Persistence Landscape

A persistence landscapes toolbox for topological statistics. 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.

References in zbMATH (referenced in 18 articles , 1 standard article )

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  1. Betthauser, Leo; Bubenik, Peter; Edwards, Parker B.: Graded persistence diagrams and persistence landscapes (2022)
  2. Zhao, Yan; Wang, Yanying; Ding, Yanhong; Han, Huiyun: Topological data analysis for the energy and stability of endohedral metallofullerenes (2022)
  3. Calcina, Sabrina S.; Gameiro, Marcio: Parameter estimation in systems exhibiting spatially complex solutions via persistent homology and machine learning (2021)
  4. Divol, Vincent; Lacombe, Théo: Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport (2021)
  5. Bubenik, Peter: The persistence landscape and some of its properties (2020)
  6. Bubenik, Peter; Hull, Michael; Patel, Dhruv; Whittle, Benjamin: Persistent homology detects curvature (2020)
  7. Gidea, Marian; Goldsmith, Daniel; Katz, Yuri; Roldan, Pablo; Shmalo, Yonah: Topological recognition of critical transitions in time series of cryptocurrencies (2020)
  8. Hess, Kathryn: Topological adventures in neuroscience (2020)
  9. Shen, Chen; Patrangenaru, Vic: Topological object data analysis methods with an application to medical imaging (2020)
  10. Som, Anirudh; Ramamurthy, Karthikeyan Natesan; Turaga, Pavan: Geometric metrics for topological representations (2020)
  11. Turner, Katharine; Spreemann, Gard: Same but different: distance correlations between topological summaries (2020)
  12. Vipond, Oliver: Multiparameter persistence landscapes (2020)
  13. Patrangenaru, Vic; Bubenik, Peter; Paige, Robert L.; Osborne, Daniel: Challenges in topological object data analysis (2019)
  14. Alan Hylton, Gregory Henselman-Petrusek, Janche Sang, Robert Short: Tuning the Performance of a Computational Persistent Homology Package (2018) arXiv
  15. Bubenik, Peter; Vergili, Tane: Topological spaces of persistence modules and their properties (2018)
  16. Dłotko, Paweł; Wanner, Thomas: Rigorous cubical approximation and persistent homology of continuous functions (2018)
  17. Kusano, Genki; Fukumizu, Kenji; Hiraoka, Yasuaki: Kernel method for persistence diagrams via kernel embedding and weight factor (2018)
  18. Bubenik, Peter; Dłotko, Paweł: A persistence landscapes toolbox for topological statistics (2017)