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Volumn 3, Issue 2, 2010, Pages 123-224

Randomized algorithms for matrices and data

Author keywords

[No Author keywords available]

Indexed keywords

APPLICATION DOMAINS; ASYMPTOTIC THEORIES; COMPUTATIONAL ARCHITECTURE; COMPUTATIONAL TIME; MATRIX PROBLEM; MODEL DATA; NUMERICAL IMPLEMENTATION; RANDOMIZED ALGORITHMS; RESEARCH COMMUNITIES; SIMPLER ALGORITHMS;

EID: 84856463292     PISSN: 19358237     EISSN: 19358245     Source Type: Journal    
DOI: 10.1561/2200000035     Document Type: Review
Times cited : (820)

References (198)
  • 1
    • 0038166193 scopus 로고    scopus 로고
    • Database-friendly random projections: Johnson-Lindenstrauss with binary coins
    • D. Achlioptas, "Database-friendly random projections: Johnson-Lindenstrauss with binary coins," Journal of Computer and System Sciences, vol. 66, no. 4, pp. 671-687, 2003.
    • (2003) Journal of Computer and System Sciences , vol.66 , Issue.4 , pp. 671-687
    • Achlioptas, D.1
  • 2
    • 34247228045 scopus 로고    scopus 로고
    • Fast computation of low-rank matrix approximations
    • ACM
    • D. Achlioptas and F. McSherry, "Fast computation of low-rank matrix approximations," Journal of the ACM, vol. 54, no. 2, p. Article 9, 2007.
    • (2007) Journal of the , vol.54 , Issue.2 , pp. 9
    • Achlioptas, D.1    McSherry, F.2
  • 3
    • 33748109164 scopus 로고    scopus 로고
    • Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
    • STOC'06: Proceedings of the 38th Annual ACM Symposium on Theory of Computing
    • N. Ailon and B. Chazelle, "Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform," in Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pp. 557-563, 2006. (Pubitemid 44306590)
    • (2006) Proceedings of the Annual ACM Symposium on Theory of Computing , vol.2006 , pp. 557-563
    • Ailon, N.1    Chazelle, B.2
  • 4
    • 67650105330 scopus 로고    scopus 로고
    • The fast Johnson-Lindenstrauss transform and approximate nearest neighbors
    • N. Ailon and B. Chazelle, "The fast Johnson-Lindenstrauss transform and approximate nearest neighbors," SIAM Journal on Computing, vol. 39, no. 1, pp. 302-322, 2009.
    • (2009) SIAM Journal on Computing , vol.39 , Issue.1 , pp. 302-322
    • Ailon, N.1    Chazelle, B.2
  • 5
    • 75749141980 scopus 로고    scopus 로고
    • Faster dimension reduction
    • N. Ailon and B. Chazelle, "Faster dimension reduction," Communications of the ACM, vol. 53, no. 2, pp. 97-104, 2010.
    • (2010) Communications of the ACM , vol.53 , Issue.2 , pp. 97-104
    • Ailon, N.1    Chazelle, B.2
  • 8
    • 0034730140 scopus 로고    scopus 로고
    • Singular value decomposition for genome-wide expression data processing and modeling
    • O. Alter, P. O. Brown, and D. Botstein, "Singular value decomposition for genome-wide expression data processing and modeling," Proc. Natl. Acad. Sci. USA, vol. 97, no. 18, pp. 10101-10106, 2000.
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , Issue.18 , pp. 10101-10106
    • Alter, O.1    Brown, P.O.2    Botstein, D.3
  • 10
    • 63249085856 scopus 로고    scopus 로고
    • Some issues in dense linear algebra for multicore and special purpose architectures
    • University of Tennessee, May
    • M. Baboulin, J. Dongarra, and S. Tomov, "Some issues in dense linear algebra for multicore and special purpose architectures," Technical Report UT-CS-08-200, University of Tennessee, May 2008.
    • (2008) Technical Report UT-CS-08-200
    • Baboulin, M.1    Dongarra, J.2    Tomov, S.3
  • 11
    • 77955253091 scopus 로고    scopus 로고
    • Data mining and machine learning in astronomy
    • N. M. Ball and R. J. Brunner, "Data mining and machine learning in astronomy," International Journal of Modern Physics D, vol. 19, no. 7, pp. 1049- 1106, 2010.
    • (2010) International Journal of Modern Physics D , vol.19 , Issue.7 , pp. 1049-1106
    • Ball, N.M.1    Brunner, R.J.2
  • 13
    • 41549119861 scopus 로고    scopus 로고
    • On the spectrum of the normalized graph Laplacian
    • A. Banerjee and J. Jost, "On the spectrum of the normalized graph Laplacian," Linear Algebra and its Applications, vol. 428, no. 11-12, pp. 3015-3022, 2008.
    • (2008) Linear Algebra and Its Applications , vol.428 , Issue.11-12 , pp. 3015-3022
    • Banerjee, A.1    Jost, J.2
  • 14
    • 67349157147 scopus 로고    scopus 로고
    • Graph spectra as a systematic tool in computational biology
    • A. Banerjee and J. Jost, "Graph spectra as a systematic tool in computational biology," Discrete Applied Mathematics, vol. 157, no. 10, pp. 2425-2431, 2009.
    • (2009) Discrete Applied Mathematics , vol.157 , Issue.10 , pp. 2425-2431
    • Banerjee, A.1    Jost, J.2
  • 15
    • 34547811873 scopus 로고    scopus 로고
    • Graph effective resistance and distributed control: Spectral properties and applications
    • 4177510, Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
    • P. Barooah and J. P. Hespanha, "Graph effective resistances and distributed control: Spectral properties and applications," in Proceedings of the 45th IEEE Conference on Decision and Control, pp. 3479-3485, 2006. (Pubitemid 351283761)
    • (2006) Proceedings of the IEEE Conference on Decision and Control , pp. 3479-3485
    • Barooah, P.1    Hespanha, J.P.2
  • 16
    • 34547173915 scopus 로고    scopus 로고
    • An estimator for the diagonal of a matrix
    • DOI 10.1016/j.apnum.2007.01.003, PII S0168927407000244, Numerical Algorithms, Parallelis, and Aplications (2)
    • C. Bekas, E. Kokiopoulou, and Y. Saad, "An estimator for the diagonal of a matrix," Applied Numerical Mathematics, vol. 57, pp. 1214-1229, 2007. (Pubitemid 47348166)
    • (2007) Applied Numerical Mathematics , vol.57 , Issue.11-12 , pp. 1214-1229
    • Bekas, C.1    Kokiopoulou, E.2    Saad, Y.3
  • 20
    • 58849142031 scopus 로고    scopus 로고
    • Spectral methods in machine learning and new strategies for very large datasets
    • M.-A. Belabbas and P. J. Wolfe, "Spectral methods in machine learning and new strategies for very large datasets," Proc. Natl. Acad. Sci. USA, vol. 106, pp. 369-374, 2009.
