Spectral convergence of graph Laplacian and heat kernel reconstruction in L from random samples

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Dunson, DB; Wu, HT; Wu, N

Published Date

  • November 1, 2021

Published In

Volume / Issue

  • 55 /

Start / End Page

  • 282 - 336

Electronic International Standard Serial Number (EISSN)

  • 1096-603X

International Standard Serial Number (ISSN)

  • 1063-5203

Digital Object Identifier (DOI)

  • 10.1016/j.acha.2021.06.002

Citation Source

  • Scopus