We present a method for finding high density, low-dimensional structures in noisy point clouds. These structures are sets with zero Lebesgue measure with respect to the D-dimensional ambient space and belong to a d<D dimensional space. We call them "singular features." Hunting for singular features corresponds to finding unexpected or unknown structures hidden in point clouds belonging to RD. Our method outputs well defined sets of dimensions d<D. Unlike spectral clustering, the method works well in the presence of noise. We show how to find singular features by first finding ridges in the estimated density, followed by a filtering step based on the eigenvalues of the Hessian of the density.
Cite
@article{arxiv.1606.00265,
title = {Finding Singular Features},
author = {Christopher Genovese and Marco Perone-Pacifico and Isabella Verdinelli and Larry Wasserman},
journal= {arXiv preprint arXiv:1606.00265},
year = {2016}
}