    • (2009) Proc. Natl. Acad. Sci. USA , vol.106 , pp. 369-374
    • Belabbas, M.-A.1    Wolfe, P.J.2
  • 21
    • 84856498980 scopus 로고    scopus 로고
    • On the approximation of matrix products and positive definite matrices
    • Preprint: arXiv:0707.4448
    • M.-A. Belabbas and P. Wolfe, "On the approximation of matrix products and positive definite matrices," Technical report. Preprint: arXiv:0707.4448, 2007.
    • (2007) Technical Report
    • Belabbas, M.-A.1    Wolfe, P.2
  • 22
    • 31044445386 scopus 로고    scopus 로고
    • Email surveillance using non-negative matrix factorization
    • DOI 10.1007/s10588-005-5380-5
    • M. W. Berry and M. Browne, "Email surveillance using non-negative matrix factorization," Computational and Mathematical Organization Theory, vol. 11, no. 3, pp. 249-264, 2005. (Pubitemid 43118969)
    • (2005) Computational and Mathematical Organization Theory , vol.11 , Issue.3 , pp. 249-264
    • Berry, M.W.1    Browne, M.2
  • 24
    • 0035789317 scopus 로고    scopus 로고
    • Random projection in dimensionality reduction: Applications to image and text data
    • E. Bingham and H. Mannila, "Random projection in dimensionality reduction: Applications to image and text data," in Proceedings of the 7th Annual ACM SIGKDD Conference, pp. 245-250, 2001.
    • (2001) Proceedings of the 7th Annual ACM SIGKDD Conference , pp. 245-250
    • Bingham, E.1    Mannila, H.2
  • 26
    • 0032083879 scopus 로고    scopus 로고
    • Algorithm 782: Codes for rank-revealing QR factorizations of dense matrices
    • C. H. Bischof and G. Quintana-Ortí, "Algorithm 782: Codes for rank-revealing QR factorizations of dense matrices," ACM Transactions on Mathematical Software, vol. 24, no. 2, pp. 254-257, 1998. (Pubitemid 128444734)
    • (1998) ACM Transactions on Mathematical Software , vol.24 , Issue.2 , pp. 254-257
    • Bischof, C.H.1    Quintana-Orti, G.2
  • 27
    • 0032083715 scopus 로고    scopus 로고
    • Computing rank-revealing QR factorizations of dense matrices
    • C. H. Bischof and G. Quintana-Ortí, "Computing rank-revealing QR factorizations of dense matrices," ACM Transactions on Mathematical Software, vol. 24, no. 2, pp. 226-253, 1998. (Pubitemid 128444733)
    • (1998) ACM Transactions on Mathematical Software , vol.24 , Issue.2 , pp. 226-253
    • Bischof, C.H.1    Quintana-Orti, G.2
  • 28
    • 84936824655 scopus 로고
    • Power and centrality: A family of measures
    • P. Bonacich, "Power and centrality: A family of measures," The American Journal of Sociology, vol. 92, no. 5, pp. 1170-1182, 1987.
    • (1987) The American Journal of Sociology , vol.92 , Issue.5 , pp. 1170-1182
    • Bonacich, P.1
  • 29
    • 78049281558 scopus 로고    scopus 로고
    • Exploring the spectral space of low redshift QSOs
    • T. A. Boroson and T. R. Lauer, "Exploring the spectral space of low redshift QSOs," The Astronomical Journal, vol. 140, pp. 390-402, 2010.
    • (2010) The Astronomical Journal , vol.140 , pp. 390-402
    • Boroson, T.A.1    Lauer, T.R.2
  • 30
    • 84944560863 scopus 로고    scopus 로고
    • An improved approximation algorithm for the column subset selection problem
    • Preprint: arXiv:0812.4293v2
    • C. Boutsidis, M. W. Mahoney, and P. Drineas, "An improved approximation algorithm for the column subset selection problem," Technical report. Preprint: arXiv:0812.4293v2, 2008.
    • (2008) Technical Report
    • Boutsidis, C.1    Mahoney, M.W.2    Drineas, P.3
  • 34
    • 0001714858 scopus 로고
    • Diffusion in a sparsely connected space: A model for glassy relaxation
    • A. J. Bray and G. J. Rodgers, "Diffusion in a sparsely connected space: A model for glassy relaxation," Physical Review B, vol. 38, no. 16, pp. 11461- 11470, 1988.
    • (1988) Physical Review B , vol.38 , Issue.16 , pp. 11461-11470
    • Bray, A.J.1    Rodgers, G.J.2
  • 36
    • 2442565134 scopus 로고    scopus 로고
    • Massive datasets in astronomy
    • (J. Abello, P. M. Pardalos, and M. G. C. Resende, eds.), Kluwer Academic Publishers
    • R. J. Brunner, S. G. Djorgovski, T. A. Prince, and A. S. Szalay, "Massive datasets in astronomy," in Handbook of Massive Data Sets, (J. Abello, P. M. Pardalos, and M. G. C. Resende, eds.), pp. 931-979, Kluwer Academic Publishers, 2002.
    • (2002) Handbook of Massive Data Sets , pp. 931-979
    • Brunner, R.J.1    Djorgovski, S.G.2    Prince, T.A.3    Szalay, A.S.4
  • 38
    • 0000673625 scopus 로고
    • Linear least squares solutions by Householder transformations
    • P. Businger and G. H. Golub, "Linear least squares solutions by Householder transformations," Numerische Mathematik, vol. 7, pp. 269-276, 1965.
    • (1965) Numerische Mathematik , vol.7 , pp. 269-276
    • Businger, P.1    Golub, G.H.2
  • 39
    • 55549132964 scopus 로고    scopus 로고
    • Fast computation of Fourier integral operators
    • E. Candes, L. Demanet, and L. Ying, "Fast computation of Fourier integral operators," SIAM Journal on Scientific Computing, vol. 29, no. 6, pp. 2464- 2493, 2007.
    • (2007) SIAM Journal on Scientific Computing , vol.29 , Issue.6 , pp. 2464-2493
    • Candes, E.1    Demanet, L.2    Ying, L.3
  • 40
    • 34249687049 scopus 로고    scopus 로고
    • Sparsity and incoherence in compressive sampling
    • DOI 10.1088/0266-5611/23/3/008, PII S0266561107398742, 008
    • E. Candes and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems, vol. 23, no. 3, pp. 969-985, 2007. (Pubitemid 46838836)
    • (2007) Inverse Problems , vol.23 , Issue.3 , pp. 969-985
    • Candes, E.1    Romberg, J.2
  • 41
    • 71049116435 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • E. J. Candes and B. Recht, "Exact matrix completion via convex optimization," Foundations of Computational Mathematics, vol. 9, no. 6, pp. 717-772, 2009.
    • (2009) Foundations of Computational Mathematics , vol.9 , Issue.6 , pp. 717-772
    • Candes, E.J.1    Recht, B.2
  • 44
    • 0002170151 scopus 로고
    • Rank revealing QR factorizations
    • T. F. Chan, "Rank revealing QR factorizations," Linear Algebra and Its Applications, vol. 88/89, pp. 67-82, 1987.
    • (1987) Linear Algebra and Its Applications , vol.88-89 , pp. 67-82
    • Chan, T.F.1
  • 46
    • 0001138266 scopus 로고
    • Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations
    • T. F. Chan and P. C. Hansen, "Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations," SIAM Journal on Scientific and Statistical Computing, vol. 11, pp. 519-530, 1990.
