-
2
-
-
0000288016
-
Calculating the singular values and pseudoinverse of a matrix
-
G. Golub and W. Kahan, "Calculating the singular values and pseudoinverse of a matrix," J. Soc. Ind. Appl. Math. B, vol. 2, no. 2, pp. 205-224, 1965.
-
(1965)
J. Soc. Ind. Appl. Math. B
, vol.2
, Issue.2
, pp. 205-224
-
-
Golub, G.1
Kahan, W.2
-
3
-
-
0000802374
-
The approximation of one matrix by another of lower rank
-
C. Eckart and G. Young, "The approximation of one matrix by another of lower rank," Psychometrika, vol. 1, no. 3, pp. 211-218, 1936.
-
(1936)
Psychometrika
, vol.1
, Issue.3
, pp. 211-218
-
-
Eckart, C.1
Young, G.2
-
4
-
-
0034730140
-
Singular value decomposition for genome-wide expression data processing and modeling
-
Aug.
-
O. Alter, P. Brown, and D. Botstein, "Singular value decomposition for genome-wide expression data processing and modeling," Proc. Nat. Acad. Sci. United States Amer., vol. 97, no. 18, pp. 10101-10106, Aug. 2000.
-
(2000)
Proc. Nat. Acad. Sci. United States Amer.
, vol.97
, Issue.18
, pp. 10101-10106
-
-
Alter, O.1
Brown, P.2
Botstein, D.3
-
5
-
-
0027332773
-
Stopping rules in principal components analysis: A comparison of heuristical and statistical approaches
-
[Online]
-
D. Jackson. (1993). Stopping rules in principal components analysis: A comparison of heuristical and statistical approaches. Ecology [Online]. 74(8), pp. 2204-2214. Available: http://www.jstor.org/stable/10.2307/1939574
-
(1993)
Ecology
, vol.74
, Issue.8
, pp. 2204-2214
-
-
Jackson, D.1
-
6
-
-
0030961890
-
Spatial filtering of multichannel electroencephalographic recordings through principal component analysis by singular value decomposition
-
DOI 10.1097/00004691-199701000-00007
-
T. D. Lagerlund, F. W. Sharbrough, and N. E. Busacker, "Spatial filtering of multichannel electroencephalographic recordings through principal component analysis by singular value decomposition" J. Clin. Neurophysiol., vol. 14, no. 1, pp. 73-82, Jan. 1997. (Pubitemid 27220507)
-
(1997)
Journal of Clinical Neurophysiology
, vol.14
, Issue.1
, pp. 73-82
-
-
Lagerlund, T.D.1
Sharbrough, F.W.2
Busacker, N.E.3
-
7
-
-
33746512512
-
Principal components analysis corrects for stratification in genome-wide association studies
-
DOI 10.1038/ng1847, PII NG1847
-
A. L. Price, N. J. Patterson, R. M. Plenge, M. E. Weinblatt, N. A. Shadick, and D. Reich, "Principal components analysis corrects for stratification in genome-wide association studies," Nature Genet., vol. 38, no. 8, pp. 904-9, Aug. 2006. (Pubitemid 44141658)
-
(2006)
Nature Genetics
, vol.38
, Issue.8
, pp. 904-909
-
-
Price, A.L.1
Patterson, N.J.2
Plenge, R.M.3
Weinblatt, M.E.4
Shadick, N.A.5
Reich, D.6
-
8
-
-
0032114467
-
OFDM channel estimation by singular value decomposition
-
PII S0090677898051666
-
O. Edfors, M. Sandell, J.-J. van de Beek, S. K. Wilson, and P. O. Borjesson, "OFDM channel estimation by singular value decomposition," IEEE Trans. Commun., vol. 46, no. 7, pp. 931-939, Jul. 1998. (Pubitemid 128739444)
-
(1998)
IEEE Transactions on Communications
, vol.46
, Issue.7
, pp. 931-939
-
-
Edfors, O.1
Sandell, M.2
Van Beek, J.-J.D.3
Wilson, S.K.4
Borjesson, P.O.5
-
9
-
-
84937549955
-
The scree test for the number of factors
-
R. B. Cattell, "The scree test for the number of factors," Multivariate Behavioral Res., vol. 1, no. 2, pp. 245-276, 1966.
-
(1966)
Multivariate Behavioral Res.
