English

Error estimation of weighted nonlocal Laplacian on random point cloud

Numerical Analysis 2018-09-25 v1

Abstract

We analyze the convergence of the weighted nonlocal Laplacian (WNLL) on high dimensional randomly distributed data. The analysis reveals the importance of the scaling weight μP/S\mu \sim P|/|S| with P|P| and S|S| be the number of entire and labeled data, respectively. The result gives a theoretical foundation of WNLL for high dimensional data interpolation.

Cite

@article{arxiv.1809.08622,
  title  = {Error estimation of weighted nonlocal Laplacian on random point cloud},
  author = {Zuoqiang Shi and Bao Wang and Stanley J. Osher},
  journal= {arXiv preprint arXiv:1809.08622},
  year   = {2018}
}

Comments

15 pages; 2 figures

R2 v1 2026-06-23T04:15:25.863Z