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. © Institute of Mathematical Statistics, 2009.

On the path density of a gradient field / Christopher R., Genovese; PERONE PACIFICO, Marco; Verdinelli, Isabella; Larry, Wasserman. - In: ANNALS OF STATISTICS. - ISSN 0090-5364. - 37:6 A(2009), pp. 3236-3271. [10.1214/08-aos671]

On the path density of a gradient field

PERONE PACIFICO, Marco;
2009

Abstract

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. © Institute of Mathematical Statistics, 2009.
filaments; gradient field; nonparametric density estimation
On the path density of a gradient field / Christopher R., Genovese; PERONE PACIFICO, Marco; Verdinelli, Isabella; Larry, Wasserman. - In: ANNALS OF STATISTICS. - ISSN 0090-5364. - 37:6 A(2009), pp. 3236-3271. [10.1214/08-aos671]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/182620
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