On the path density of a gradient field

@misc{citeulike:2853669, 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 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.}, author = {Genovese, Christopher R. and Perone-Pacifico, Marco and Verdinelli, Isabella and Wasserman, Larry }, citeulike-article-id = {2853669}, eprint = {0805.4141}, keywords = {cosmo, filament, statistics}, month = {May}, posted-at = {2008-05-31 21:51:08}, priority = {2}, title = {On the path density of a gradient field}, url = {http://arxiv.org/abs/0805.4141}, year = {2008} }

TY - ELEC ID - citeulike:2853669 L3 - citeulike-article-id:2853669 TI - On the path density of a gradient field N2 - 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 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. KW - cosmo KW - filament KW - statistics AU - Genovese, Christopher AU - Perone-Pacifico, Marco AU - Verdinelli, Isabella AU - Wasserman, Larry PY - 2008/May/27/ UR - http://arxiv.org/abs/0805.4141 ER -