Nonparametric ridge estimation
Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, Larry Wasserman
The Annals of Statistics · 2014 · Volume 42 · Issue 4
Abstract
We study the problem of estimating the ridges of a density function. Ridge estimation is an extension of mode finding and is useful for understanding the structure of a density. It can also be used to find hidden structure in point cloud data. We show that, under mild regularity conditions, the ridges of the kernel density estimator consistently estimate the ridges of the true density. When the data are noisy measurements of a manifold, we show that the ridges are close and topologically similar to the hidden manifold. To find the estimated ridges in practice, we adapt the modified mean-shift algorithm proposed by Ozertem and Erdogmus [J. Mach. Learn. Res. 12 (2011) 1249–1286]. Some numerical experiments verify that the algorithm is accurate.
Keywords
62G05, 62G20, 62H12, Density estimation, manifold learning, Ridges
Enable JavaScript for citation tools and additional paper interactions.