex publication_date 2019/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Topological Data Analysis (TDA) is a novel, and relatively new approach to analysing high-dimensional data sets. It does this by focussing on global properties like the shape and connectivity of the data giving it a significant advantage over more conventional tools based on cluster analysis, a localised property of the data. However, some of its mathematical foundations, like algebraic topology and discrete Morse theory, are perceived as an intimidatingly steep upramp into the subject. Consequently, it has enjoyed much less popularity as a data-analysis tool than less abstract methods. This article aims to change this. By focusing on a small set of simple examples, chosen primarily for their pedagogical value, we introduce and explain TDA's two principle branches; persistent homology and the Mapper algorithm. We then illustrate the universality of the method by discussing its application to the intriguing data set of fast radio burst (FRB) observations. We close the article with a discussion of the resilience of topological data analysis to noise and some statistical and computational challenges faced by the method.