메뉴 건너뛰기




Volumn 36, Issue 6, 2008, Pages 2791-2817

Finite sample approximation results for principal component analysis: A matrix perturbation approach

Author keywords

Matrix perturbation; Phase transition; Principal component analysis; Random matrix theory; Spiked covariance model

Indexed keywords


EID: 62349121558     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS618     Document Type: Article
Times cited : (294)

References (37)
  • 1
    • 0001699986 scopus 로고
    • Asymptotic theory for principal component analysis
    • MR0145620
    • ANDERSON, T. W. (1963). Asymptotic theory for principal component analysis. Ann. Math. Statist. 34 122-148. MR0145620
    • (1963) Ann. Math. Statist , vol.34 , pp. 122-148
    • ANDERSON, T.W.1
  • 2
    • 62349141350 scopus 로고    scopus 로고
    • ANDERSON, T. W. (1984). An Introduction to Multivariate Statistical Analysis, 2nd ed. Wiley, New York. MR0771294
    • ANDERSON, T. W. (1984). An Introduction to Multivariate Statistical Analysis, 2nd ed. Wiley, New York. MR0771294
  • 3
    • 27644476898 scopus 로고    scopus 로고
    • Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
    • MR2165575
    • BAIK, J., BEN AROUS, G. and PECHE, S. (2005). Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 1643-1697. MR2165575
    • (2005) Ann. Probab , vol.33 , pp. 1643-1697
    • BAIK, J.1    BEN AROUS, G.2    PECHE, S.3
  • 4
    • 33646507506 scopus 로고    scopus 로고
    • Eigenvalues of large sample covariance matrices of spiked population models
    • MR2279680
    • BAIK, J. and SILVERSTEIN, J. W. (2006). Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal. 97 1382-1408. MR2279680
    • (2006) J. Multivariate Anal , vol.97 , pp. 1382-1408
    • BAIK, J.1    SILVERSTEIN, J.W.2
  • 5
    • 21344477172 scopus 로고    scopus 로고
    • BIEHL, M. and MIETZNER, A. (1994). Statistical- mechanics of unsupervised structure recognition. J. Phys. A 27 1885. MR1280357
    • BIEHL, M. and MIETZNER, A. (1994). Statistical- mechanics of unsupervised structure recognition. J. Phys. A 27 1885. MR1280357
  • 6
    • 0029532242 scopus 로고
    • Improved linear discrimination using time frequency dictionaries
    • BUCKHEIT, J. and DONOHO, D. L. (1995). Improved linear discrimination using time frequency dictionaries. Proc. SPIE 2569 540-551.
    • (1995) Proc. SPIE , vol.2569 , pp. 540-551
    • BUCKHEIT, J.1    DONOHO, D.L.2
  • 7
    • 0012070851 scopus 로고    scopus 로고
    • DAVIDSON, K. R. and SZAREK, S. (2001). Local operator theory, random matrices and Banach spaces. In Handbook on the Geometry of Banach Spaces (W. B. Johnson and J. Linden-strauss, eds.) 1 317-366. North-Holland, Amsterdam. MR1863696
    • DAVIDSON, K. R. and SZAREK, S. (2001). Local operator theory, random matrices and Banach spaces. In Handbook on the Geometry of Banach Spaces (W. B. Johnson and J. Linden-strauss, eds.) 1 317-366. North-Holland, Amsterdam. MR1863696
  • 8
    • 0014751986 scopus 로고
    • The rotation of eigenvectors by a perturbation. III
    • MR0264450
    • DAVIS, C. and KAHAN, W. M. (1970). The rotation of eigenvectors by a perturbation. III. SIAMJ. Numer. Anal. 70 1-47. MR0264450
    • (1970) SIAMJ. Numer. Anal , vol.70 , pp. 1-47
    • DAVIS, C.1    KAHAN, W.M.2
  • 9
    • 33846999295 scopus 로고    scopus 로고
    • On the empirical distribution of eigenvalues of large-dimensional information-plus- noise type matrices
    • MR2322123
    • DOZIER, R. B. and SILVERSTEIN, J. W. (2007). On the empirical distribution of eigenvalues of large-dimensional information-plus- noise type matrices. J. Multivariate Anal. 98 678-694. MR2322123
