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The hypothesis that high dimensional data tend to lie in the vicinity of a low dimensional manifold is the basis of manifold learning.
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Aide-memoire. high-dimensional data analysis: The curses and blessings of dimensionality, 2000
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Learning and design of principal curves
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Some applications of concentration inequalities to statistics
Massart, P · 2000
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Nonlinear dimensionality reduction by locally linear embedding
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Tenenbaum, J. B., Silva, V., and Langford, J. C · 2000
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The Concentration of Measure Phenomenon
Ledoux, M · 2001
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Grouping and dimensionality reduction by locally linear embedding
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Combinatorics of random processes and sections of convex bodies
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Unsupervised learning of image manifolds by semidefinite programming
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Random projection trees and low dimensional manifolds
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Finding the homology of submanifolds with high confidence from random samples
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Topology and data
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The c m c^{m} norm of a function with prescribed jets ii
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Regularized principal manifolds
Smola, A. J., and Williamson, R. C · 2001
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Principal manifolds and nonlinear dimension reduction via local tangent space alignment
Zhang, Z., and Zha, H · 2002
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Laplacian eigenmaps for dimensionality reduction and data representation
Belkin, M., and Niyogi, P · 2003
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Introduction to statistical learning theory
Bousquet, O., Boucheron, S., and Lugosi, G · 2003
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Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
Donoho, D. L., and Grimes, C · 2003
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Interpolation and extrapolation of smooth functions by linear operators
Fefferman, C · 2005
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On the sample complexity of learning smooth cuts on a manifold
Narayanan, H., and Niyogi, P · 2009
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K -dimensional coding schemes in hilbert spaces
Maurer, A., and Pontil, M · 2010
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On the sample complexity of testing the manifold hypothesis
Narayanan, H., and Mitter, S · 2010
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Probabilistic recovery of multiple subspaces in point clouds by geometric ℓ p \ell_{p} minimization
Lerman, G., and Zhang, T · 2011
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Manifold estimation and singular deconvolution under hausdorff loss
Christopher R. Genovese, Marco Perone-Pacifico, I. V., and Wasserman, L · 2012
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