Convergence of Laplacian Eigenmaps and its Rate for Submanifolds with Singularities
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Abstract (arXiv)
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 Oleft(left(log n/nright)1/(m+2)right), where m and n denote the dimension of the manifold and the sample size, respectively.
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References · 4
- 2018Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operatorcited by 70
- 2019Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphscited by 18
- 2016The embedding dimension of Laplacian eigenfunction mapscited by 8
- 2016Four lectures on probabilistic methods for data sciencecited by 5
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