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

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Modelirovanie i Analiz Informatsionnykh Sistem, 2013, Volume 20, Number 6, Pages 111–120 (Mi mais347)

This article is cited in 12 scientific papers (total in 12 papers)

On the Bootstrap for Persistence Diagrams and Landscapes

F. Chazal^a, B. T. Fasy^b, F. Lecci^c, A. Rinaldo^c, A. Singh^d, L. Wasserman^c

^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

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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.

Received: 01.11.2013

Document Type: Article

UDC: 512.664

Language: English

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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https://www.mathnet.ru/eng/mais347

https://www.mathnet.ru/eng/mais/v20/i6/p111

This publication is cited in the following 12 articles:

Rosenstock S., “Learning From the Shape of Data”, Philos. Sci., 88:5 (2021), 1033–1044
Vipond O., “Multiparameter Persistence Landscapes”, J. Mach. Learn. Res., 21 (2020)
Turner K., “Medians of Populations of Persistence Diagrams”, Homol. Homotopy Appl., 22:1 (2020), 255–282
Kusano G., “on the Expectation of a Persistence Diagram By the Persistence Weighted Kernel”, Jpn. J. Ind. Appl. Math., 36:3, SI (2019), 861–892
Biscio Ch.A.N., Moller J., “the Accumulated Persistence Function, a New Useful Functional Summary Statistic For Topological Data Analysis, With a View to Brain Artery Trees and Spatial Point Process Applications”, J. Comput. Graph. Stat., 28:3 (2019), 671–681
Patrangenaru V., Bubenik P., Paige R.L., Osborne D., “Challenges in Topological Object Data Analysis”, Sankhya Ser. A, 81:1, SI (2019), 244–271
Hofer Ch.D., Kwitt R., Niethammer M., “Learning Representations of Persistence Barcodes”, J. Mach. Learn. Res., 20 (2019), 126
Brecheteau C., “a Statistical Test of Isomorphism Between Metric-Measure Spaces Using the Distance-to-a-Measure Signature”, Electron. J. Stat., 13:1 (2019), 795–849
P. Bubenik, P. Dlotko, “A Persistence Landscapes Toolbox For Topological Statistics”, J. Symb. Comput., 78:SI (2017), 91–114
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
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
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

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

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