    • (2007) J. Multivariate Anal , vol.98 , pp. 678-694
    • DOZIER, R.B.1    SILVERSTEIN, J.W.2
  • 10
    • 0001381004 scopus 로고
    • On Wielandt's inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix
    • MR1091849
    • EATON, M. and TYLER, D. E. (1991). On Wielandt's inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix. Ann. Statist. 19 260-271. MR1091849
    • (1991) Ann. Statist , vol.19 , pp. 260-271
    • EATON, M.1    TYLER, D.E.2
  • 11
    • 46749089905 scopus 로고    scopus 로고
    • Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
    • MR2308592
    • EL KAROUI, N. (2007). Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices. Ann. Probab. 35 663-714. MR2308592
    • (2007) Ann. Probab , vol.35 , pp. 663-714
    • EL KAROUI, N.1
  • 12
    • 0000793351 scopus 로고
    • On the sampling theory of the roots of determinantal equations
    • MR0000127
    • GIRSHICK, M. A. (1939). On the sampling theory of the roots of determinantal equations. Ann. Math. Statist. 10 203-204. MR0000127
    • (1939) Ann. Math. Statist , vol.10 , pp. 203-204
    • GIRSHICK, M.A.1
  • 13
    • 62349117501 scopus 로고    scopus 로고
    • HORN, R. A. and JOHNSON, C. R. (1990). Matrix Analysis. Cambridge Univ. Press. MR1084815
    • HORN, R. A. and JOHNSON, C. R. (1990). Matrix Analysis. Cambridge Univ. Press. MR1084815
  • 14
    • 0037389951 scopus 로고    scopus 로고
    • PCA learning for sparse high-dimensional data
    • HOYLE, D. C. and RATTRAY, M. (2003). PCA learning for sparse high-dimensional data, Europhys. Lett. 62 117-123.
    • (2003) Europhys. Lett , vol.62 , pp. 117-123
    • HOYLE, D.C.1    RATTRAY, M.2
  • 16
    • 73649111433 scopus 로고    scopus 로고
    • Refined perturbation bounds for eigenvalues of Hermitian and non-Hermitian matrices
    • To appear
    • IPSEN, I. C. F. and NADLER, B. (2008). Refined perturbation bounds for eigenvalues of Hermitian and non-Hermitian matrices. SIAM J. Matrix Anal. Appl. To appear.
    • (2008) SIAM J. Matrix Anal. Appl
    • IPSEN, I.C.F.1    NADLER, B.2
  • 18
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • MR1863961
    • JOHNSTONE, I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 295-327. MR1863961
    • (2001) Ann. Statist , vol.29 , pp. 295-327
    • JOHNSTONE, I.M.1
  • 20
    • 62349124392 scopus 로고    scopus 로고
    • JOLLIFFE, I. T. (2002). Principal Component Analysis, 2nd ed. Springer, New York. MR2036084
    • JOLLIFFE, I. T. (2002). Principal Component Analysis, 2nd ed. Springer, New York. MR2036084
  • 22
    • 50249159453 scopus 로고    scopus 로고
    • Determining the number of components in a factor model from limited noisy data
    • KRITCHMAN, S. and NADLER, B. (2008). Determining the number of components in a factor model from limited noisy data. Chemom. Int. Lab. Sys. 94 19-32.
    • (2008) Chemom. Int. Lab. Sys , vol.94 , pp. 19-32
    • KRITCHMAN, S.1    NADLER, B.2
  • 23
    • 0000815369 scopus 로고
    • Tests of significance for the latent roots of covariance and correlation matrices
    • MR0078610
    • LAWLEY, D. N. (1956). Tests of significance for the latent roots of covariance and correlation matrices. Biometrika 43 128-136. MR0078610
    • (1956) Biometrika , vol.43 , pp. 128-136
    • LAWLEY, D.N.1
  • 24
    • 0000263234 scopus 로고
    • Distribution for some sets of random matrices
    • MARČENKO, V. A. and PASTUR, L. A. (1967). Distribution for some sets of random matrices. Math. USSR-Sb 1 457-483.
    • (1967) Math. USSR-Sb , vol.1 , pp. 457-483
