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Volumn 236, Issue 7, 2012, Pages 1708-1723

A multilevel approach for nonnegative matrix factorization

Author keywords

Image processing; Multigrid multilevel methods; Nonnegative matrix factorization

Indexed keywords

ALTERNATING LEAST SQUARES; COMPUTATIONAL BIOLOGY; DIMENSIONAL SPACES; MULTI-GRID; MULTILEVEL APPROACH; MULTILEVEL METHOD; MULTIPLICATIVE UPDATES; NON-NEGATIVE MATRIX; NON-NEGATIVITY; NONNEGATIVE LEAST SQUARES; NONNEGATIVE MATRIX FACTORIZATION; STANDARD IMAGES; TEXT MINING;

EID: 83655167175     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2011.10.002     Document Type: Article
Times cited : (22)

References (38)
  • 1
    • 0028561099 scopus 로고
    • Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values
    • P. Paatero, and U. Tapper Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values Environmetrics 5 1994 111 126
    • (1994) Environmetrics , vol.5 , pp. 111-126
    • Paatero, P.1    Tapper, U.2
  • 2
    • 0033592606 scopus 로고    scopus 로고
    • Learning the parts of objects by nonnegative matrix factorization
    • D. Lee, and H. Seung Learning the parts of objects by nonnegative matrix factorization Nature 401 1999 788 791
    • (1999) Nature , vol.401 , pp. 788-791
    • Lee, D.1    Seung, H.2
  • 3
    • 73249153369 scopus 로고    scopus 로고
    • On the complexity of nonnegative matrix factorization
    • S. Vavasis On the complexity of nonnegative matrix factorization SIAM Journal on Optimization 20 2009 1364 1377
    • (2009) SIAM Journal on Optimization , vol.20 , pp. 1364-1377
    • Vavasis, S.1
  • 5
    • 67349093319 scopus 로고    scopus 로고
    • Non-negative matrix factorization based on alternating non-negativity constrained least squares and active set method
    • H. Kim, and H. Park Non-negative matrix factorization based on alternating non-negativity constrained least squares and active set method SIAM Journal on Matrix Analysis and Applications 30 2 2008 713 730
    • (2008) SIAM Journal on Matrix Analysis and Applications , vol.30 , Issue.2 , pp. 713-730
    • Kim, H.1    Park, H.2
  • 7
    • 67049160153 scopus 로고    scopus 로고
    • Toward faster nonnegative matrix factorization: A new algorithm and comparisons
    • J. Kim, H. Park, Toward faster nonnegative matrix factorization: a new algorithm and comparisons, in: Proc. of IEEE Int. Conf. on Data Mining, 2008, pp. 353362.
    • (2008) Proc. of IEEE Int. Conf. on Data Mining , pp. 353-362
    • Kim, J.1    Park, H.2
  • 8
    • 84863012243 scopus 로고    scopus 로고
    • Fast nonnegative matrix factorization: An active-set-like method and comparisons
    • (in press)
    • J. Kim, H. Park, Fast nonnegative matrix factorization: an active-set-like method and comparisons, SIAM Journal on Scientific Computing (2011) (in press).
    • (2011) SIAM Journal on Scientific Computing
    • Kim, J.1    Park, H.2
  • 9
    • 24944500827 scopus 로고    scopus 로고
    • Fast algorithm for the solution of large-scale non-negativity-constrained least squares problems
    • DOI 10.1002/cem.889
    • M. Van Benthem, and M. Keenan Fast algorithm for the solution of large-scale non-negativity constrained least squares problems Journal of Chemometrics 18 2004 441 450 (Pubitemid 41327531)
    • (2004) Journal of Chemometrics , vol.18 , Issue.10 , pp. 441-450
    • Van Benthem, M.H.1    Keenan, M.R.2
  • 10
    • 84969715286 scopus 로고    scopus 로고
    • Nonnegativity constraints in numerical analysis
    • A. Bultheel, R. Cools, World Scientific Press
    • D. Chen, and R. Plemmons Nonnegativity constraints in numerical analysis A. Bultheel, R. Cools, Symposium on the Birth of Numerical Analysis 2009 World Scientific Press
    • (2009) Symposium on the Birth of Numerical Analysis
    • Chen, D.1    Plemmons, R.2
  • 12
    • 0022736170 scopus 로고
    • An iterative image space reconstruction algorithm suitable for volume ect
    • M.E. Daube-Witherspoon, and G. Muehllehner An iterative image space reconstruction algorithm suitable for volume ect. IEEE Transactions on Medical Imaging 5 1986 61 66 (Pubitemid 16613321)
    • (1986) IEEE Transactions on Medical Imaging , vol.5 , Issue.2 , pp. 61-66
    • Daube-Witherspoon, M.E.1    Muehllehner, G.2
  • 13
    • 36348966695 scopus 로고    scopus 로고
    • On the convergence of multiplicative update algorithms for nonnegative matrix factorization
    • C.-J. Lin On the convergence of multiplicative update algorithms for nonnegative matrix factorization IEEE Transactions on Neural Networks 2007
