CONVERGENCE OF THE WEIGHTED NONLOCAL LAPLACIAN ON RANDOM POINT CLOUD

• 作者: Zuoqiang Shi Bao Wang
• 来源期刊: 计算数学（英文版）
• 年，卷（期）: 2021,（6）
• 页码范围: 865-879
• 页数: 15页
• 语种: 英文
• DOI: 10.4208/jcm.2104-m2020-0309

摘要

We analyze the convergence of the weighted nonlocal Laplacian (WNLL) on the high dimensional randomly distributed point cloud.Our analysis reveals the importance of the scaling weight,μ ～ |P|/|S| with |P| and |S| being the number of entire and labeled data,respectively,in WNLL.The established result gives a theoretical foundation of the WNLL for high dimensional data interpolation.