Think globally, fit locally under the manifold setup: asymptotic analysis of locally linear embedding

DOI10.1214/17-AOS1676zbMath1405.62058arXiv1703.04058OpenAlexW2595579230WikidataQ125835170 ScholiaQ125835170MaRDI QIDQ1990602

Hau-Tieng Wu, Nan Wu

Publication date: 25 October 2018

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.04058

zbMATH Keywords

dimension reductionmeasurement errordiffusion mapslocally linear embeddinglocally linear regression

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05) Nonparametric estimation (62G05) Learning and adaptive systems in artificial intelligence (68T05) Partial differential equations on manifolds; differential operators (58J99)

Related Items (8)

Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation ⋮ Rates of the strong uniform consistency for the kernel-type regression function estimators with general kernels on manifolds ⋮ Learning low-dimensional nonlinear structures from high-dimensional noisy data: an integral operator approach ⋮ Diffusion maps for embedded manifolds with boundary with applications to PDEs ⋮ Spectral convergence of graph Laplacian and heat kernel reconstruction in \(L^\infty\) from random samples ⋮ Connecting dots: from local covariance to empirical intrinsic geometry and locally linear embedding ⋮ Embeddings of Riemannian manifolds with finite eigenvector fields of connection Laplacian ⋮ Data-driven efficient solvers for Langevin dynamics on manifold in high dimensions

Uses Software

• t-SNE

Cites Work

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