A persistence landscapes toolbox for topological statistics

@article{Bubenik2017APL,
  title={A persistence landscapes toolbox for topological statistics},
  author={Peter Bubenik and Pawel Dlotko},
  journal={ArXiv},
  year={2017},
  volume={abs/1501.00179}
}
  • Peter Bubenik, Pawel Dlotko
  • Published 2017
  • Mathematics, Computer Science
  • ArXiv
  • 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… CONTINUE READING
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    References

    SHOWING 1-10 OF 80 REFERENCES
    Statistical topological data analysis using persistence landscapes
    • Peter Bubenik
    • Mathematics, Computer Science
    • J. Mach. Learn. Res.
    • 2015
    • 388
    • PDF
    Stochastic Convergence of Persistence Landscapes and Silhouettes
    • 75
    • PDF
    On the Bootstrap for Persistence Diagrams and Landscapes
    • 46
    • PDF
    Statistical topology using persistence landscapes
    • 34
    • PDF
    Confidence sets for persistence diagrams
    • 169
    • PDF
    Persistence Images: An Alternative Persistent Homology Representation
    • 13
    • PDF
    Probability measures on the space of persistence diagrams
    • 159
    • PDF
    Persistence Images: A Stable Vector Representation of Persistent Homology
    • 229
    • PDF
    Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis
    • 172
    • PDF
    A stable multi-scale kernel for topological machine learning
    • 210
    • PDF