Spectral Convergence of Diffusion Maps: Improved Error Bounds and an Alternative Normalization

DOI10.1137/20M1344093zbMath1486.65237arXiv2006.02037OpenAlexW3175639804MaRDI QIDQ5001373

Sebastian Reich, Caroline L. Wormell

Publication date: 19 July 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.02037

zbMATH Keywords

kernel methodsdiffusion mapsgraph LaplacianSinkhorn problem

Mathematics Subject Classification ID

Markov processes: estimation; hidden Markov models (62M05) Learning and adaptive systems in artificial intelligence (68T05) Estimates of eigenvalues in context of PDEs (35P15) Diffusion processes (60J60) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (12)

Lipschitz Regularity of Graph Laplacians on Random Data Clouds ⋮ Clustering Dynamics on Graphs: From Spectral Clustering to Mean Shift Through Fokker–Planck Interpolation ⋮ Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation ⋮ Spectral analysis of weighted Laplacians arising in data clustering ⋮ Approximations of the connection Laplacian spectra ⋮ Scaling positive random matrices: concentration and asymptotic convergence ⋮ Robust Inference of Manifold Density and Geometry by Doubly Stochastic Scaling ⋮ Learning low-dimensional nonlinear structures from high-dimensional noisy data: an integral operator approach ⋮ Affine-invariant ensemble transform methods for logistic regression ⋮ Spectral convergence of graph Laplacian and heat kernel reconstruction in \(L^\infty\) from random samples ⋮ Manifold learning with arbitrary norms ⋮ Analysis of the feedback particle filter with diffusion map based approximation of the gain

Uses Software

• ApproxFun
• GitHub

Cites Work

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