The Annals of Statistics
- Ann. Statist.
- Volume 37, Number 6A (2009), 3236-3271.
On the path density of a gradient field
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.
Ann. Statist., Volume 37, Number 6A (2009), 3236-3271.
First available in Project Euclid: 17 August 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Genovese, Christopher R.; Perone-Pacifico, Marco; Verdinelli, Isabella; Wasserman, Larry. On the path density of a gradient field. Ann. Statist. 37 (2009), no. 6A, 3236--3271. doi:10.1214/08-AOS671. https://projecteuclid.org/euclid.aos/1250515386