Error estimation of weighted nonlocal Laplacian on random point cloud
Provides theoretical justification for a known method (WNLL) in high-dimensional interpolation, but the result is incremental as it formalizes existing empirical understanding.
The paper analyzes the convergence of weighted nonlocal Laplacian on high-dimensional random point clouds, showing the importance of the scaling weight μ ∼ |P|/|S| and providing a theoretical foundation for its use in data interpolation.
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.