The Geometry of Nonparametric Filament Estimation
Statistics Theory
2015-03-13 v2 Instrumentation and Methods for Astrophysics
Statistics Theory
Abstract
We consider the problem of estimating filamentary structure from planar point process data. We make some connections with computational geometry and we 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.
Cite
@article{arxiv.1003.5536,
title = {The Geometry of Nonparametric Filament Estimation},
author = {Christopher R. Genovese and Marco Perone-Pacifico and Isabella Verdinelli and Larry Wasserman},
journal= {arXiv preprint arXiv:1003.5536},
year = {2015}
}
Comments
substantial revision