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We analyse the reconstruction error of principal component analysis (PCA) and prove non-asymptotic upper bounds for the corresponding excess risk.
Some new bounds on perturbation of subspaces
C. Davis and W. M. Kahan · 1969
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Asymptotic theory for the principal component analysis of a vector random function: some applications to statistical inference
J. Dauxois, A. Pousse, and Y. Romain · 1982
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An introduction to multivariate statistical analysis
T. W. Anderson · 1984
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Probability distributions on Banach spaces
N. N. Vakhania, V. I. Tarieladze, and S. A. Chobanyan · 1987
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Local Rademacher complexities
P. L. Bartlett, O. Bousquet, and S. Mendelson · 2005
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On the eigenspectrum of the Gram matrix and the generalisation error of kernel PCA
J. Shawe-Taylor, C. Williams, N. Cristianin, and J. Kandola · 2005
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Statistical properties of kernel principal component analysis
G. Blanchard, O. Bousquet, and L. Zwald · 2007
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Deviation inequalities on largest eigenvalues
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T. Cai, Z. Ma, and Y. Wu · 2013
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Minimax sparse principal subspace estimation in high dimensions
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Concentration inequalities for sums and martingales
B. Bercu, B. Delyon, and E. Rio · 2015
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Theoretical foundations of functional data analysis, with an introduction to linear operators
T. Hsing and R. Eubank · 2015
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High-dimensional principal projections
A. Mas and F. Ruymgaart · 2015
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A useful variant of the Davis-Kahan theorem for statisticians
Y. Yu, T. Wang, and R. J. Samworth · 2015
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