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Principal component analysis (PCA) is fundamental to statistical machine learning.
On lines and planes of closest fit to systems of point in space
Pearson, K · 1901
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Analysis of a complex of statistical variables into principal components
Hotelling, H · 1933
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Asymptotic theory for principal component analysis
Anderson, T. W · 1963
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Perturbation theory for linear operators
Kato, T · 1966
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The rotation of eigenvectors by a perturbation. iii
Davis, C · 1970
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Matrix perturbation theory
Stewart, G. W · 1990
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A second-order perturbation expansion for the svd
Vaccaro, R. J · 1994
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Stochastic processes and random variables in function spaces
Bosq, D · 2000
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On the distribution of the largest eigenvalue in principal components analysis
Johnstone, I. M · 2001
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Distributed clustering using collective principal component analysis
Kargupta, H · 2001
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Inference for density families using functional principal component analysis
Kneip, A · 2001
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Principal component analysis for dimension reduction in massive distributed data sets
Qu, Y · 2002
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Perturbation analysis for subspace decomposition with applications in subspace-based algorithms
Xu, Z · 2002
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
Baik, J · 2005
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Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
Paul, D · 2007
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Finite sample approximation results for principal component analysis: A matrix perturbation approach
Nadler, B · 2008
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On consistency and sparsity for principal components analysis in high dimensions
Johnstone, I. M · 2009
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PCA consistency in high dimension, low sample size context
Jung, S · 2009
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Second order accurate distributed eigenvector computation for extremely large matrices
El Karoui, N · 2010
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Recovering low-rank matrices from few coefficients in any basis
Gross, D · 2011
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Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
Halko, N · 2011
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Distributed principal subspace estimation in wireless sensor networks
Li, L · 2011
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Matrix computations
Golub, G. H · 2012
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Asymptotics of the principal components estimator of large factor models with weakly influential factors
Onatski, A · 2012
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Singular vector perturbation under gaussian noise
Wang, R · 2015
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A useful variant of the Davis–Kahan theorem for statisticians
Yu, Y · 2015
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Optimal principal component analysis in distributed and streaming models
Boutsidis, C · 2016
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Integrating multiple random sketches for singular value decomposition
Chen, T.-L · 2016
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Robust low-rank matrix recovery
Fan, J · 2016
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Asymptotics and concentration bounds for bilinear forms of spectral projectors of sample covariance
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Augmented sparse principal component analysis for high dimensional data
Paul, D · 2012
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Introduction to the non-asymptotic analysis of random matrices
Vershynin, R · 2012
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Sparse PCA: Optimal rates and adaptive estimation
Cai, T. T · 2013
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Consistency of sparse PCA in high dimension, low sample size contexts
Shen, D · 2013
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Minimax sparse principal subspace estimation in high dimensions
Vu, V. Q · 2013
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Divide and conquer kernel ridge regression
Zhang, Y · 2013
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Koltchinskii, V · 2016
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Sub-gaussian estimators of the mean of a random matrix with heavy-tailed entries
Minsker, S · 2016
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Non-asymptotic upper bounds for the reconstruction error of PCA
Reiss, M · 2016
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The statistics and mathematics of high dimension low sample size asymptotics
Shen, D · 2016
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Randomized single-view algorithms for low-rank matrix approximation
Tropp, J. A · 2016
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Parallelizing spectral algorithms for kernel learning
Blanchard, G · 2017
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Communication-efficient algorithms for distributed stochastic principal component analysis
Garber, D · 2017
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Learning theory of distributed spectral algorithms
Guo, Z.-C · 2017
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Concentration inequalities and moment bounds for sample covariance operators
Koltchinskii, V · 2017
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Communication-efficient sparse regression
Lee, J. D · 2017
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Asymptotics of empirical eigen-structure for ultra-high dimensional spiked covariance model
Wang, W · 2017
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Estimation of the covariance structure of heavy-tailed distributions
Wei, X · 2017
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