, vol.1
, Issue.2
, pp. 245-276
-
-
Cattell, R.B.1
-
10
-
-
84951601886
-
Cross-validatory estimation of the number of components in factor and principal components models
-
[Online]
-
S. Wold. (1978). Cross-validatory estimation of the number of components in factor and principal components models. Technometrics [Online]. 20(4), pp. 397-405. Available: http://www.tandfonline.com/doi/pdf/10.1080/00401706.1978. 10489693
-
(1978)
Technometrics
, vol.20
, Issue.4
, pp. 397-405
-
-
Wold, S.1
-
12
-
-
71549165598
-
Bi-cross-validation of the SVD and the nonnegative matrix factorization
-
(Jun.). [Online]
-
A. B. Owen and P. O. Perry. (2009, Jun.). Bi-cross-validation of the SVD and the nonnegative matrix factorization. Ann. Appl. Statist. [Online]. 3(2), pp. 564-594. Available: http://projecteuclid.org/euclid.aoas/1245676186
-
(2009)
Ann. Appl. Statist.
, vol.3
, Issue.2
, pp. 564-594
-
-
Owen, A.B.1
Perry, P.O.2
-
13
-
-
84901021663
-
-
Ph.D. thesis, Dept. Statist., Stanford Univ., Stanford, CA, USA
-
P. O. Perry, "Cross validation for unsupervised learning," Ph.D. thesis, Dept. Statist., Stanford Univ., Stanford, CA, USA, 2009.
-
(2009)
Cross Validation for Unsupervised Learning
-
-
Perry, P.O.1
-
15
-
-
0034826231
-
Spectral analysis of data
-
Y. Azar, A. Fiat, A. R. Karlin, F. McSherry, and J. Saia, "Spectral analysis of data," in Proc. 33rd Annu. ACM Symp. Theory Comput., 2001, pp. 619-626. (Pubitemid 32865779)
-
(2001)
Conference Proceedings of the Annual ACM Symposium on Theory of Computing
, pp. 619-626
-
-
Azar, Y.1
Fiat, A.2
Karlin, A.3
McSherry, F.4
Saia, J.5
-
16
-
-
62349112885
-
Covariance regularization by thresholding
-
(Dec.). [Online]
-
P. J. Bickel and E. Levina. (2008, Dec.). Covariance regularization by thresholding. Ann. Statist. [Online]. 36(6), pp. 2577-2604. Available: http://projecteuclid.org/euclid.aos/1231165180
-
(2008)
Ann. Statist.
, vol.36
, Issue.6
, pp. 2577-2604
-
-
Bickel, P.J.1
Levina, E.2
-
19
-
-
77956897560
-
Matrix completion from a few entries
-
Jun.
-
R. H. Keshavan, A. Montanari, and S. Oh, "Matrix completion from a few entries," IEEE Trans. Inf. Theory, vol. 56, no. 6, pp. 2980-2998, Jun. 2010.
-
(2010)
IEEE Trans. Inf. Theory
, vol.56
, Issue.6
, pp. 2980-2998
-
-
Keshavan, R.H.1
Montanari, A.2
Oh, S.3
-
22
-
-
84876797915
-
Reconstruction of a low-rank matrix in the presence of Gaussian noise
-
Jul.
-
A. A. Shabalin and A. B. Nobel, "Reconstruction of a low-rank matrix in the presence of Gaussian noise," J. Multivariate Anal., vol. 118, pp. 67-76, Jul. 2013.
-
(2013)
J. Multivariate Anal.
, vol.118
, pp. 67-76
-
-
Shabalin, A.A.1
Nobel, A.B.2
-
23
-
-
0035641726
-
On the distribution of the largest eigenvalue in principal components analysis
-
I. M. Johnstone, "On the distribution of the largest eigenvalue in principal components analysis," Ann. Statist., vol. 29, no. 2, pp. 295-327, 2001.
-
(2001)
Ann. Statist.
, vol.29
, Issue.2
, pp. 295-327
-
-
Johnstone, I.M.1
-
24
-
-
84904622584
-
-
Dept. Statist., Stanford Univ., Stanford, CA, USA, Tech. Rep. 2013-10
-
D. L. Donoho, M. Gavish, and I. M. Johnstone, "Optimal shrinkage of eigenvalues in the spiked covariance model," Dept. Statist., Stanford Univ., Stanford, CA, USA, Tech. Rep. 2013-10, 2013.
-
(2013)
Optimal Shrinkage of Eigenvalues in the Spiked Covariance Model
-
-
Donoho, D.L.1
Gavish, M.2
Johnstone, I.M.3
-
25
-
-
84862305511
-
The singular values and vectors of low rank perturbations of large rectangular random matrices
-
Oct.
