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We consider recovery of low-rank matrices from noisy data by shrinkage of singular values, in which a single, univariate nonlinearity is applied to each of the empirical singular values.
The approximation of one matrix by another of lower rank
Carl Eckart and Gale Young · 1936
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Calculating the Singular Values and Pseudo-Inverse of a Matrix
Gene H. Golub and William Kahan · 1965
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The scree test for the number of factors
Raymond B. Cattell · 1966
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On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
Y Q Yin, Zhidong Bai, and P R Krishnaiah · 1988
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Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches
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Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
Zhidong Bai and YQ Yin · 1993
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David L. Donoho, Iain M. Johnstone, Gerard Kerkyacharian, and Dominique Picard · 1995
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De-Noising by Soft-Thresholding
David L. Donoho · 1995
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Spatial filtering of multichannel electroencephalographic recordings through principal component analysis by singular value decomposition
Terrence D. Lagerlund, Frank W. Sharbrough, and Neil E. Busacker · 1997
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OFDM channel estimation by singular value decomposition
Ove Edfors and Magnus Sandell · 1998
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Minimax estimation via wavelet shrinkage
David L. Donoho and Iain M. Johnstone · 1998
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Singular value decomposition for genome-wide expression data processing and modeling
Orly Alter, Patrick O. Brown, and David Botstein · 2000
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On the distribution of the largest eigenvalue in principal components analysis
Iain M. Johnstone · 2001
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Principal components analysis corrects for stratification in genome-wide association studies
Alkes L. Price, Nick J. Patterson, Robert M. Plenge, Michael E. Weinblatt, Nancy A. Shadick, and David Reich · 2006
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Asymptotics of Sample Eigenstructure for a Large Dimensional Spiked Covariance Model
Debashis Paul · 2007
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On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices
R. Brent Dozier and Jack W. Silverstein · 2007
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An Introduction to Random Matrices
Greg W. Anderson, Alice Guionnet, and Ofer Zeitouni · 2010
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Estimation of high-dimensional low-rank matrices
Angelika Rohde and Alexandre B. Tsybakov · 2011
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Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
Vladimir Koltchinskii, Karim Lounici, and Alexandre B. Tsybakov · 2011
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The singular values and vectors of low rank perturbations of large rectangular random matrices
Florent Benaych-Georges and Raj Rao Nadakuditi · 2012
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Optimal shrinkage of eigenvalues in the Spiked Covariance Model
David L. Donoho, Matan Gavish, and Iain M. Johnstone · 2013
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Reconstruction of a low-rank matrix in the presence of Gaussian noise
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Minimax Risk of Matrix Denoising by Singular Value Thresholding
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Code supplement to ”Optimal Shrinkage of Singular Values” http://purl.stanford.edu/kv623gt2817, 2015
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