Abstract
In the manifold setting, we provide a series of spectral convergence results quantifying how the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator in the L∞ sense. Based on these results, convergence of the proposed heat kernel approximation algorithm, as well as the convergence rate, to the exact heat kernel is guaranteed. To our knowledge, this is the first work exploring the spectral convergence in the L∞ sense and providing a numerical heat kernel reconstruction from the point cloud with theoretical guarantees.
Original language | English (US) |
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Pages (from-to) | 282-336 |
Number of pages | 55 |
Journal | Applied and Computational Harmonic Analysis |
Volume | 55 |
DOIs | |
State | Published - Nov 2021 |
Keywords
- Graph Laplacian
- Heat kernel
- Laplace-Beltrami operator
- Manifold learning
ASJC Scopus subject areas
- Applied Mathematics