A persistence landscapes toolbox for topological statistics

作者：Bubenik Peter; Dlotko Pawel

来源：Journal of Symbolic Computation, 2017, 78: 91-114.

DOI：10.1016/j.jsc.2016.03.009

• Topological data analysis
• Persistent homology
• Statistical topology
• Topological machine learning
• Intrinsic dimension

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.

• 出版日期2017-2