# Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation

@article{Cheng2021EigenconvergenceOG, title={Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation}, author={Xiuyuan Cheng and Nan Wu}, journal={ArXiv}, year={2021}, volume={abs/2101.09875} }

This work studies the spectral convergence of graph Laplacian to the Laplace-Beltrami operator when the graph affinity matrix is constructed from N random samples on a d-dimensional manifold embedded in a possibly high dimensional space. By analyzing Dirichlet form convergence and constructing candidate approximate eigenfunctions via convolution with manifold heat kernel, we prove that, with Gaussian kernel, one can set the kernel bandwidth parameter ∼ (logN/N) such that the eigenvalue… Expand

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