Open Access
December 2009 On the path density of a gradient field
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, Larry Wasserman
Ann. Statist. 37(6A): 3236-3271 (December 2009). DOI: 10.1214/08-AOS671


We consider the problem of reliably finding filaments in point clouds. Realistic data sets often have numerous filaments of various sizes and shapes. Statistical techniques exist for finding one (or a few) filaments but these methods do not handle noisy data sets with many filaments. Other methods can be found in the astronomy literature but they do not have rigorous statistical guarantees. We propose the following method. Starting at each data point we construct the steepest ascent path along a kernel density estimator. We locate filaments by finding regions where these paths are highly concentrated. Formally, we define the density of these paths and we construct a consistent estimator of this path density.


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Christopher R. Genovese. Marco Perone-Pacifico. Isabella Verdinelli. Larry Wasserman. "On the path density of a gradient field." Ann. Statist. 37 (6A) 3236 - 3271, December 2009.


Published: December 2009
First available in Project Euclid: 17 August 2009

zbMATH: 1191.62062
MathSciNet: MR2549559
Digital Object Identifier: 10.1214/08-AOS671

Primary: 62G07 , 62G20 , 62G99

Keywords: Filaments , gradient field , Nonparametric density estimation

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6A • December 2009
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