Mathematical analysis on out-of-sample extensions

DOI10.1142/S021969131850042XzbMath1403.68216arXiv1804.09784OpenAlexW2963951517WikidataQ129972774 ScholiaQ129972774MaRDI QIDQ4689135

Jian-zhong Wang

Publication date: 15 October 2018

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.09784

zbMATH Keywords

dimensionality reductionreproducing kernel Hilbert spaceNyström approximationout-of-sample extension

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Uses Software

• Isomap

Cites Work

• Updating kernel methods in spectral decomposition by affinity perturbations
• Principal component analysis.
• Diffusion maps
• Geometric harmonics: a novel tool for multiscale out-of-sample extension of empirical functions
• Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Nonlinear Dimensionality Reduction
• Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
• Theory of Reproducing Kernels
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