메뉴 건너뛰기




Volumn 31, Issue 3, 2009, Pages 1100-1124

A randomized algorithm for principal component analysis

Author keywords

Lanczos; Low rank; Power; Principal component analysis; Singular value decomposition

Indexed keywords

EFFICIENT ALGORITHM; LANCZOS; LOW RANK; LOW RANK APPROXIMATIONS; MATRIX; NUMERICAL EXAMPLE; POWER; RANDOMIZED ALGORITHMS; SPECTRAL NORMS; THEORETICAL RESULT;

EID: 72449140504     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/080736417     Document Type: Article
Times cited : (372)

References (37)
  • 2
    • 34247228045 scopus 로고    scopus 로고
    • Fast computation of low-rank matrix approximations
    • article
    • D. ACHLIOPTAS AND F. MCSHERRY, Fast computation of low-rank matrix approximations, J. ACM, 54 (2007), article 9.
    • (2007) J. ACM , vol.54 , pp. 9
    • Achlioptas, D.1    McSherry, F.2
  • 3
    • 0001326391 scopus 로고
    • Some applications of the rank revealing QR factorization
    • T. F. CHAN AND P. C. HANSEN, Some applications of the rank revealing QR factorization, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 727-741.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 727-741
    • Chan, T.F.1    Hansen, P.C.2
  • 4
    • 33746136466 scopus 로고    scopus 로고
    • Condition numbers of gaussian random matrices
    • Z. CHEN AND J. J. DONGARRA, Condition numbers of Gaussian random matrices, SIAM J. Matrix Anal. Appl., 27 (2005), pp. 603-620.
    • (2005) SIAM J. Matrix Anal. Appl. , vol.27 , pp. 603-620
    • Chen, Z.1    Dongarra, J.J.2
  • 9
    • 0001290746 scopus 로고
    • Estimating extremal eigenvalues and condition numbers of matrices
    • J. D. DIXON, Estimating extremal eigenvalues and condition numbers of matrices, SIAM J. Numer. Anal., 20 (1983), pp. 812-814.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 812-814
    • Dixon, J.D.1
  • 16
    • 0040942625 scopus 로고    scopus 로고
    • Quick approximation to matrices and applications
    • A. FRIEZE AND R. KANNAN, Quick approximation to matrices and applications, Combinatorica, 19 (1999), pp. 175-220.
    • (1999) Combinatorica , vol.19 , pp. 175-220
    • Frieze, A.1    Kannan, R.2
  • 18
    • 20444476106 scopus 로고    scopus 로고
    • Fast monte-carlo algorithms for finding low-rank approximations
    • A. FRIEZE, R. KANNAN, AND S. VEMPALA, Fast Monte-Carlo algorithms for finding low-rank approximations, J. ACM, 51 (2004), pp. 1025-1041.
    • (2004) J. ACM , vol.51 , pp. 1025-1041
    • Frieze, A.1    Kannan, R.2    Vempala, S.3
  • 20
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed., Johns Hopkins University Press, Baltimore, MD
    • G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 22
    • 27544513989 scopus 로고    scopus 로고
    • Pseudo-skeleton approximations by matrices of maximal volume
    • S. A. GOREINOV, E. E. TYRTYSHNIKOV, AND N. L. ZAMARASHKIN, Pseudo-skeleton approximations by matrices of maximal volume, Math. Notes, 62 (1997), pp. 515-519.
    • (1997) Math. Notes , vol.62 , pp. 515-519
    • Goreinov, S.A.1    Tyrtyshnikov, E.E.2    Zamarashkin, N.L.3
  • 24
    • 0003216822 scopus 로고    scopus 로고
    • Efficient algorithms for computing a strong rank-revealing QR factorization
    • M. GU AND S. C. EISENSTAT, Efficient algorithms for computing a strong rank-revealing QR factorization, SIAM J. Sci. Comput., 17 (1996), pp. 848-869.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 848-869
    • Gu, M.1    Eisenstat, S.C.2
  • 26
    • 0043178250 scopus 로고
    • Estimating the largest eigenvalue by the power and lanczos algorithms with a random start
    • J. KUCZYŃSKI AND H. WOŹNIAKOWSKI, Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 1094- 1122.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 1094-1122
    • Kuczyński, J.1    Woźniakowski, H.2
  • 28
    • 58849086813 scopus 로고    scopus 로고
    • CUR matrix decompositions for improved data analysis
    • M. W. MAHONEY AND P. DRINEAS, CUR matrix decompositions for improved data analysis, Proc. Natl. Acad. Sci. USA, 106 (2009), pp. 697-702.
    • (2009) Proc. Natl. Acad. Sci. USA , vol.106 , pp. 697-702
    • Mahoney, M.W.1    Drineas, P.2
  • 29
    • 38049187128 scopus 로고    scopus 로고
    • Technical report 1361, Yale University, Department of Computer Science, New Haven, CT, 2006. Available in the form referenced in the present paper at
    • P.-G. MARTINSSON, V. ROKHLIN, AND M. TYGERT, A Randomized Algorithm for the Approximation of Matrices, Technical report 1361, Yale University, Department of Computer Science, New Haven, CT, 2006. Available in the form referenced in the present paper at http://www.cs.yale.edu/publications/ techreports/tr1361.pdf and in revised form (with renumbered lemmas) at http://www.cs.yale.edu/~tygert/randapp.pdf.
    • A Randomized Algorithm for the Approximation of Matrices
    • Martinsson, P.-G.1    Rokhlin, V.2    Tygert, M.3
  • 32
    • 35348901208 scopus 로고    scopus 로고
    • Improved approximation algorithms for large matrices via random projections
    • Berkeley, CA, IEEE Computer Society, Washington, D.C.
    • T. SARLÓS, Improved approximation algorithms for large matrices via random projections, in Proceedings of the Forty-Seventh Annual IEEE Symposium on Foundations of Computer Science, Berkeley, CA, IEEE Computer Society, Washington, D.C., 2006, pp. 143-152.
    • (2006) Proceedings of the Forty-Seventh Annual IEEE Symposium on Foundations of Computer Science , pp. 143-152
    • Sarlós, T.1
  • 33
    • 72449121227 scopus 로고    scopus 로고
    • Technical report, Eötvös Loránd University, Informatics Laboratory, Budapest, Hungary, Available online at
    • T. SARLÓS, Improved Approximation Algorithms for Large Matrices via Random Projections, Long Form, Technical report, Eötvös Loránd University, Informatics Laboratory, Budapest, Hungary, 2006. Available online at http://www.ilab.sztaki.hu/~stamas/publications/rplong. pdf.
    • (2006) Improved Approximation Algorithms for Large Matrices via Random Projections, Long Form
    • Sarlós, T.1
  • 34
    • 48349138074 scopus 로고    scopus 로고
    • Less is more: Compact matrix decomposition for large sparse graphs
    • J. SUN, Y. XIE, H. ZHANG, AND C. FALOUTSOS, Less is more: Compact matrix decomposition for large sparse graphs, Stat. Anal. Data Min., 1 (2008), pp. 6-22.
    • (2008) Stat. Anal. Data Min. , vol.1 , pp. 6-22
    • Sun, J.1    Xie, Y.2    Zhang, H.3    Faloutsos, C.4
  • 35
    • 0038805356 scopus 로고    scopus 로고
    • Incomplete cross approximation in the mosaic-skeleton method
    • E. E. TYRTYSHNIKOV, Incomplete cross approximation in the mosaic-skeleton method, Computing, 64 (2000), pp. 367-380.
    • (2000) Computing , vol.64 , pp. 367-380
    • Tyrtyshnikov, E.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.