    • (1990) SIAM Journal on Scientific and Statistical Computing , vol.11 , pp. 519-530
    • Chan, T.F.1    Hansen, P.C.2
  • 49
    • 84972496372 scopus 로고
    • Influential observations, high leverage points, and outliers in linear regression
    • S. Chatterjee and A. S. Hadi, "Influential observations, high leverage points, and outliers in linear regression," Statistical Science, vol. 1, no. 3, pp. 379-393, 1986.
    • (1986) Statistical Science , vol.1 , Issue.3 , pp. 379-393
    • Chatterjee, S.1    Hadi, A.S.2
  • 54
    • 78649910530 scopus 로고    scopus 로고
    • On selecting a maximum volume sub-matrix of a matrix and related problems
    • A. Civril and M. Magdon-Ismail, "On selecting a maximum volume sub-matrix of a matrix and related problems," Theoretical Computer Science, vol. 410, pp. 4801-4811, 2009.
    • (2009) Theoretical Computer Science , vol.410 , pp. 4801-4811
    • Civril, A.1    Magdon-Ismail, M.2
  • 56
  • 57
    • 0009819537 scopus 로고    scopus 로고
    • A robust classification of galaxy spectra: Dealing with noisy and incomplete data
    • A. J. Connolly and A. S. Szalay, "A robust classification of galaxy spectra: Dealing with noisy and incomplete data," The Astronomical Journal, vol. 117, no. 5, pp. 2052-2062, 1999.
    • (1999) The Astronomical Journal , vol.117 , Issue.5 , pp. 2052-2062
    • Connolly, A.J.1    Szalay, A.S.2
  • 59
    • 84968470212 scopus 로고
    • An algorithm for the machine calculation of complex Fourier series
    • J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Mathematics of Computation, vol. 19, no. 90, pp. 297-301, 1965.
    • (1965) Mathematics of Computation , vol.19 , Issue.90 , pp. 297-301
    • Cooley, J.W.1    Tukey, J.W.2
  • 61
    • 0037236821 scopus 로고    scopus 로고
    • An elementary proof of a theorem of Johnson and Lindenstrauss
    • S. Dasgupta and A. Gupta, "An elementary proof of a theorem of Johnson and Lindenstrauss," Random Structures and Algorithms, vol. 22, no. 1, pp. 60-65, 2003.
    • (2003) Random Structures and Algorithms , vol.22 , Issue.1 , pp. 60-65
    • Dasgupta, S.1    Gupta, A.2
  • 62
    • 84856460967 scopus 로고
    • Subsampling algorithms for semidefinite programming
    • Preprint: arXiv: 0803
    • A. d'Aspremont, "Subsampling algorithms for semidefinite programming," Technical Report. Preprint: arXiv:0803.1990, 2008.
    • (1990) Technical Report , pp. 2008
    • D'Aspremont, A.1
  • 67
    • 0005428798 scopus 로고
    • Testing for the inclusion of variables in linear regression by a randomisation technique
    • N. R. Draper and D. M. Stoneman, "Testing for the inclusion of variables in linear regression by a randomisation technique," Technometrics, vol. 8, no. 4, pp. 695-699, 1966.
    • (1966) Technometrics , vol.8 , Issue.4 , pp. 695-699
    • Draper, N.R.1    Stoneman, D.M.2
  • 68
    • 3142750484 scopus 로고    scopus 로고
    • Clustering large graphs via the singular value decomposition
    • P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay, "Clustering large graphs via the singular value decomposition," Machine Learning, vol. 56, no. 1-3, pp. 9-33, 2004.
    • (2004) Machine Learning , vol.56 , Issue.1-3 , pp. 9-33
    • Drineas, P.1    Frieze, A.2    Kannan, R.3    Vempala, S.4    Vinay, V.5
  • 69
    • 33751115359 scopus 로고    scopus 로고
    • Fast Monte Carlo algorithms for matrices I: Approximating matrix multiplication
    • DOI 10.1137/S0097539704442684
    • P. Drineas, R. Kannan, and M. W. Mahoney, "Fast Monte Carlo algorithms for matrices I: Approximating matrix multiplication," SIAM Journal on Computing, vol. 36, pp. 132-157, 2006. (Pubitemid 46374021)
    • (2006) SIAM Journal on Computing , vol.36 , Issue.1 , pp. 132-157
    • Drineas, P.1    Kannan, R.2    Mahoney, M.W.3
  • 70
    • 33751075906 scopus 로고    scopus 로고
    • Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix
    • DOI 10.1137/S0097539704442696
    • P. Drineas, R. Kannan, and M. W. Mahoney, "Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix," SIAM Journal on Computing, vol. 36, pp. 158-183, 2006. (Pubitemid 46374022)
    • (2006) SIAM Journal on Computing , vol.36 , Issue.1 , pp. 158-183
    • Drineas, P.1    Kannan, R.2    Mahoney, M.W.3
  • 71
    • 33751097630 scopus 로고    scopus 로고
    • Fast Monte Carlo algorithms for matrices III: Computing a compressed approximate matrix decomposition
    • DOI 10.1137/S0097539704442702
    • P. Drineas, R. Kannan, and M. W. Mahoney, "Fast Monte Carlo algorithms for matrices III: Computing a compressed approximate matrix decomposition," SIAM Journal on Computing, vol. 36, pp. 184-206, 2006. (Pubitemid 46374023)
    • (2006) SIAM Journal on Computing , vol.36 , Issue.1 , pp. 184-206
    • Drineas, P.1    Kannan, R.2    Mahoney, M.W.3
  • 72
    • 77957857734 scopus 로고    scopus 로고
    • Inferring geographic coordinates of origin for Europeans using small panels of ancestry informative markers
    • no. 8
    • P. Drineas, J. Lewis, and P. Paschou, "Inferring geographic coordinates of origin for Europeans using small panels of ancestry informative markers," PLoS ONE, vol. 5, no. 8, no. 8, p. e11892, 2010.
    • (2010) PLoS ONE , vol.5 , Issue.8
    • Drineas, P.1    Lewis, J.2    Paschou, P.3
  • 73
    • 84856484816 scopus 로고    scopus 로고
    • Fast approximation of matrix coherence and statistical leverage
    • Preprint: arXiv: 1109.3843
    • P. Drineas, M. Magdon-Ismail, M. W. Mahoney, and D. P. Woodruff, "Fast approximation of matrix coherence and statistical leverage," Technical report. Preprint: arXiv:1109.3843, 2011.