-
F. Benaych-Georges and R. R. Nadakuditi, "The singular values and vectors of low rank perturbations of large rectangular random matrices," J. Multivariate Anal., vol. 111, pp. 120-135, Oct. 2012.
-
(2012)
J. Multivariate Anal.
, vol.111
, pp. 120-135
-
-
Benaych-Georges, F.1
Nadakuditi, R.R.2
-
26
-
-
0001136512
-
On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
-
Y. Q. Yin, Z. D. Bai, and P. R. Krishnaiah, "On the limit of the largest eigenvalue of the large dimensional sample covariance matrix," Probab. Theory Rel. Fields, vol. 78, no. 4, pp. 509-521, 1988.
-
(1988)
Probab. Theory Rel. Fields
, vol.78
, Issue.4
, pp. 509-521
-
-
Yin, Y.Q.1
Bai, Z.D.2
Krishnaiah, P.R.3
-
27
-
-
0001758959
-
Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
-
Y. Q. Yin and Z. D. Bai, "Limit of the smallest eigenvalue of a large dimensional sample covariance matrix," Ann. Probab., vol. 21, no. 3, pp. 1275-1294, 1993.
-
(1993)
Ann. Probab.
, vol.21
, Issue.3
, pp. 1275-1294
-
-
Yin, Y.Q.1
Bai, Z.D.2
-
28
-
-
84928552564
-
-
Dept. Statist., Stanford Univ., Stanford, CA, USA, Tech. Rep. 2014-08
-
D. L. Donoho and M. Gavish, "Optimal shrinkage of singular values," Dept. Statist., Stanford Univ., Stanford, CA, USA, Tech. Rep. 2014-08, 2014.
-
(2014)
Optimal Shrinkage of Singular Values
-
-
Donoho, D.L.1
Gavish, M.2
-
29
-
-
77951291046
-
A singular value thresholding algorithm for matrix completion
-
[Online]
-
J.-F. Cai, E. J. Candès, and Z. Shen. (2008). A singular value thresholding algorithm for matrix completion. SIAM J. Optim. [Online]. 20(4), pp. 1956-1982. Available: http://arxiv.org/abs/0810.3286
-
(2008)
SIAM J. Optim.
, vol.20
, Issue.4
, pp. 1956-1982
-
-
Cai, J.-F.1
Candès, E.J.2
Shen, Z.3
-
30
-
-
84883334291
-
Unbiased risk estimates for singular value thresholding and spectral estimators
-
Oct.
-
E. J. Candès, C. A. Sing-long, and J. D. Trzasko, "Unbiased risk estimates for singular value thresholding and spectral estimators," IEEE Trans. Signal Process., vol. 61, no. 19, pp. 4643-4657, Oct. 2012.
-
(2012)
IEEE Trans. Signal Process.
, vol.61
, Issue.19
, pp. 4643-4657
-
-
Candès, E.J.1
Sing-Long, C.A.2
Trzasko, J.D.3
-
31
-
-
84878150088
-
-
Dept. Statist., Stanford Univ., Stanford, CA, USA, Tech. Rep. 2013-03
-
D. L. Donoho and M. Gavish, "Minimax risk of matrix denoising by singular value thresholding," Dept. Statist., Stanford Univ., Stanford, CA, USA, Tech. Rep. 2013-03, 2013.
-
(2013)
Minimax Risk of Matrix Denoising by Singular Value Thresholding
-
-
Donoho, D.L.1
Gavish, M.2
-
32
-
-
70349646485
-
Non-parametric detection of the number of signals: Hypothesis testing and random matrix theory
-
Oct.
-
S. Kritchman and B. Nadler, "Non-parametric detection of the number of signals: Hypothesis testing and random matrix theory," IEEE Trans. Signal Process., vol. 57, no. 10, pp. 3930-3941, Oct. 2009.
-
(2009)
IEEE Trans. Signal Process.
, vol.57
, Issue.10
, pp. 3930-3941
-
-
Kritchman, S.1
Nadler, B.2
-
33
-
-
63849341672
-
Central limit theorems for eigenvalues in a spiked population model
-
Jun.
-
Z. Bai and J.-F. Yao, "Central limit theorems for eigenvalues in a spiked population model," Ann. l'Inst. Henri Poincare B, Probab. Statist., vol. 44, no. 3, pp. 447-474, Jun. 2008.
-
(2008)
Ann. L'inst. Henri Poincare B, Probab. Statist.
, vol.44
, Issue.3
, pp. 447-474
-
-
Bai, Z.1
Yao, J.-F.2
|