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A persistence landscapes toolbox for topological statistics. (English) Zbl 1348.68186
Summary: 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.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
55N35 Other homology theories in algebraic topology
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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