Convergence of Laplacian Eigenmaps and its Rate for Submanifolds with Singularities

10/15/2021

∙

by   Masayuki Aino, et al.

∙

0

∙

share

In this paper, we give a spectral approximation result for the Laplacian on submanifolds of Euclidean spaces with singularities by the ϵ-neighborhood graph constructed from random points on the submanifold. Our convergence rate for the eigenvalue of the Laplacian is O((log n/n)^1/(m+2)), where m and n denote the dimension of the manifold and the sample size, respectively.