    • (2011) Technical Report
    • Drineas, P.1    Magdon-Ismail, M.2    Mahoney, M.W.3    Woodruff, D.P.4
  • 74
    • 29244453931 scopus 로고    scopus 로고
    • On the Nyström method for approximating a Gram matrix for improved kernel-based learning
    • P. Drineas and M. W. Mahoney, "On the Nyström method for approximating a Gram matrix for improved kernel-based learning," Journal of Machine Learning Research, vol. 6, pp. 2153-2175, 2005. (Pubitemid 41832630)
    • (2005) Journal of Machine Learning Research , vol.6 , pp. 2153-2175
    • Drineas, P.1    Mahoney, M.W.2
  • 78
    • 0141711679 scopus 로고    scopus 로고
    • Wavelet-based numerical homogenization with applications
    • (T. J. Barth, T. F. Chan, and R. Haimes, eds.), Springer
    • B. Engquist and O. Runborg, "Wavelet-based numerical homogenization with applications," in Multiscale and Multiresolution Methods: Theory and Applications, LNCSE, (T. J. Barth, T. F. Chan, and R. Haimes, eds.), pp. 97-148, Springer, 2001.
    • (2001) Multiscale and Multiresolution Methods: Theory and Applications, LNCSE , pp. 97-148
    • Engquist, B.1    Runborg, O.2
  • 79
    • 48249115600 scopus 로고    scopus 로고
    • Fast directional multilevel algorithms for oscillatory kernels
    • B. Engquist and L. Ying, "Fast directional multilevel algorithms for oscillatory kernels," SIAM Journal on Scientific Computing, vol. 29, pp. 1710-1737, 2007.
    • (2007) SIAM Journal on Scientific Computing , vol.29 , pp. 1710-1737
    • Engquist, B.1    Ying, L.2
  • 81
  • 82
    • 21144466780 scopus 로고
    • A numerical study of sparse random matrices
    • S. N. Evangelou, "A numerical study of sparse random matrices," Journal of Statistical Physics, vol. 69, no. 1-2, pp. 361-383, 1992.
    • (1992) Journal of Statistical Physics , vol.69 , Issue.1-2 , pp. 361-383
    • Evangelou, S.N.1
  • 83
  • 85
    • 84974824176 scopus 로고    scopus 로고
    • An artificial neural network approach to the classification of galaxy spectra
    • S. R. Folkes, O. Lahav, and S. J. Maddox, "An artificial neural network approach to the classification of galaxy spectra," Mon. Not. R. Astron. Soc., vol. 283, no. 2, pp. 651-665, 1996.
    • (1996) Mon. Not. R. Astron. Soc. , vol.283 , Issue.2 , pp. 651-665
    • Folkes, S.R.1    Lahav, O.2    Maddox, S.J.3
  • 86
    • 38249043588 scopus 로고
    • Rank and null space calculations using matrix decomposition without column interchanges
    • L. V. Foster, "Rank and null space calculations using matrix decomposition without column interchanges," Linear Algebra and Its Applications, vol. 74, pp. 47-71, 1986.
    • (1986) Linear Algebra and Its Applications , vol.74 , pp. 47-71
    • Foster, L.V.1
  • 88
    • 38249031101 scopus 로고
    • The Johnson-Lindenstrauss lemma and the sphericity of some graphs
    • P. Frankl and H. Maehara, "The Johnson-Lindenstrauss lemma and the sphericity of some graphs," Journal of Combinatorial Theory Series A, vol. 44, no. 3, pp. 355-362, 1987.
    • (1987) Journal of Combinatorial Theory Series A , vol.44 , Issue.3 , pp. 355-362
    • Frankl, P.1    Maehara, H.2
  • 89
    • 0040942625 scopus 로고    scopus 로고
    • Quick approximation to matrices and applications
    • A. Frieze and R. Kannan, "Quick approximation to matrices and applications," Combinatorica, vol. 19, no. 2, pp. 175-220, 1999.
    • (1999) Combinatorica , vol.19 , Issue.2 , pp. 175-220
    • Frieze, A.1    Kannan, R.2
  • 90
    • 20444476106 scopus 로고    scopus 로고
    • Fast Monte-Carlo algorithms for finding low-rank approximations
    • DOI 10.1145/1039488.1039494
    • A. Frieze, R. Kannan, and S. Vempala, "Fast Monte-Carlo algorithms for finding low-rank approximations," Journal of the ACM, vol. 51, no. 6, pp. 1025- 1041, 2004. (Pubitemid 40818314)
    • (2004) Journal of the ACM , vol.51 , Issue.6 , pp. 1025-1041
    • Frieze, A.1    Kannan, R.2    Vempala, S.3
  • 91
    • 51249182622 scopus 로고
    • The eigenvalues of random symmetric matrices
    • Z. Füredi and J. Komlós, "The eigenvalues of random symmetric matrices," Combinatorica, vol. 1, no. 3, pp. 233-241, 1981.
    • (1981) Combinatorica , vol.1 , Issue.3 , pp. 233-241
    • Füredi, Z.1    Komlós, J.2
  • 92
    • 4243709314 scopus 로고
    • Localization in ensemble of sparse random matrices
    • Y. V. Fyodorov and A. D. Mirlin, "Localization in ensemble of sparse random matrices," Physical Review Letters, vol. 67, pp. 2049-2052, 1991.
    • (1991) Physical Review Letters , vol.67 , pp. 2049-2052
    • Fyodorov, Y.V.1    Mirlin, A.D.2
  • 94
    • 77952733655 scopus 로고    scopus 로고
    • Sparse recovery using sparse matrices
    • A. Gilbert and P. Indyk, "Sparse recovery using sparse matrices," Proceedings of the IEEE, vol. 98, no. 6, pp. 937-947, 2010.
    • (2010) Proceedings of the IEEE , vol.98 , Issue.6 , pp. 937-947
    • Gilbert, A.1    Indyk, P.2
  • 96
    • 4043141148 scopus 로고    scopus 로고
    • Spectra and eigenvectors of scale-free networks
    • K.-I. Goh, B. Kahng, and D. Kim, "Spectra and eigenvectors of scale-free networks," Physical Review E, vol. 64, p. 051903, 2001.
    • (2001) Physical Review e , vol.64 , pp. 051903
    • Goh, K.-I.1    Kahng, B.2    Kim, D.3
  • 97
    • 84856437351 scopus 로고    scopus 로고
    • Bridging the gap between numerical linear algebra, theoretical computer science, and data applications
    • October
    • G. H. Golub, M. W. Mahoney, P. Drineas, and L.-H. Lim, "Bridging the gap between numerical linear algebra, theoretical computer science, and data applications," SIAM News, vol. 39, no. 8, October 2006.
    • (2006) SIAM News , vol.39 , Issue.8
    • Golub, G.H.1    Mahoney, M.W.2    Drineas, P.3    Lim, L.-H.4
  • 99
    • 0037790752 scopus 로고    scopus 로고
    • The maximum-volume concept in approximation by low-rank matrices
    • S. A. Goreinov and E. E. Tyrtyshnikov, "The maximum-volume concept in approximation by low-rank matrices," Contemporary Mathematics, vol. 280, pp. 47-51, 2001.
    • (2001) Contemporary Mathematics , vol.280 , pp. 47-51
    • Goreinov, S.A.1    Tyrtyshnikov, E.E.2
  • 101
  • 102
    • 0141829814 scopus 로고    scopus 로고
    • Construction and arithmetics of H-matrices
    • L. Grasedyck and W. Hackbusch, "Construction and arithmetics of H-matrices," Computing, vol. 70, no. 4, pp. 295-334, 2003.
    • (2003) Computing , vol.70 , Issue.4 , pp. 295-334
    • Grasedyck, L.1    Hackbusch, W.2
  • 103
    • 0000396658 scopus 로고
    • A fast algorithm for particle simulations
    • L. Greengard and V. Rokhlin, "A fast algorithm for particle simulations," Journal of Computational Physics, vol. 73, no. 2, pp. 325-348, 1987.
    • (1987) Journal of Computational Physics , vol.73 , Issue.2 , pp. 325-348
    • Greengard, L.1    Rokhlin, V.2
  • 104
    • 85011484616 scopus 로고    scopus 로고
    • A new version of the fast multipole method for the Laplace equation in three dimensions
    • L. Greengard and V. Rokhlin, "A new version of the fast multipole method for the Laplace equation in three dimensions," Acta Numerica, vol. 6, pp. 229-269, 1997.
    • (1997) Acta Numerica , vol.6 , pp. 229-269
    • Greengard, L.1    Rokhlin, V.2
  • 105
    • 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 rankrevealing QR factorization," SIAM Journal on Scientific Computing, vol. 17, pp. 848-869, 1996. (Pubitemid 126621180)
    • (1996) SIAM Journal of Scientific Computing , vol.17 , Issue.4 , pp. 848-869
    • Gu, M.1    Eisenstat, S.C.2
  • 106
    • 80052705262 scopus 로고    scopus 로고
    • An algorithm for the principal component analysis of large data sets
    • Preprint: arXiv: 1007.5510
    • N. Halko, P.-G. Martinsson, Y. Shkolnisky, and M. Tygert, "An algorithm for the principal component analysis of large data sets," Technical report. Preprint: arXiv:1007.5510, 2010.
    • (2010) Technical Report
    • Halko, N.1    Martinsson, P.-G.2    Shkolnisky, Y.3    Tygert, M.4
  • 107
    • 79960425522 scopus 로고    scopus 로고
    • Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
    • no. 2
    • N. Halko, P.-G. Martinsson, and J. A. Tropp, "Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions," SIAM Review, vol. 53, no. 2, no. 2, pp. 217-288, 2011.
    • (2011) SIAM Review , vol.53 , Issue.2 , pp. 217-288
    • Halko, N.1    Martinsson, P.-G.2    Tropp, J.A.3
  • 110
    • 84948783167 scopus 로고
    • The hat matrix in regression and ANOVA
    • D. C. Hoaglin and R. E. Welsch, "The hat matrix in regression and ANOVA," The American Statistician, vol. 32, no. 1, pp. 17-22, 1978.
    • (1978) The American Statistician , vol.32 , Issue.1 , pp. 17-22
    • Hoaglin, D.C.1    Welsch, R.E.2
  • 111
    • 84968501766 scopus 로고
    • Rank-revealing QR factorizations and the singular value decomposition
    • Y. P. Hong and C. T. Pan, "Rank-revealing QR factorizations and the singular value decomposition," Mathematics of Computation, vol. 58, pp. 213-232, 1992.
    • (1992) Mathematics of Computation , vol.58 , pp. 213-232
    • Hong, Y.P.1    Pan, C.T.2
  • 112
    • 0347362608 scopus 로고    scopus 로고
    • Principal component analysis for selection of optimal SNP-sets that capture intragenic genetic variation
    • DOI 10.1002/gepi.10292
    • B. D. Horne and N. J. Camp, "Principal component analysis for selection of optimal SNP-sets that capture intragenic genetic variation," Genetic Epidemiology, vol. 26, no. 1, pp. 11-21, 2004. (Pubitemid 38036640)
    • (2004) Genetic Epidemiology , vol.26 , Issue.1 , pp. 11-21
    • Horne, B.D.1    Camp, N.J.2
  • 114
    • 80053569053 scopus 로고    scopus 로고
    • Efficient genomewide selection of PCA-correlated tSNPs for genotype imputation
    • A. Javed, P. Drineas, M. W. Mahoney, and P. Paschou, "Efficient genomewide selection of PCA-correlated tSNPs for genotype imputation," Annals of Human Genetics, vol. 75, no. 6, pp. 707-722, 2011.
    • (2011) Annals of Human Genetics , vol.75 , Issue.6 , pp. 707-722
    • Javed, A.1    Drineas, P.2    Mahoney, M.W.3    Paschou, P.4
  • 115
    • 0001654702 scopus 로고
    • Extensions of Lipshitz mapping into Hilbert space
    • W. B. Johnson and J. Lindenstrauss, "Extensions of Lipshitz mapping into Hilbert space," Contemporary Mathematics, vol. 26, pp. 189-206, 1984.
    • (1984) Contemporary Mathematics , vol.26 , pp. 189-206
    • Johnson, W.B.1    Lindenstrauss, J.2
  • 116
    • 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," Annals of Statistics, vol. 29, no. 2, pp. 295-327, 2001.
    • (2001) Annals of Statistics , vol.29 , Issue.2 , pp. 295-327
    • Johnstone, I.M.1
  • 117
    • 62749130805 scopus 로고    scopus 로고
    • Effective resistance of Gromov-hyperbolic graphs: Application to asymptotic sensor network problems
    • DOI 10.1109/CDC.2007.4434878, 4434878, Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
    • E. A. Jonckheere, M. Lou, J. Hespanha, and P. Barooah, "Effective resistance of Gromov-hyperbolic graphs: Application to asymptotic sensor network problems," in Proceedings of the 46th IEEE Conference on Decision and Control, pp. 1453-1458, 2007. (Pubitemid 351277358)
    • (2007) Proceedings of the IEEE Conference on Decision and Control , pp. 1453-1458
    • Jonckheere, E.A.1    Lou, M.2    Hespanha, J.3    Barooah, P.4
  • 118
    • 79955739996 scopus 로고    scopus 로고
    • A derandomized sparse Johnson-Lindenstrauss transform
    • Preprint: arXiv: 1006.3585
    • D. M. Kane and J. Nelson, "A derandomized sparse Johnson-Lindenstrauss transform," Technical Report. Preprint: arXiv:1006.3585, 2010.
    • (2010) Technical Report
    • Kane, D.M.1    Nelson, J.2
  • 119
    • 79955739996 scopus 로고    scopus 로고
    • Sparser Johnson-Lindenstrauss transforms
    • Preprint: arXiv: 1012.1577
    • D. M. Kane and J. Nelson, "Sparser Johnson-Lindenstrauss transforms," Technical Report. Preprint: arXiv:1012.1577, 2010.
    • (2010) Technical Report
    • Kane, D.M.1    Nelson, J.2
  • 121
    • 85008044987 scopus 로고    scopus 로고
    • Matrix factorization techniques for recommender systems
    • Y. Koren, R. Bell, and C. Volinsky, "Matrix factorization techniques for recommender systems," IEEE Computer, vol. 42, no. 8, pp. 30-37, 2009.
    • (2009) IEEE Computer , vol.42 , Issue.8 , pp. 30-37
    • Koren, Y.1    Bell, R.2    Volinsky, C.3
  • 122
    • 52349112409 scopus 로고    scopus 로고
    • Spectra of sparse random matrices
    • R. Kühn, "Spectra of sparse random matrices," J. of Physics A: Math. and Theor, vol. 41, p. 295002, 2008.
    • (2008) J. of Physics A: Math. and Theor , vol.41 , pp. 295002
    • Kühn, R.1
  • 125
    • 0038217829 scopus 로고    scopus 로고
    • Vector algebra in the analysis of genome-wide expression data
    • F. G. Kuruvilla, P. J. Park, and S. L. Schreiber, "Vector algebra in the analysis of genome-wide expression data," Genome Biology, vol. 3, no. 3, pp. research0011.1-0011.11, 2002.
    • (2002) Genome Biology , vol.3 , Issue.3 , pp. 00111-001111
    • Kuruvilla, F.G.1    Park, P.J.2    Schreiber, S.L.3
  • 129
    • 79952901900 scopus 로고    scopus 로고
    • Fast construction of hierarchical matrix representation from matrix-vector multiplication
    • L. Lin, J. Lu, and L. Ying, "Fast construction of hierarchical matrix representation from matrix-vector multiplication," Journal of Computational Physics, vol. 230, pp. 4071-4087, 2011.
    • (2011) Journal of Computational Physics , vol.230 , pp. 4071-4087
    • Lin, L.1    Lu, J.2    Ying, L.3
  • 131
    • 6344233909 scopus 로고    scopus 로고
    • Finding haplotype tagging SNPs by use of principal components analysis
    • DOI 10.1086/425587
    • Z. Lin and R. B. Altman, "Finding haplotype tagging SNPs by use of principal components analysis," American Journal of Human Genetics, vol. 75, pp. 850-861, 2004. (Pubitemid 39390492)
    • (2004) American Journal of Human Genetics , vol.75 , Issue.5 , pp. 850-861
    • Lin, Z.1    Altman, R.B.2
  • 132
    • 84856484853 scopus 로고    scopus 로고
    • Divide-and-conquer matrix factorization
    • Preprint: arXiv: 1107.0789
    • L. Mackey, A. Talwalkar, and M. I. Jordan, "Divide-and-conquer matrix factorization," Technical report. Preprint: arXiv:1107.0789, 2011.
    • (2011) Technical Report
    • MacKey, L.1    Talwalkar, A.2    Jordan, M.I.3
  • 134
    • 84856433654 scopus 로고    scopus 로고
    • Row sampling for matrix algorithms via a noncommutative Bernstein bound
    • Preprint: arXiv: 1008.0587
    • M. Magdon-Ismail, "Row sampling for matrix algorithms via a noncommutative Bernstein bound," Technical report. Preprint: arXiv:1008.0587, 2010.
    • (2010) Technical Report
    • Magdon-Ismail, M.1
  • 136
    • 84856456644 scopus 로고    scopus 로고
    • Computation in large-scale scientific and Internet data applications is a focus of MMDS 2010
    • Preprint: arXiv: 1012.4231
    • M. W. Mahoney, "Computation in large-scale scientific and Internet data applications is a focus of MMDS 2010," Technical report. Preprint: arXiv:1012.4231, 2010.
    • (2010) Technical Report
    • Mahoney, M.W.1
  • 137
    • 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, vol. 106, pp. 697-702, 2009.
    • (2009) Proc. Natl. Acad. Sci. USA , vol.106 , pp. 697-702
    • Mahoney, M.W.1    Drineas, P.2
  • 138
    • 84856464036 scopus 로고    scopus 로고
    • Algorithmic and statistical challenges in modern large-scale data analysis are the focus of MMDS 2008
    • Preprint: arXiv: 0812.3702
    • M. W. Mahoney, L.-H. Lim, and G. E. Carlsson, "Algorithmic and statistical challenges in modern large-scale data analysis are the focus of MMDS 2008," Technical report. Preprint: arXiv:0812.3702, 2008.
    • (2008) Technical Report
    • Mahoney, M.W.1    Lim, L.-H.2    Carlsson, G.E.3
  • 140
    • 84856501277 scopus 로고    scopus 로고
    • Rapid factorization of structured matrices via randomized sampling
    • Preprint: arXiv: 0806.2339
    • P.-G. Martinsson, "Rapid factorization of structured matrices via randomized sampling," Technical Report. Preprint: arXiv:0806.2339, 2008.
    • (2008) Technical Report
    • Martinsson, P.-G.1
  • 142
    • 52349087217 scopus 로고    scopus 로고
    • On variants of the Johnson-Lindenstrauss lemma
    • J. Matousek, "On variants of the Johnson-Lindenstrauss lemma," Random Structures and Algorithms, vol. 33, no. 2, pp. 142-156, 2008.
    • (2008) Random Structures and Algorithms , vol.33 , Issue.2 , pp. 142-156
    • Matousek, J.1
  • 143
    • 76949095068 scopus 로고    scopus 로고
    • Principal component analysis of SDSS stellar spectra
    • R. C. McGurk, A. E. Kimball, and Z. Ivezić, "Principal component analysis of SDSS stellar spectra," The Astronomical Journal, vol. 139, pp. 1261-1268, 2010.
    • (2010) The Astronomical Journal , vol.139 , pp. 1261-1268
    • McGurk, R.C.1    Kimball, A.E.2    Ivezić, Z.3
  • 144
    • 84856464035 scopus 로고    scopus 로고
    • LSRN: A parallel iterative solver for strongly over- or under-determined systems
    • Preprint: arXiv:arXiv: 1109.5981
    • X. Meng, M. A. Saunders, and M. W. Mahoney, "LSRN: A parallel iterative solver for strongly over- or under-determined systems," Technical report. Preprint: arXiv:arXiv:1109.5981, 2011.
    • (2011) Technical Report
    • Meng, X.1    Saunders, M.A.2    Mahoney, M.W.3
  • 145
    • 0038728035 scopus 로고    scopus 로고
    • Selection of genetic markers for association analyses, using linkage disequilibrium and haplotypes
    • DOI 10.1086/376561
    • Z. Meng, D. V. Zaykin, C. F. Xu, M. Wagner, and M. G. Ehm, "Selection of genetic markers for association analyses, using linkage disequilibrium and haplotypes," American Journal of Human Genetics, vol. 73, no. 1, pp. 115-130, 2003. (Pubitemid 36793785)
    • (2003) American Journal of Human Genetics , vol.73 , Issue.1 , pp. 115-130
    • Meng, Z.1    Zaykin, D.V.2    Xu, C.-F.3    Wagner, M.4    Ehm, M.G.5
  • 146
    • 0018080152 scopus 로고
    • Synthetic maps of human gene frequencies in Europeans
    • P. Menozzi, A. Piazza, and L. Cavalli-Sforza, "Synthetic maps of human gene frequencies in Europeans," Science, vol. 201, no. 4358, pp. 786-792, 1978.
    • (1978) Science , vol.201 , Issue.4358 , pp. 786-792
    • Menozzi, P.1    Piazza, A.2    Cavalli-Sforza, L.3
  • 148
    • 36149035179 scopus 로고
    • Universality of level correlation function of sparse random matrices
    • A. D. Mirlin and Y. V. Fyodorov, "Universality of level correlation function of sparse random matrices," J. Phys. A: Math. Gen, vol. 24, pp. 2273-2286, 1991.
