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Volumn 41, Issue 2, 2013, Pages 772-801

Sparse principal component analysis and iterative thresholding

Author keywords

Dimension reduction; High dimensional statistics; Principal component analysis; Principal subspace; Sparsity; Spiked covariance model; Thresholding

Indexed keywords


EID: 84877623616     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-AOS1097     Document Type: Article
Times cited : (292)

References (36)
  • 1
    • 69049101180 scopus 로고    scopus 로고
    • High-dimensional analysis of semidefinite relaxations for sparse principal components
    • MR2541450
    • AMINI, A. A. and WAINWRIGHT, M. J. (2009). High-dimensional analysis of semidefinite relaxations for sparse principal components. Ann. Statist. 37 2877-2921. MR2541450.
    • (2009) Ann. Statist. , vol.37 , pp. 2877-2921
    • Amini, A.A.1    Wainwright, M.J.2
  • 2
    • 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
  • 3
    • 34548514458 scopus 로고    scopus 로고
    • A direct formulation for sparse pca using semidefinite programming
    • (electronic), MR2353806
    • D'ASPREMONT, A., EL GHAOUI, L., JORDAN, M. I. and LANCKRIET, G. R. G. (2007). A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49 434- 448 (electronic). MR2353806.
    • (2007) SIAM Rev. , vol.49 , pp. 434-448
    • D'aspremont, A.1    El Ghaoui, L.2    Jordan, M.I.3    Lanckriet, G.R.G.4
  • 4
    • 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. SIAM J. Numer. Anal. 7 1-46. MR0264450.
    • (1970) SIAM J. Numer. Anal. , vol.7 , pp. 1-46
    • Davis, C.1    Kahan, W.M.2
  • 5
    • 0027873602 scopus 로고
    • Unconditional bases are optimal bases for data compression and for statistical estimation
    • MR1256530
    • DONOHO, D. L. (1993). Unconditional bases are optimal bases for data compression and for statistical estimation. Appl. Comput. Harmon. Anal. 1 100-115. MR1256530.
    • (1993) Appl. Comput. Harmon. Anal. , vol.1 , pp. 100-115
    • Donoho, D.L.1
  • 6
    • 1542784498 scopus 로고    scopus 로고
    • Variable selection via nonconcave penalized likelihood and its oracle properties
    • MR1946581
    • FAN, J. and LI, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348-1360. MR1946581.
    • (2001) J. Amer. Statist. Assoc. , vol.96 , pp. 1348-1360
    • Fan, J.1    Li, R.2
  • 7
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed. Johns Hopkins Univ. Press, Baltimore, MD. MR1417720
    • GOLUB, G. H. and VAN LOAN, C. F. (1996). Matrix Computations, 3rd ed. Johns Hopkins Univ. Press, Baltimore, MD. MR1417720.
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 8
    • 58149421595 scopus 로고
    • Analysis of a complex of statistical variables into principal components
    • 498-520
    • HOTELLING, H. (1933). Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24 417-441, 498-520.
    • (1933) J. Educ. Psychol. , vol.24 , pp. 417-441
    • Hotelling, H.1
  • 9
    • 42749102750 scopus 로고    scopus 로고
    • Principal-component-analysis eigenvalue spectra from data with symmetry-breaking structure
    • HOYLE, D. C. and RATTRAY, M. (2004). Principal-component-analysis eigenvalue spectra from data with symmetry-breaking structure. Phys. Rev. E (3) 69 026124.
    • (2004) Phys. Rev. E , vol.69 , Issue.3 , pp. 026124
    • Hoyle, D.C.1    Rattray, M.2
  • 10
    • 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
  • 11
    • 66549088006 scopus 로고    scopus 로고
    • On consistency and sparsity for principal components analysis in high dimensions
    • MR2751448
    • JOHNSTONE, I. M. and LU, A. Y. (2009). On consistency and sparsity for principal components analysis in high dimensions. J. Amer. Statist. Assoc. 104 682-693. MR2751448.
    • (2009) J. Amer. Statist. Assoc. , vol.104 , pp. 682-693
    • Johnstone, I.M.1    Lu, A.Y.2
  • 12
    • 0141941674 scopus 로고    scopus 로고
    • A modified principal component technique based on the lasso
    • MR2002634
    • JOLLIFFE, I. T., TRENDAFILOV, N. T. and UDDIN, M. (2003). A modified principal component technique based on the LASSO. J. Comput. Graph. Statist. 12 531-547. MR2002634.
    • (2003) J. Comput. Graph. Statist. , vol.12 , pp. 531-547
    • Jolliffe, I.T.1    Trendafilov, N.T.2    Uddin, M.3
  • 13
    • 70249103304 scopus 로고    scopus 로고
    • Pca consistency in high dimension, low sample size context
    • MR2572454
    • JUNG, S. and MARRON, J. S. (2009). PCA consistency in high dimension, low sample size context. Ann. Statist. 37 4104-4130. MR2572454.
    • (2009) Ann. Statist. , vol.37 , pp. 4104-4130
    • Jung, S.1    Marron, J.S.2
  • 17
    • 62349121558 scopus 로고    scopus 로고
    • Finite sample approximation results for principal component analysis: A matrix perturbation approach
    • MR2485013
    • NADLER, B. (2008). Finite sample approximation results for principal component analysis: A matrix perturbation approach. Ann. Statist. 36 2791-2817. MR2485013.
    • (2008) Ann. Statist. , vol.36 , pp. 2791-2817
    • Nadler, B.1
  • 18
    • 66549085511 scopus 로고    scopus 로고
    • On consistency and sparsity for principal components analysis in high dimensions
    • Discussion of, by I. M. Johnstone and A. Y. Lu., MR2751449
    • NADLER, B. (2009). Discussion of "On consistency and sparsity for principal components analysis in high dimensions, " by I. M. Johnstone and A. Y. Lu. J. Amer. Statist. Assoc. 104 694-697. MR2751449.
    • (2009) J. Amer. Statist. Assoc. , vol.104 , pp. 694-697
    • Nadler, B.1
  • 19
    • 84860588430 scopus 로고    scopus 로고
    • Asymptotics of the principal components estimator of large factor models with weakly influential factors
    • MR2923766
    • ONATSKI, A. (2012). Asymptotics of the principal components estimator of large factor models with weakly influential factors. J. Econometrics 168 244-258. MR2923766.
    • (2012) J. Econometrics , vol.168 , pp. 244-258
    • Onatski, A.1
  • 21
    • 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
  • 23
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • PEARSON, K. (1901). On lines and planes of closest fit to systems of points in space. Philos. Mag. Ser. 6 2 559-572.
    • (1901) Philos. Mag. Ser. , vol.6 , Issue.2 , pp. 559-572
    • Pearson, K.1
  • 25
    • 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
  • 27
    • 43049086717 scopus 로고    scopus 로고
    • Sparse principal component analysis via regularized low rank matrix approximation
    • MR2419336
    • SHEN, H. and HUANG, J. Z. (2008). Sparse principal component analysis via regularized low rank matrix approximation. J. Multivariate Anal. 99 1015-1034. MR2419336.
    • (2008) J. Multivariate Anal. , vol.99 , pp. 1015-1034
    • Shen, H.1    Huang, J.Z.2
  • 30
    • 77951130963 scopus 로고    scopus 로고
    • Sparse variable pca using geodesic steepest descent
    • MR2518261
    • ULFARSSON, M. O. and SOLO, V. (2008). Sparse variable PCA using geodesic steepest descent. IEEE Trans. Signal Process. 56 5823-5832. MR2518261.
    • (2008) IEEE Trans. Signal Process. , vol.56 , pp. 5823-5832
    • Ulfarsson, M.O.1    Solo, V.2
  • 32
    • 0021892197 scopus 로고
    • Detection of signals by information theoretic criteria
    • MR0788604
    • WAX, M. and KAILATH, T. (1985). Detection of signals by information theoretic criteria. IEEE Trans. Acoust. Speech Signal Process. 33 387-392. MR0788604.
    • (1985) IEEE Trans. Acoust. Speech Signal Process , vol.33 , pp. 387-392
    • Wax, M.1    Kailath, T.2
  • 33
    • 0002790288 scopus 로고
    • Perturbation bounds in connection with singular value decomposition
    • MR0309968
    • WEDIN, P.-Å. (1972). Perturbation bounds in connection with singular value decomposition. Nordisk Tidskr. Informationsbehandling (BIT) 12 99-111. MR0309968.
    • (1972) Nordisk Tidskr, Informationsbehandling (BIT) , vol.12 , pp. 99-111
    • Wedin, P.-Å.1
  • 34
    • 70149096300 scopus 로고    scopus 로고
    • A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis
    • WITTEN, D. M., TIBSHIRANI, R. and HASTIE, T. (2009). A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 10 515-534.
    • (2009) Biostatistics , vol.10 , pp. 515-534
    • Witten, D.M.1    Tibshirani, R.2    Hastie, T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.