A persistence landscapes toolbox for topological statistics

TL;DR

This paper introduces efficient algorithms and a software toolbox for computing persistence landscapes, enabling their integration with statistical and machine learning methods for topological data analysis.

Contribution

It provides the first efficient algorithms and implementation for calculating persistence landscapes, their averages, and distances, facilitating their use in data analysis.

Findings

Persistence landscapes differ across dimensions for sampled spheres and boxes.

Algorithms enable fast computation of landscapes and their statistical summaries.

Implementation supports practical applications in topological data analysis.

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.