    • (1991) J. Phys. A: Math. Gen , vol.24 , pp. 2273-2286
    • Mirlin, A.D.1    Fyodorov, Y.V.2
  • 149
    • 70349143977 scopus 로고    scopus 로고
    • Spectral and dynamical properties in classes of sparse networks with mesoscopic inhomogeneities
    • M. Mitrović and B. Tadić, "Spectral and dynamical properties in classes of sparse networks with mesoscopic inhomogeneities," Physical Review E, vol. 80, p. 026123, 2009.
    • (2009) Physical Review e , vol.80 , pp. 026123
    • Mitrović, M.1    Tadić, B.2
  • 151
    • 3142781787 scopus 로고    scopus 로고
    • Boston: Foundations and Trends in Theoretical Computer Science. Now Publishers Inc
    • S. Muthukrishnan, Data Streams: Algorithms and Applications. Boston: Foundations and Trends in Theoretical Computer Science. Now Publishers Inc, 2005.
    • (2005) Data Streams: Algorithms and Applications
    • Muthukrishnan, S.1
  • 152
    • 13944252976 scopus 로고    scopus 로고
    • A measure of betweenness centrality based on random walks
    • DOI 10.1016/j.socnet.2004.11.009, PII S0378873304000681
    • M. E. J. Newman, "A measure of betweenness centrality based on random walks," Social Networks, vol. 27, pp. 39-54, 2005. (Pubitemid 40272648)
    • (2005) Social Networks , vol.27 , Issue.1 , pp. 39-54
    • Newman, M.E.J.1
  • 155
    • 84976657333 scopus 로고
    • Algorithm 583: LSQR: Sparse linear equations and least-squares problems
    • C. C. Paige and M. A. Saunders, "Algorithm 583: LSQR: Sparse linear equations and least-squares problems," ACM Transactions on Mathematical Software, vol. 8, no. 2, pp. 195-209, 1982.
    • (1982) ACM Transactions on Mathematical Software , vol.8 , Issue.2 , pp. 195-209
    • Paige, C.C.1    Saunders, M.A.2
  • 156
    • 0034392123 scopus 로고    scopus 로고
    • On the existence and computation of rank-revealing LU factorizations
    • C.-T. Pan, "On the existence and computation of rank-revealing LU factorizations," Linear Algebra and Its Applications, vol. 316, pp. 199-222, 2000.
    • (2000) Linear Algebra and Its Applications , vol.316 , pp. 199-222
    • Pan, C.-T.1
  • 157
    • 0001972217 scopus 로고    scopus 로고
    • Bounds on singular values revealed by QR factorizations
    • C. T. Pan and P. T. P. Tang, "Bounds on singular values revealed by QR factorizations," BIT Numerical Mathematics, vol. 39, pp. 740-756, 1999.
    • (1999) BIT Numerical Mathematics , vol.39 , pp. 740-756
    • Pan, C.T.1    Tang, P.T.P.2
  • 160
    • 33947140286 scopus 로고    scopus 로고
    • A signal processing application of randomized low-rank approximations
    • 1628618, 2005 IEEE/SP 13th Workshop on Statistical Signal Processing - Book of Abstracts
    • P. Parker, P. J. Wolfe, and V. Tarok, "A signal processing application of randomized low-rank approximations," in Proceedings of the 13th IEEE Workshop on Statistical Signal Processing, pp. 345-350, 2005. (Pubitemid 46402254)
    • (2005) IEEE Workshop on Statistical Signal Processing Proceedings , vol.2005 , pp. 345-350
    • Parker, P.1    Wolfe, P.J.2    Tarokh, V.3
  • 162
    • 78649635740 scopus 로고    scopus 로고
    • Ancestry informative markers for fine-scale individual assignment to worldwide populations
    • doi:10.1136/jmg.2010.078212
    • P. Paschou, J. Lewis, A. Javed, and P. Drineas, "Ancestry informative markers for fine-scale individual assignment to worldwide populations," Journal of Medical Genetics, 2010. doi:10.1136/jmg.2010. 078212.
    • (2010) Journal of Medical Genetics
    • Paschou, P.1    Lewis, J.2    Javed, A.3    Drineas, P.4
  • 163
    • 33845995419 scopus 로고    scopus 로고
    • Intra- and interpopulation genotype reconstruction from tagging SNPs
    • DOI 10.1101/gr.5741407
    • P. Paschou, M. W. Mahoney, A. Javed, J. R. Kidd, A. J. Pakstis, S. Gu, K. K. Kidd, and P. Drineas, "Intra- and interpopulation genotype reconstruction from tagging SNPs," Genome Research, vol. 17, no. 1, pp. 96-107, 2007. (Pubitemid 46041671)
    • (2007) Genome Research , vol.17 , Issue.1 , pp. 96-107
    • Paschou, P.1    Mahoney, M.W.2    Javed, A.3    Kidd, J.R.4    Pakstis, A.J.5    Gu, S.6    Kidd, K.K.7    Drineas, P.8
  • 164
    • 34848879778 scopus 로고    scopus 로고
    • PCA-correlated SNPs for structure identification in worldwide human populations
    • DOI 10.1371/journal.pgen.0030160
    • P. Paschou, E. Ziv, E. G. Burchard, S. Choudhry, W. Rodriguez-Cintron, M. W. Mahoney, and P. Drineas, "PCA-correlated SNPs for structure identification in worldwide human populations," PLoS Genetics, vol. 3, pp. 1672- 1686, 2007. (Pubitemid 47510260)
    • (2007) PLoS Genetics , vol.3 , Issue.9 , pp. 1672-1686
    • Paschou, P.1    Ziv, E.2    Burchard, E.G.3    Choudhry, S.4    Rodriguez-Cintron, W.5    Mahoney, M.W.6    Drineas, P.7
  • 165
    • 33846006923 scopus 로고    scopus 로고
    • Population structure and eigenanalysis
    • DOI 10.1371/journal.pgen.0020190
    • N. Patterson, A. L. Price, and D. Reich, "Population structure and eigenanalysis," PLoS Genetics, vol. 2, no. 12, pp. 2074-2093, 2006. (Pubitemid 46045188)
    • (2006) PLoS Genetics , vol.2 , Issue.12 , pp. 2074-2093
    • Patterson, N.1    Price, A.L.2    Reich, D.3
  • 167
    • 0038568622 scopus 로고
    • Density of states of a sparse random matrix
    • G. J. Rodgers and A. J. Bray, "Density of states of a sparse random matrix," Physical Review B, vol. 37, no. 7, pp. 3557-3562, 1988.
    • (1988) Physical Review B , vol.37 , Issue.7 , pp. 3557-3562
    • Rodgers, G.J.1    Bray, A.J.2
  • 169
    • 51649090940 scopus 로고    scopus 로고
    • A fast randomized algorithm for overdetermined linear least-squares regression
    • V. Rokhlin and M. Tygert, "A fast randomized algorithm for overdetermined linear least-squares regression," Proc. Natl. Acad. Sci. USA, vol. 105, no. 36, pp. 13212-13217, 2008.
