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arXiv · 2110.08138

Convergence of Laplacian Eigenmaps and its Rate for Submanifolds with Singularities

Masayuki Aino
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Abstract

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

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Masayuki Aino. 2021-10-15. Convergence of Laplacian Eigenmaps and its Rate for Submanifolds with Singularities. https://arxiv.org/abs/2110.08138

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