Error estimation of weighted nonlocal Laplacian on random point cloud
Zuoqiang Shi, Bao Wang, Stanley Osher · arXiv (Cornell University) · 2018
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 $μ\sim P|/|S|$ with $|P|$ and $|S|$ be the number of entire and labeled data, respectively. The result gives a theoretical foundation of WNLL for high dimensional data interpolation.