SuRF: Subspace Ridge Finder

This paper deals with a nonparametric method for estimating the ridges of a density function. Ridge estimation is useful for understanding the structure of a density. It can also be used to find hidden structure in point cloud data: when the data are noisy measurements of a manifold, under mild conditions the ridges are close and topologically similar to the hidden manifold. We propose a new estimation procedure called SuRF and study its rate of convergence.