    • (2008) Proc. Natl. Acad. Sci. USA , vol.105 , Issue.36 , pp. 13212-13217
    • Rokhlin, V.1    Tygert, M.2
  • 170
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • DOI 10.1126/science.290.5500.2323
    • S. T. Roweis and L. K. Saul, "Nonlinear dimensionality reduction by local linear embedding," Science, vol. 290, pp. 2323-2326, 2000. (Pubitemid 32041578)
    • (2000) Science , vol.290 , Issue.5500 , pp. 2323-2326
    • Roweis, S.T.1    Saul, L.K.2
  • 171
    • 0033541884 scopus 로고    scopus 로고
    • Random vectors in the isotropic position
    • M. Rudelson, "Random vectors in the isotropic position," Journal of Functional Analysis, vol. 164, no. 1, pp. 60-72, 1999.
    • (1999) Journal of Functional Analysis , vol.164 , Issue.1 , pp. 60-72
    • Rudelson, M.1
  • 172
    • 34547728320 scopus 로고    scopus 로고
    • Sampling from large matrices: An approach through geometric functional analysis
    • M. Rudelson and R. Vershynin, "Sampling from large matrices: An approach through geometric functional analysis," Journal of the ACM, vol. 54, no. 4, p. Article 21, 2007.
    • (2007) Journal of the ACM , vol.54 , Issue.4 , pp. 21
    • Rudelson, M.1    Vershynin, R.2
  • 173
    • 77249154060 scopus 로고    scopus 로고
    • Numerical methods for electronic structure calculations of materials
    • Y. Saad, J. R. Chelikowsky, and S. M. Shontz, "Numerical methods for electronic structure calculations of materials," SIAM Review, vol. 52, no. 1, pp. 3-54, 2010.
    • (2010) SIAM Review , vol.52 , Issue.1 , pp. 3-54
    • Saad, Y.1    Chelikowsky, J.R.2    Shontz, S.M.3
  • 174
    • 35348901208 scopus 로고    scopus 로고
    • Improved approximation algorithms for large matrices via random projections
    • DOI 10.1109/FOCS.2006.37, 4031351, 47th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2006
    • T. Sarlós, "Improved approximation algorithms for large matrices via random projections," in Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pp. 143-152, 2006. (Pubitemid 351175504)
    • (2006) Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS , pp. 143-152
    • Sarlos, T.1
  • 175
    • 33750733400 scopus 로고    scopus 로고
    • Spectral methods for dimensionality reduction
    • (O. Chapelle, B. Schoelkopf, and A. Zien, eds.), MIT Press
    • L. K. Saul, K. Q. Weinberger, J. H. Ham, F. Sha, and D. D. Lee, "Spectral methods for dimensionality reduction," in Semisupervised Learning, (O. Chapelle, B. Schoelkopf, and A. Zien, eds.), pp. 293-308, MIT Press, 2006.
    • (2006) Semisupervised Learning , pp. 293-308
    • Saul, L.K.1    Weinberger, K.Q.2    Ham, J.H.3    Sha, F.4    Lee, D.D.5
  • 177
    • 61849141270 scopus 로고    scopus 로고
    • Adaptive beamforming using fast low-rank covariance matrix approximations
    • D. N. Spendley and P. J. Wolfe, "Adaptive beamforming using fast low-rank covariance matrix approximations," in Proceedings of the IEEE Radar Conference, pp. 1-5, 2008.
    • (2008) Proceedings of the IEEE Radar Conference , pp. 1-5
    • Spendley, D.N.1    Wolfe, P.J.2
  • 179
    • 0040117178 scopus 로고    scopus 로고
    • Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix
    • G. Stewart, "Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix," Numerische Mathematik, vol. 83, pp. 313-323, 1999.
    • (1999) Numerische Mathematik , vol.83 , pp. 313-323
    • Stewart, G.1
  • 184
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • DOI 10.1126/science.290.5500.2319
    • J. B. Tenenbaum, V. de Silva, and J. C. Langford, "A global geometric framework for nonlinear dimensionality reduction," Science, vol. 290, pp. 2319-2323, 2000. (Pubitemid 32041577)
    • (2000) Science , vol.290 , Issue.5500 , pp. 2319-2323
    • Tenenbaum, J.B.1    De Silva, V.2    Langford, J.C.3
  • 185
    • 79959503826 scopus 로고    scopus 로고
    • The international HapMap project
    • The International HapMap Consortium
    • The International HapMap Consortium, "The International HapMap Project," Nature, vol. 426, pp. 789-796, 2003.
    • (2003) Nature , vol.426 , pp. 789-796
  • 186
    • 79959524146 scopus 로고    scopus 로고
    • A haplotype map of the human genome
    • The International HapMap Consortium
    • The International HapMap Consortium, "A haplotype map of the human genome," Nature, vol. 437, pp. 1299-1320, 2005.
    • (2005) Nature , vol.437 , pp. 1299-1320
  • 187
    • 84969213492 scopus 로고    scopus 로고
    • Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls
    • The Wellcome Trust Case Control Consortium
    • The Wellcome Trust Case Control Consortium, "Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls," Nature, vol. 447, pp. 661-678, 2007.
    • (2007) Nature , vol.447 , pp. 661-678
  • 189
    • 0001639411 scopus 로고
    • Efficient computing of regression diagnostics
    • P. F. Velleman and R. E. Welsch, "Efficient computing of regression diagnostics," The American Statistician, vol. 35, no. 4, pp. 234-242, 1981.
    • (1981) The American Statistician , vol.35 , Issue.4 , pp. 234-242
    • Velleman, P.F.1    Welsch, R.E.2
  • 191
    • 2542430932 scopus 로고    scopus 로고
    • Singular value decomposition and principal component analysis
    • (D. P. Berrar, W. Dubitzky, and M. Granzow, eds.), Kluwer
    • M. E. Wall, A. Rechtsteiner, and L. M. Rocha, "Singular value decomposition and principal component analysis," in A Practical Approach to Microarray Data Analysis, (D. P. Berrar, W. Dubitzky, and M. Granzow, eds.), pp. 91-109, Kluwer, 2003.
    • (2003) A Practical Approach to Microarray Data Analysis , pp. 91-109
    • Wall, M.E.1    Rechtsteiner, A.2    Rocha, L.M.3
  • 196
    • 42449110882 scopus 로고
    • An information flow model for conflict and fission in small groups
    • W. W. Zachary, "An information flow model for conflict and fission in small groups," Journal of Anthropological Research, vol. 33, pp. 452-473, 1977.
    • (1977) Journal of Anthropological Research , vol.33 , pp. 452-473
    • Zachary, W.W.1
  • 197
    • 77957779140 scopus 로고    scopus 로고
    • Clustered Nyström method for large scale manifold learning and dimension reduction
    • K. Zhang and J. T. Kwok, "Clustered Nyström method for large scale manifold learning and dimension reduction," IEEE Transactions on Neural Networks, vol. 21, no. 10, pp. 1576-1587, 2010.
    • (2010) IEEE Transactions on Neural Networks , vol.21 , Issue.10 , pp. 1576-1587
    • Zhang, K.1    Kwok, J.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.