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The Geometry of Nonparametric Filament Estimation

Author

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  • Christopher R. Genovese
  • Marco Perone-Pacifico
  • Isabella Verdinelli
  • Larry Wasserman

Abstract

We consider the problem of estimating filamentary structure from d -dimensional point process data. We make some connections with computational geometry and develop nonparametric methods for estimating the filaments. We show that, under weak conditions, the filaments have a simple geometric representation as the medial axis of the data distribution’s support. Our methods convert an estimator of the support’s boundary into an estimator of the filaments. We also find the rates of convergence of our estimators. Proofs of all results are in the supplementary material available online.

Suggested Citation

  • Christopher R. Genovese & Marco Perone-Pacifico & Isabella Verdinelli & Larry Wasserman, 2012. "The Geometry of Nonparametric Filament Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 788-799, June.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:788-799
    DOI: 10.1080/01621459.2012.682527
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    Cited by:

    1. Alberto Rodríguez-Casal & Paula Saavedra-Nieves, 2022. "Spatial distribution of invasive species: an extent of occurrence approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 416-441, June.
    2. Pulkkinen, Seppo, 2015. "Ridge-based method for finding curvilinear structures from noisy data," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 89-109.
    3. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 761-796, September.
    4. Cuevas, Antonio & Llop, Pamela & Pateiro-López, Beatriz, 2014. "On the estimation of the medial axis and inner parallel body," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 171-185.
    5. Kunhui Zhang & Yen-Chi Chen, 2021. "Refined Mode-Clustering via the Gradient of Slope," Stats, MDPI, vol. 4(2), pages 1-23, June.

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