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Volumn 34, Issue 4, 2013, Pages 1464-1499

Faster subset selection for matrices and applications

Author keywords

Feature selection; K means clustering; Low rank approximations; Low stretch spanning trees; Sparse approximation; Subset selection; Volume sampling

Indexed keywords

K-MEANS CLUSTERING; LOW RANK APPROXIMATIONS; SPANNING TREE; SPARSE APPROXIMATIONS; SUBSET SELECTION;

EID: 84892412888     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/120867287     Document Type: Article
Times cited : (114)

References (57)
  • 2
    • 0029249995 scopus 로고
    • A graph-theoretic game and its application to the k-server problem
    • N. Alon, R. M. Karp, D. Peleg, and D. West, A graph-theoretic game and its application to the k-server problem, SIAM J. Comput., 24 (1995), pp. 78-100.
    • (1995) SIAM J. Comput. , vol.24 , pp. 78-100
    • Alon, N.1    Karp, R.M.2    Peleg, D.3    West, D.4
  • 3
    • 77953821242 scopus 로고    scopus 로고
    • Blendenpik: Supercharging LAPACK's leastsquares solver
    • H. Avron, P. Maymounkov, and S. Toledo, Blendenpik: Supercharging LAPACK's leastsquares solver, SIAM J. Sci. Comput., 32 (2010), pp. 1217-1236.
    • (2010) SIAM J. Sci. Comput. , vol.32 , pp. 1217-1236
    • Avron, H.1    Maymounkov, P.2    Toledo, S.3
  • 7
    • 51249179251 scopus 로고
    • Invertibility of large submatrices with applications to the geometry of banach spaces and harmonic analysis
    • J. Bourgain and L. Tzafriri, Invertibility of large submatrices with applications to the geometry of banach spaces and harmonic analysis, Israel J. Math., 57 (1987), pp. 137-224.
    • (1987) Israel J. Math. , vol.57 , pp. 137-224
    • Bourgain, J.1    Tzafriri, L.2
  • 9
    • 84884370204 scopus 로고    scopus 로고
    • Topics in matrix sampling algorithms
    • Rensselaer Polytechnic Institute, May
    • C. Boutsidis, Topics in matrix sampling algorithms, Ph.D. thesis, Rensselaer Polytechnic Institute, May, 2011.
    • (2011) Ph.D. Thesis
    • Boutsidis, C.1
  • 11
    • 84892421360 scopus 로고    scopus 로고
    • Deterministic feature selection for k-means clustering
    • C. Boutsidis and M. Magdon-Ismail, Deterministic feature selection for k-means clustering, arxiv: 1109.5664, 2011.
    • (2011) Arxiv: 1109.5664
    • Boutsidis, C.1    Magdon-Ismail, M.2
  • 15
    • 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
  • 17
    • 84872617323 scopus 로고    scopus 로고
    • Exponential inapproximability of selecting a maximum volume sub-matrix
    • A. Çivril and M. Magdon-Ismail, Exponential inapproximability of selecting a maximum volume sub-matrix, Algorithmica, 65 (2013), pp. 159-176.
    • (2013) Algorithmica , vol.65 , pp. 159-176
    • Çivril, A.1    Magdon-Ismail, M.2
  • 18
    • 78649910530 scopus 로고    scopus 로고
    • On selecting a maximum volume sub-matrix of a matrix and related problems
    • A. Çivril and M. Magdon-Ismail, On selecting a maximum volume sub-matrix of a matrix and related problems, Theoret. Comput. Sci., 410 (2009), pp. 4801-4811.
    • (2009) Theoret. Comput. Sci. , vol.410 , pp. 4801-4811
    • Çivril, A.1    Magdon-Ismail, M.2
  • 20
    • 79951680943 scopus 로고    scopus 로고
    • A note on subset selection for matrices
    • F. R. de Hoog and R. M. M. Mattheij, A note on subset selection for matrices, Linear Algebra Appl., 434 (2011), pp. 1845-1850.
    • (2011) Linear Algebra Appl. , vol.434 , pp. 1845-1850
    • De Hoog, F.R.1    Mattheij, R.M.M.2
  • 23
    • 33751115359 scopus 로고    scopus 로고
    • Mahoney, Fast Monte Carlo algorithms for matrices I: Approximating matrix multiplication
    • P. Drineas, R. Kannan, and M. W. Mahoney, Fast Monte Carlo algorithms for matrices I: Approximating matrix multiplication, SIAM J. Comput., 36 (2006), pp. 132-157.
    • (2006) SIAM J. Comput. , vol.36 , pp. 132-157
    • Drineas, P.1    Kannan, R.2
  • 26
    • 0001371240 scopus 로고
    • Relative perturbation techniques for singular value problems
    • S. C. Eisenstat and I. C. F. Ipsen, Relative perturbation techniques for singular value problems, SIAM J. Numer. Anal., 32 (1995), pp. 1972-1988.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1972-1988
    • Eisenstat, S.C.1    Ipsen, I.C.F.2
  • 28
    • 33745232326 scopus 로고    scopus 로고
    • Algorithm 853: An efficient algorithm for solving rank-deficient least squares problems
    • L. Foster and R. Kommu, Algorithm 853: An efficient algorithm for solving rank-deficient least squares problems, ACM Trans. Math. Software, 32 (2006), pp. 157-165.
    • (2006) ACM Trans. Math. Software , vol.32 , pp. 157-165
    • Foster, L.1    Kommu, R.2
  • 29
    • 84892391547 scopus 로고    scopus 로고
    • The spectral norm error of the naive Nystrom extension
    • A. Gittens, The spectral norm error of the naive Nystrom extension, arXiv:1110.5305, 2011.
    • (2011) Arxiv: 1110.5305
    • Gittens, A.1
  • 30
