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A persistence landscapes toolbox for topological statistics

Peter Bubenik 1 Dlotko Pawel 2
2 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
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.
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https://hal.inria.fr/hal-01258875
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Submitted on : Friday, January 22, 2016 - 9:21:43 PM
Last modification on : Friday, May 21, 2021 - 6:12:01 PM
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  • HAL Id : hal-01258875, version 1
  • ARXIV : 1501.00179

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Peter Bubenik, Dlotko Pawel. A persistence landscapes toolbox for topological statistics. Journal of Symbolic Computation, Elsevier, 2016. ⟨hal-01258875⟩

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