On the path density of a gradient field

Details On the path density of a gradient field On the path density of a gradient field

2008-05-27

arxiv.org/abs/0805.4141v2

Annals of Statistics 2009, Vol. 37, No. 6A, 3236-3271

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-AOS671 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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