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In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years.
Multidimensional scaling: I. theory and method
Warren S Torgerson · 1952
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C1 isometric imbeddings
John Nash · 1954
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Dynamic Programming
Richard Bellman · 1957
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Curvature measures
Herbert Federer · 1959
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On the mean accuracy of statistical pattern recognizers
G Hughes · 1968
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Numerical methods for computing angles between linear subspaces
Ake Björck and Gene H Golub · 1973
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Self-organization of orientation sensitive cells in the striate cortex
Chr Von der Malsburg · 1973
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Drawing contours from arbitrary data points
Dermot H McLain · 1974
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Surfaces generated by moving least squares methods
Peter Lancaster and Kes Salkauskas · 1981
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Self-organized formation of topologically correct feature maps
Teuvo Kohonen · 1982
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Matrix perturbation theory
Gilbert W Stewart · 1990
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Gtm: A principled alternative to the self-organizing map
Christopher M Bishop, Markus Svensén, and Christopher KI Williams · 1996
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Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets
Pierre Demartines and Jeanny Hérault · 1997
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The approximation power of moving least-squares
David Levin · 1998
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Nonlinear component analysis as a kernel eigenvalue problem
Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller · 1998
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High-dimensional data analysis: The curses and blessings of dimensionality
David L Donoho et al · 2000
Cited alongside, same era.
Nonlinear dimensionality reduction by locally linear embedding
Sam T Roweis and Lawrence K Saul · 2000
Cited alongside, same era.
A global geometric framework for nonlinear dimensionality reduction
Joshua B Tenenbaum, Vin De Silva, and John C Langford · 2000
Cited alongside, same era.
Self-organizing maps
Teuvo Kohonen · 2001
Cited alongside, same era.
Matrix Algorithms: Volume II: Eigensystems
Gilbert W Stewart · 2001
Cited alongside, same era.
Efficient simplicial reconstructions of manifolds from their samples
Daniel Freedman · 2002
Cited alongside, same era.
Diffusion maps
Ronald R Coifman and Stéphane Lafon · 2006
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Manifold denoising
Matthias Hein and Markus Maier · 2006
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An introduction to nonlinear dimensionality reduction by maximum variance unfolding
Kilian Q Weinberger and Lawrence K Saul · 2006
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Nonlinear dimensionality reduction
John A Lee and Michel Verleysen · 2007
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Locally linear denoising on image manifolds
Dian Gong, Fei Sha, and Gérard Medioni · 2010
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Geographically weighted principal components analysis
Paul Harris, Chris Brunsdon, and Martin Charlton · 2011
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Fundamentals of differential geometry
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Ian Jolliffe · 2002
Cited alongside, same era.
Computing and rendering point set surfaces
Marc Alexa, Johannes Behr, Daniel Cohen-Or, Shachar Fleishman, David Levin, and Claudio T Silva · 2003
Cited alongside, same era.
Laplacian eigenmaps for dimensionality reduction and data representation
Mikhail Belkin and Partha Niyogi · 2003
Cited alongside, same era.
Think globally, fit locally: unsupervised learning of low dimensional manifolds
Lawrence K Saul and Sam T Roweis · 2003
Cited alongside, same era.
Mesh-independent surface interpolation
David Levin · 2004
Cited alongside, same era.
An as-short-as-possible introduction to the least squares, weighted least squares and moving least squares methods for scattered data approximation and interpolation
Andrew Nealen · 2004
Cited alongside, same era.
Serge Lang · 2012
Later among the works it cites.
Linear Algebra and Its Applications
P.D. Lax · 2013
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Perturbation theory for normal operators
Armin Rainer · 2013
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Manifold reconstruction using tangential delaunay complexes
Jean-Daniel Boissonnat and Arijit Ghosh · 2014
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Matrix decompositions using sub-gaussian random matrices
Yariv Aizenbud and Amir Averbuch · 2016
Closest in time.
Approximation of functions over manifolds: A moving least-squares approach
Barak Sober, Yariv Aizenbud, and David Levin · 2017
Closest in time.
Structuring High Dimensional Data: A Moving Least-Squares Projective Approach to Analyze Manifold Data
Barak Sober · 2018
Closest in time.
Approximating the span of principal components via iterative least-squares
Yariv Aizenbud and Barak Sober · 2019
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