The Geometry of Nonparametric Filament Estimation

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

Journal of the American Statistical Association, 2012, vol. 107, issue 498, 788-799

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.

Date: 2012
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Citations: View citations in EconPapers (5)

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DOI: 10.1080/01621459.2012.682527

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