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

Publication ,  Journal Article
Dunson, DB; Wu, HT; Wu, N
Published in: Applied and Computational Harmonic Analysis
November 1, 2021

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.

Duke Scholars

Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

November 1, 2021

Volume

55

Start / End Page

282 / 336

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Dunson, D. B., Wu, H. T., & Wu, N. (2021). Spectral convergence of graph Laplacian and heat kernel reconstruction in L from random samples. Applied and Computational Harmonic Analysis, 55, 282–336. https://doi.org/10.1016/j.acha.2021.06.002
Dunson, D. B., H. T. Wu, and N. Wu. “Spectral convergence of graph Laplacian and heat kernel reconstruction in L from random samples.” Applied and Computational Harmonic Analysis 55 (November 1, 2021): 282–336. https://doi.org/10.1016/j.acha.2021.06.002.
Dunson DB, Wu HT, Wu N. Spectral convergence of graph Laplacian and heat kernel reconstruction in L from random samples. Applied and Computational Harmonic Analysis. 2021 Nov 1;55:282–336.
Dunson, D. B., et al. “Spectral convergence of graph Laplacian and heat kernel reconstruction in L from random samples.” Applied and Computational Harmonic Analysis, vol. 55, Nov. 2021, pp. 282–336. Scopus, doi:10.1016/j.acha.2021.06.002.
Dunson DB, Wu HT, Wu N. Spectral convergence of graph Laplacian and heat kernel reconstruction in L from random samples. Applied and Computational Harmonic Analysis. 2021 Nov 1;55:282–336.
Journal cover image

Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

November 1, 2021

Volume

55

Start / End Page

282 / 336

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics