메뉴 건너뛰기




Volumn 59, Issue 1, 2013, Pages 546-572

Outlier-robust PCA: The high-dimensional case

Author keywords

Dimension reduction; outlier; principal component analysis (PCA); robustness; statistical learning

Indexed keywords

BREAKDOWN POINTS; CORRUPTED DATA; DATA SETS; DIMENSION REDUCTION; HIGH-DIMENSIONAL; OPTIMAL SOLUTIONS; OUTLIER; REAL-WORLD APPLICATION; ROBUST ALGORITHM; ROBUST PRINCIPAL COMPONENT ANALYSIS; STATISTICAL LEARNING;

EID: 84871742039     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2012.2212415     Document Type: Article
Times cited : (136)

References (41)
  • 1
    • 0346061723 scopus 로고    scopus 로고
    • High-dimensional data analysis: The curses and blessings of dimensionality
    • Los Angeles, CA
    • D. L. Donoho, "High-dimensional data analysis: The curses and blessings of dimensionality," presented at the presented at the Amer. Math. Soc.-Math. Challenges 21st Century, Los Angeles, CA, 2000.
    • (2000) The Amer. Math. Soc.-Math. Challenges 21st Century
    • Donoho, D.L.1
  • 2
    • 0035641726 scopus 로고    scopus 로고
    • 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
  • 4
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • K. Pearson, "On lines and planes of closest fit to systems of points in space," Philosoph. Mag., vol. 2, no. 6, pp. 559-572, 1901.
    • (1901) Philosoph. Mag. , vol.2 , Issue.6 , pp. 559-572
    • Pearson, K.1
  • 7
    • 84950884569 scopus 로고
    • Robust estimation of dispersion matrices and principal components
    • S. J. Devlin, R. Gnanadesikan, and J. R. Kettenring, "Robust estimation of dispersion matrices and principal components," J. Amer. Statist. Assoc., vol. 76, no. 374, pp. 354-362, 1981.
    • (1981) J. Amer. Statist. Assoc. , vol.76 , Issue.374 , pp. 354-362
    • Devlin, S.J.1    Gnanadesikan, R.2    Kettenring, J.R.3
  • 8
    • 0029184173 scopus 로고
    • Robust principal component analysis by selforganizing rules based on statistical physics approach
    • Jan
    • L. Xu and A. L. Yuille, "Robust principal component analysis by selforganizing rules based on statistical physics approach," IEEE Trans. Neural Netw., vol. 6, no. 1, pp. 131-143, Jan. 1995.
    • (1995) IEEE Trans. Neural Netw. , vol.6 , Issue.1 , pp. 131-143
    • Xu, L.1    Yuille, A.L.2
  • 9
    • 0032594808 scopus 로고    scopus 로고
    • Robust algorithms for principal component analysis
    • T. N. Yang and S. D. Wang, "Robust algorithms for principal component analysis," Pattern Recognit. Lett., vol. 20, no. 9, pp. 927-933, 1999.
    • (1999) Pattern Recognit. Lett. , vol.20 , Issue.9 , pp. 927-933
    • Yang, T.N.1    Wang, S.D.2
  • 10
    • 0001088628 scopus 로고    scopus 로고
    • Principal component analysis based on robust estimators of the covariance or correlation matrix: Influence functions and efficiencies
    • C. Croux and G. Hasebroeck, "Principal component analysis based on robust estimators of the covariance or correlation matrix: Influence functions and efficiencies," Biometrika, vol. 87, no. 3, pp. 603-618, 2000.
    • (2000) Biometrika , vol.87 , Issue.3 , pp. 603-618
    • Croux, C.1    Hasebroeck, G.2
  • 12
    • 0141742284 scopus 로고    scopus 로고
    • A framework for robust subspace learning
    • 3
    • F. De la Torre and M. J. Black, "A framework for robust subspace learning," Int. J. Comput. Vision, vol. 54, no. 1/2/3, pp. 117-142, 2003.
    • (2003) Int. J. Comput. Vision , vol.54 , Issue.1-2 , pp. 117-142
    • De La Torre, F.1    Black, M.J.2
  • 13
    • 34248577801 scopus 로고    scopus 로고
    • Algorithms for Projection-Pursuit robust principal component analysis
    • C. Croux, P. Filzmoser, and M. Oliveira, "Algorithms for Projection-Pursuit robust principal component analysis," Chemometrics Intell. Lab. Syst., vol. 87, no. 2, pp. 218-225, 2007.
    • (2007) Chemometrics Intell. Lab. Syst. , vol.87 , Issue.2 , pp. 218-225
    • Croux, C.1    Filzmoser, P.2    Oliveira, M.3
  • 15
    • 9444294513 scopus 로고    scopus 로고
    • Subspace detection: A robust statistics formulation
    • S. Dasgupta, "Subspace detection: A robust statistics formulation," in Proc. 16th Annu. Conf. Learning Theory, 2003, pp. 734-734.
    • (2003) Proc. 16th Annu. Conf. Learning Theory , pp. 734-734
    • Dasgupta, S.1
  • 16
    • 75249095624 scopus 로고    scopus 로고
    • Learning halfspaces with malicious noise
    • A. Klivans, P. Long, and R. Servedio, "Learning halfspaces with malicious noise," J. Mach. Learning Res., vol. 10, pp. 2715-2740, 2009.
    • (2009) J. Mach. Learning Res. , vol.10 , pp. 2715-2740
    • Klivans, A.1    Long, P.2    Servedio, R.3
  • 18
    • 13444287831 scopus 로고    scopus 로고
    • ROBPCA: A new approach to robust principal component analysis
    • M. Hubert, P. J. Rousseeuw, and K. Branden, "ROBPCA: A new approach to robust principal component analysis," Technometr., vol. 47, no. 1, pp. 64-79, 2005.
    • (2005) Technometr. , vol.47 , Issue.1 , pp. 64-79
    • Hubert, M.1    Rousseeuw, P.J.2    Branden, K.3
  • 19
    • 0002564033 scopus 로고
    • Multivariate estimation with high breakdown point
    • W. Grossman, G. Pflug, I. Vincze, and W. Wertz, Eds. Dordrecht, The Netherlands: Reidel
    • P. J. Rousseeuw, "Multivariate estimation with high breakdown point," in Mathematical Statistics and Applications, W. Grossman, G. Pflug, I. Vincze, and W. Wertz, Eds. Dordrecht, The Netherlands: Reidel, 1985, pp. 283-297.
    • (1985) Mathematical Statistics and Applications , pp. 283-297
    • Rousseeuw, P.J.1
  • 20
    • 0002063041 scopus 로고
    • Robust-estimators of multivariate location and scatter
    • R. Maronna, "Robust-estimators of multivariate location and scatter," Ann. Statist., vol. 4, pp. 51-67, 1976.
    • (1976) Ann. Statist. , vol.4 , pp. 51-67
    • Maronna, R.1
  • 21
    • 0000435292 scopus 로고
    • The ordering of multivariate data
    • V. Barnett, "The ordering of multivariate data," J. Royal Statist. Soc. Series, A, vol. 138, pp. 318-344, 1976.
    • (1976) J. Royal Statist. Soc. Series, A , vol.138 , pp. 318-344
    • Barnett, V.1
  • 22
    • 0001409593 scopus 로고
    • A method of bivariate trimming for robust estimation of the correlation coefficient
    • A. Bebbington, "A method of bivariate trimming for robust estimation of the correlation coefficient," Appl. Statist., vol. 27, pp. 221-228, 1978.
    • (1978) Appl. Statist. , vol.27 , pp. 221-228
    • Bebbington, A.1
  • 23
    • 0001409590 scopus 로고
    • Estimation of correlation coefficients by ellipsoidal trimming
    • D. Titterington, "Estimation of correlation coefficients by ellipsoidal trimming," Appl. Statist., vol. 27, pp. 227-234, 1978.
    • (1978) Appl. Statist. , vol.27 , pp. 227-234
    • Titterington, D.1
  • 27
    • 1542718241 scopus 로고
    • New tools for residual analysis
    • A. Dempster and M. Gasko-Green, "New tools for residual analysis," Ann. Statist., vol. 9, no. 5, pp. 945-959, 1981.
    • (1981) Ann. Statist. , vol.9 , Issue.5 , pp. 945-959
    • Dempster, A.1    Gasko-Green, M.2
  • 28
    • 0002954125 scopus 로고