    • 0004236492 scopus 로고    scopus 로고
    • Johns Hopkins University Press, 3rd ed., Baltimore
    • G. Golub and C. V. Loan, Matrix Computations, Johns Hopkins University Press, 3rd ed., Baltimore, 1996.
    • (1996) Matrix Computations
    • Golub, G.1    Loan, C.V.2
  • 32
    • 21844524545 scopus 로고
    • Downdating the singular value decomposition
    • M. Gu and S. C. Eisenstat, Downdating the singular value decomposition, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 793-810.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 793-810
    • Gu, M.1    Eisenstat, S.C.2
  • 33
    • 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
  • 34
    • 3042538274 scopus 로고    scopus 로고
    • Strong rank revealing Cholesky factorization
    • M. Gu and L. Miranian, Strong rank revealing Cholesky factorization, Electron. Trans. Numer. Anal., 17 (2004), pp. 76-92.
    • (2004) Electron. Trans. Numer. Anal. , vol.17 , pp. 76-92
    • Gu, M.1    Miranian, L.2
  • 36
    • 0023570429 scopus 로고
    • The truncated SVD as a method for regularization
    • P. C. Hansen, The truncated SVD as a method for regularization, BIT, 27 (1987), pp. 534-553.
    • (1987) BIT , vol.27 , pp. 534-553
    • Hansen, P.C.1
  • 37
    • 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, Math. Comput., 58 (1992), pp. 213-232.
    • (1992) Math. Comput. , vol.58 , pp. 213-232
    • Hong, Y.P.1    Pan, C.T.2
  • 38
  • 39
    • 79960422161 scopus 로고    scopus 로고
    • Rank-deficient nonlinear least squares problems and subset selection
    • I. C. F. Ipsen, C. T. Kelley, and S. R. Pope, Rank-deficient nonlinear least squares problems and subset selection, SIAM J. Numer. Anal., 49 (2011), pp. 1244-1266.
    • (2011) SIAM J. Numer. Anal. , vol.49 , pp. 1244-1266
    • Ipsen, I.C.F.1    Kelley, C.T.2    Pope, S.R.3
  • 40
    • 60549088916 scopus 로고    scopus 로고
    • Sensor selection via convex optimization
    • S. Joshi and S. Boyd, Sensor selection via convex optimization, IEEE Trans. Signal Process., 57 (2009), pp. 451-462.
    • (2009) IEEE Trans. Signal Process. , vol.57 , pp. 451-462
    • Joshi, S.1    Boyd, S.2
  • 41
    • 33745662129 scopus 로고    scopus 로고
    • Parameterized complexity and improved inapproximability for computing the largest j-simplex in a v-polytope
    • I. Koutis, Parameterized complexity and improved inapproximability for computing the largest j-simplex in a v-polytope, Inform. Process. Lett., 100 (2006), pp. 8-13.
    • (2006) Inform. Process. Lett. , vol.100 , pp. 8-13
    • Koutis, I.1
  • 44
    • 0036823865 scopus 로고    scopus 로고
    • NP-hardness of largest contained and smallest containing simplices for v-and h-polytopes
    • A. Packer, NP-hardness of largest contained and smallest containing simplices for v-and h-polytopes, Discrete Comput. Geom., 28 (2002), pp. 349-377.
    • (2002) Discrete Comput. Geom. , vol.28 , pp. 349-377
    • Packer, A.1
  • 45
    • 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 Appl., 316 (2000), pp. 199-222.
    • (2000) Linear Algebra Appl. , vol.316 , pp. 199-222
    • Pan, C.-T.1
  • 47
    • 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, J. ACM, 54 (2007) 21.
    • (2007) J. ACM , vol.54 , pp. 21
    • Rudelson, M.1    Vershynin, R.2
  • 50
    • 84865555238 scopus 로고    scopus 로고
    • An elementary proof of the restricted invertibility theorem
    • D. A. Spielman and N. Srivastava, An elementary proof of the restricted invertibility theorem, Israel J. Math., 190 (2012), pp. 1-9.
    • (2012) Israel J. Math. , vol.190 , pp. 1-9
    • Spielman, D.A.1    Srivastava, N.2
  • 52
    • 84877917566 scopus 로고    scopus 로고
    • A note on preconditioning by low-stretch spanning trees
    • D. A. Spielman and J. Woo, A note on preconditioning by low-stretch spanning trees, arXiv:0903.2816, 2009.
    • (2009) Arxiv: 0903.2816
    • Spielman, D.A.1    Woo, J.2
  • 53
    • 80052645998 scopus 로고    scopus 로고
    • Improved analysis of the subsampled randomized Hadamard transform
    • J. Tropp, Improved analysis of the subsampled randomized Hadamard transform, Adv. Adapt. Data Anal., 3 (2011), pp. 115-126.
    • (2011) Adv. Adapt. Data Anal. , vol.3 , pp. 115-126
    • Tropp, J.1
  • 55
    • 84862017782 scopus 로고    scopus 로고
    • A note on sums of independent random matrices after ahlswede-winter
    • available online at
    • R. Vershynin, A Note on Sums of Independent Random Matrices after Ahlswede-Winter, Lecture Notes, 2010, available online at http://www-personal. umich.edu/romanv/teaching/reading-group/ahlswede-winter.pdf.
    • (2010) Lecture Notes
    • Vershynin, R.1
  • 57
    • 84892381606 scopus 로고    scopus 로고
    • A matrix hyperbolic cosine algorithm and applications
    • A. Zouzias, A matrix hyperbolic cosine algorithm and applications, arXiv:1103.2793, 2011.
    • (2011) Arxiv: 1103.2793
    • Zouzias, A.1


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