A persistence landscapes toolbox for topological statistics. (January 2017)

• Record Type: Journal Article
• Authors: Bubenik, Peter; Dłotko, Paweł
• Is Part Of: Journal of symbolic computation. Volume 78(2017)
• Page Start: 91
• Page End: 114
• Publication Date: 2017-01
• Subjects: Topological data analysis -- Persistent homology -- Statistical topology -- Topological machine learning -- Intrinsic dimension; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.03.009
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological summary that can be easily combined with tools from statistics and machine learning. We give efficient algorithms for calculating persistence landscapes, their averages, and distances between such averages. We discuss an implementation of these algorithms and some related procedures. These are intended to facilitate the combination of statistics and machine learning with topological data analysis. We present an experiment showing that the low-dimensional persistence landscapes of points sampled from spheres (and boxes) of varying dimensions differ.