    • Robust estimates, residuals, and outlier detection with multiresponse data
    • R. Gnanadesikan and J. R. Kettenring, "Robust estimates, residuals, and outlier detection with multiresponse data," Biometrics, vol. 28, pp. 81-124, 1972.
    • (1972) Biometrics , vol.28 , pp. 81-124
    • Gnanadesikan, R.1    Kettenring, J.R.2
  • 29
    • 0016750222 scopus 로고
    • Robust estimation and outlier detection with correlation coefficients
    • S. J. Devlin, R. Gnanadesikan, and J. R. Kettenring, "Robust estimation and outlier detection with correlation coefficients," Biometrika, vol. 62, pp. 531-545, 1975.
    • (1975) Biometrika , vol.62 , pp. 531-545
    • Devlin, S.J.1    Gnanadesikan, R.2    Kettenring, J.R.3
  • 30
    • 18744376591 scopus 로고    scopus 로고
    • High breakdown estimators for principal components: The projection-pursuit approach revisited
    • C. Croux and A. Ruiz-Gazen, "High breakdown estimators for principal components: the projection-pursuit approach revisited," J. Multivariate Anal., vol. 95, no. 1, pp. 206-226, 2005.
    • (2005) J. Multivariate Anal. , vol.95 , Issue.1 , pp. 206-226
    • Croux, C.1    Ruiz-Gazen, A.2
  • 31
    • 71049116435 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • E. Candès and B. Recht, "Exact matrix completion via convex optimization," Found. Comput. Math., vol. 9, pp. 717-772, 2009.
    • (2009) Found. Comput. Math. , vol.9 , pp. 717-772
    • Candès, E.1    Recht, B.2
  • 36
    • 84860244942 scopus 로고    scopus 로고
    • Robust PCA via outlier pursuit
    • May to be ublished
    • H. Xu, C. Caramanis, and S. Sanghavi, "Robust PCA via outlier pursuit," IEEE Trans. Inf. Theory, vol. 58, no. 5, pp. 3047-3064, May 2012, to be published.
    • (2012) IEEE Trans. Inf. Theory , vol.58 , Issue.5 , pp. 3047-3064
    • Xu, H.1    Caramanis, C.2    Sanghavi, S.3
  • 37
    • 84859831899 scopus 로고    scopus 로고
    • Two proposals for robust PCA using semidefinite programming
    • M. McCoy and J. Tropp, "Two proposals for robust PCA using semidefinite programming," Electron. J. Statist., vol. 5, pp. 1123-1160, 2011.
    • (2011) Electron. J. Statist. , vol.5 , pp. 1123-1160
    • McCoy, M.1    Tropp, J.2
  • 39
    • 0002570938 scopus 로고    scopus 로고
    • Kernel principal component analysis
    • B. Schölkopf, C. Burges, and A. J. Smola, Eds. Cambridge, MA: MIT Press
    • B. Schölkopf, A. J. Smola, and K. R. Müller, "Kernel principal component analysis," in Advances in Kernel Methods-Support Vector Learning, B. Schölkopf, C. Burges, and A. J. Smola, Eds. Cambridge, MA: MIT Press, 1999, pp. 327-352.
    • (1999) Advances in Kernel Methods-Support Vector Learning , pp. 327-352
    • Schölkopf, B.1    Smola, A.J.2    Müller, K.R.3
  • 40
    • 79960675858 scopus 로고    scopus 로고
    • Robust principal component analysis?
    • E. Candès, X. Li, Y. Ma, and J. Wright, "Robust principal component analysis?," J. ACM, vol. 58, pp. 1-37, 2011.
    • (2011) J. ACM , vol.58 , pp. 1-37
    • Candès, E.1    Li, X.2    Ma, Y.3    Wright, J.4
  • 41
    • 0012070851 scopus 로고    scopus 로고
    • Local operator theory, random matrices and banach spaces
    • W. Johnson and J. Lindenstrauss, Eds. New York: Elsevier
    • K. Davidson and S. Szarek, "Local operator theory, random matrices and banach spaces," in Handbook on the Geometry of Banach Spaces, W. Johnson and J. Lindenstrauss, Eds. New York: Elsevier, 2001, pp. 317-366.
    • (2001) Handbook on the Geometry of Banach Spaces , pp. 317-366
    • Davidson, K.1    Szarek, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.