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  5. CONVERGENCE OF THE WEIGHTED NONLOCAL LAPLACIAN ON RANDOM POINT CLOUD

CONVERGENCE OF THE WEIGHTED NONLOCAL LAPLACIAN ON RANDOM POINT CLOUD

来源 :计算数学（英文版） | 被引量 : 0次 | 上传用户：goer
【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 dat
【作 者】
：
Zuoqiang Shi Bao Wang 
【机 构】
：
Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China;Department of Mathemati
【出 处】
：
计算数学（英文版）
【发表日期】
：
2021年6期
【关键词】
：
Weighted nonlocal Laplacian Laplace-Beltrami operator Point cloud High-dimension 
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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.
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