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Model. Anal. Inform. Sist., 2013, Volume 20, Number 6, Pages 111–120 (Mi mais347)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Bootstrap for Persistence Diagrams and Landscapes

F. Chazala, B. T. Fasyb, F. Leccic, A. Rinaldoc, A. Singhd, L. Wassermanc

a INRIA Saclay
b Computer Science Department, Tulane University, Stanley Thomas 303 New Orleans, LA 70118
c Department of Statistics, Carnegie Mellon University, Baker Hall 132 Pittsburgh, PA 15213
d Machine Learning Department, Carnegie Mellon University, Gates Hillman Centers, 8203 5000 Forbes Avenue Pittsburgh, PA 15213-3891

Abstract: Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive confidence sets for persistence diagrams and confidence bands for persistence landscapes.
The article is published in the author's wording.

Keywords: persistent homology, bootstrap, topological data analysis.

Full text: PDF file (1106 kB)
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UDC: 512.664
Received: 01.11.2013
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Citation: F. Chazal, B. T. Fasy, F. Lecci, A. Rinaldo, A. Singh, L. Wasserman, “On the Bootstrap for Persistence Diagrams and Landscapes”, Model. Anal. Inform. Sist., 20:6 (2013), 111–120

Citation in format AMSBIB
\Bibitem{ChaFasLec13}
\by F.~Chazal, B.~T.~Fasy, F.~Lecci, A.~Rinaldo, A.~Singh, L.~Wasserman
\paper On the Bootstrap for Persistence Diagrams and Landscapes
\jour Model. Anal. Inform. Sist.
\yr 2013
\vol 20
\issue 6
\pages 111--120
\mathnet{http://mi.mathnet.ru/mais347}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Way M.J., Gazis P.R., Scargle J.D., “Structure in the 3D Galaxy Distribution. II. Voids and Watersheds of Local Maxima and Minima”, Astrophys. J., 799:1 (2015), 95  crossref  isi  scopus
    2. Chazal F., Fasy B.T., Lecci F., Rinaldo A., Wasserman L., “Stochastic Convergence of Persistence Landscapes and Silhouettes”, J. Comput. Geom., 6:2, SI (2015), 140–161  mathscinet  isi
    3. V. Kovacev-Nikolic, P. Bubenik, D. Nikolic, G. Heo, “Using Persistent Homology and Dynamical Distances To Analyze Protein Binding”, Stat. Appl. Genet. Mol. Biol., 15:1 (2016), 19–38  crossref  mathscinet  isi  scopus
    4. P. Bubenik, P. Dlotko, “A Persistence Landscapes Toolbox For Topological Statistics”, J. Symb. Comput., 78:SI (2017), 91–114  crossref  mathscinet  zmath  isi  scopus
  • Моделирование и анализ информационных систем
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