    • MARČENKO, V.A.1    PASTUR, L.A.2
  • 25
    • 23044465317 scopus 로고    scopus 로고
    • Partial least squares, Beer's law and the net analyte signal: Statistical modeling and analysis
    • NADLER, B. and COIFMAN, R. R. (2005). Partial least squares, Beer's law and the net analyte signal: Statistical modeling and analysis. J. Chemometrics 19 45-54.
    • (2005) J. Chemometrics , vol.19 , pp. 45-54
    • NADLER, B.1    COIFMAN, R.R.2
  • 26
    • 27644451742 scopus 로고    scopus 로고
    • The prediction error in CLS and PLS: The importance of feature selection prior to multivariate calibration
    • NADLER, B. and COIFMAN, R. R. (2005). The prediction error in CLS and PLS: The importance of feature selection prior to multivariate calibration. J. Chemom. 19 107-118.
    • (2005) J. Chemom , vol.19 , pp. 107-118
    • NADLER, B.1    COIFMAN, R.R.2
  • 28
    • 38249017274 scopus 로고
    • Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices
    • MR1071882
    • O'LEARY, D. P. and STEWART, G. W. (1990). Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices. J. Comput. Phys. 90 497-505. MR1071882
    • (1990) J. Comput. Phys , vol.90 , pp. 497-505
    • O'LEARY, D.P.1    STEWART, G.W.2
  • 30
    • 62349119929 scopus 로고    scopus 로고
    • PARLETT, B. N. (1980). The Symmetric Eigenvalue Problem. Prentice-Hall, Englewood Cliffs, NJ. MR0570116
    • PARLETT, B. N. (1980). The Symmetric Eigenvalue Problem. Prentice-Hall, Englewood Cliffs, NJ. MR0570116
  • 31
    • 38549175880 scopus 로고    scopus 로고
    • Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
    • MR2399865
    • PAUL, D. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statist. Sinica 17 1617-1642. MR2399865
    • (2007) Statist. Sinica , vol.17 , pp. 1617-1642
    • PAUL, D.1
  • 32
    • 0012958376 scopus 로고    scopus 로고
    • A Gaussian scenario for unsupervised learning
    • REIMANN, P., VAN DEN BROECK, C. and BEX, G. J. (1996). A Gaussian scenario for unsupervised learning. J. Phys. A 29 3521-3535.
    • (1996) J. Phys. A , vol.29 , pp. 3521-3535
    • REIMANN, P.1    VAN DEN BROECK, C.2    BEX, G.J.3
  • 33
    • 0000602132 scopus 로고
    • On the empirical distribution of eigenvalues of a class of large-dimensional random matrices
    • MR1345534
    • SILVERSTEIN, J. W. and BAI, Z. D. (1995). On the empirical distribution of eigenvalues of a class of large-dimensional random matrices. J. Multivariate Anal. 54 175-192. MR1345534
    • (1995) J. Multivariate Anal , vol.54 , pp. 175-192
    • SILVERSTEIN, J.W.1    BAI, Z.D.2
  • 34
    • 58149320175 scopus 로고
    • Analysis of the limiting spectral distribution of large-dimensional random matrices
    • MR1345541
    • SILVERSTEIN, J. W. and CHOI, S. I. (1995). Analysis of the limiting spectral distribution of large-dimensional random matrices. J. Multivariate Anal. 54 295-309. MR1345541
    • (1995) J. Multivariate Anal , vol.54 , pp. 295-309
    • SILVERSTEIN, J.W.1    CHOI, S.I.2
  • 35
    • 0025566497 scopus 로고
    • Stochastic perturbation theory
    • MR1084571
    • STEWART, G. W. (1990). Stochastic perturbation theory. SIAM Rev. 32 579-610. MR1084571
    • (1990) SIAM Rev , vol.32 , pp. 579-610
    • STEWART, G.W.1
  • 37
    • 21344488435 scopus 로고    scopus 로고
    • WATKIN, T. H. and NADAL, J.-P. (1994). Optimal unsupervised learning. J. Phys. A 27 1899-1915.MR1280358
    • WATKIN, T. H. and NADAL, J.-P. (1994). Optimal unsupervised learning. J. Phys. A 27 1899-1915.MR1280358


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.