Publications [#357498] of Hau-Tieng Wu
Papers Published
- Dunson, DB; Wu, HT; Wu, N. "Spectral convergence of graph Laplacian and heat kernel reconstruction in Lā from random samples." Applied and Computational Harmonic Analysis 55 (November, 2021): 282-336. [doi]
(last updated on 2024/08/25)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 Lā 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 Lā sense and providing a numerical heat kernel reconstruction from the point cloud with theoretical guarantees.