    • (2007) IEEE Transactions on Neural Networks
    • Lin, C.-J.1
  • 14
    • 74449093327 scopus 로고    scopus 로고
    • Nonnegative factorization and the maximum edge biclique problem
    • N. Gillis, F. Glineur, Nonnegative factorization and the maximum edge biclique problem, CORE Discussion Paper 2008/64, 2008.
    • (2008) CORE Discussion Paper , vol.64 , pp. 2008
    • Gillis, N.1    Glineur, F.2
  • 15
    • 77956285552 scopus 로고    scopus 로고
    • On the rate of convergence of the image space reconstruction algorithm
    • J. Han, L. Han, M. Neumann, and U. Prasad On the rate of convergence of the image space reconstruction algorithm Operators and Matrices 3 1 2009 41 58
    • (2009) Operators and Matrices , vol.3 , Issue.1 , pp. 41-58
    • Han, J.1    Han, L.2    Neumann, M.3    Prasad, U.4
  • 16
    • 37749030729 scopus 로고    scopus 로고
    • Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization
    • Springer
    • A. Cichocki, R. Zdunek, and S. Amari Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization Lecture Notes in Computer Science vol. 4666 2007 Springer 169 176
    • (2007) Lecture Notes in Computer Science , vol.4666 , pp. 169-176
    • Cichocki, A.1    Zdunek, R.2    Amari, S.3
  • 17
    • 74449093261 scopus 로고    scopus 로고
    • Fast local algorithms for large scale nonnegative matrix and tensor factorizations
    • A. Cichocki, and A.-H. Phan Fast local algorithms for large scale nonnegative matrix and tensor factorizations IEICE Transactions on Fundamentals of Electronics E92-A 3 2009 708 721
    • (2009) IEICE Transactions on Fundamentals of Electronics , vol.92 , Issue.3 , pp. 708-721
    • Cichocki, A.1    Phan, A.-H.2
  • 20
    • 80455168744 scopus 로고    scopus 로고
    • FastNMF: Highly efficient monotonic fixed-point nonnegative matrix factorization algorithm with good applicability
    • 033004
    • L. Li, and Y.-J. Zhang FastNMF: highly efficient monotonic fixed-point nonnegative matrix factorization algorithm with good applicability Journal of Electronic Imaging 18 2009 033004
    • (2009) Journal of Electronic Imaging , vol.18
    • Li, L.1    Zhang, Y.-J.2
  • 22
    • 0004219794 scopus 로고
    • Pitman Research Notes in Mathematic Series Longman Scientific & Technical UK
    • J.H. Bramble Multigrid Methods Pitman Research Notes in Mathematic Series vol. 294 1995 Longman Scientific & Technical UK
    • (1995) Multigrid Methods , vol.294
    • Bramble, J.H.1
  • 23
    • 0000000860 scopus 로고
    • Guide to multigrid development
    • W. Hackbusch, U. Trottenberg, Lecture Notes in Mathematics Springer
    • A. Brandt Guide to multigrid development W. Hackbusch, U. Trottenberg, Multigrid Methods Lecture Notes in Mathematics vol. 960 1982 Springer 220 312
    • (1982) Multigrid Methods , vol.960 , pp. 220-312
    • Brandt, A.1
  • 28
    • 35548969471 scopus 로고    scopus 로고
    • Projected gradient methods for nonnegative matrix factorization
    • MIT Press
    • C.-J. Lin Projected gradient methods for nonnegative matrix factorization Neural Computation 19 2007 2756 2779 MIT Press
    • (2007) Neural Computation , vol.19 , pp. 2756-2779
    • Lin, C.-J.1
  • 30
    • 56449106635 scopus 로고    scopus 로고
    • Fast Newton-type methods for the least squares nonnegative matrix approximation problem
    • I. Dhillon, D. Kim, S. Sra, Fast Newton-type methods for the least squares nonnegative matrix approximation problem, in: Proc. of SIAM Conf. on Data Mining, 2007.
    • (2007) Proc. of SIAM Conf. on Data Mining
    • Dhillon, I.1    Kim, D.2    Sra, S.3
  • 34
    • 60549111308 scopus 로고    scopus 로고
    • Tensor methods for hyperspectral data analysis: A space object material identification study
    • Q. Zhang, H. Wang, R. Plemmons, and P. Pauca Tensor methods for hyperspectral data analysis: a space object material identification study Journal of the Optical Society of America A 25 12 2008 3001 3012
    • (2008) Journal of the Optical Society of America A , vol.25 , Issue.12 , pp. 3001-3012
    • Zhang, Q.1    Wang, H.2    Plemmons, R.3    Pauca, P.4
  • 35
    • 33646682646 scopus 로고    scopus 로고
    • Nonnegative matrix factorization for spectral data analysis
    • DOI 10.1016/j.laa.2005.06.025, PII S002437950500340X
    • P. Pauca, J. Piper, and R. Plemmons Nonnegative matrix factorization for spectral data analysis Linear Algebra and its Applications 406 1 2006 29 47 (Pubitemid 43737212)
    • (2006) Linear Algebra and Its Applications , vol.416 , Issue.1 , pp. 29-47
    • Pauca, V.P.1    Piper, J.2    Plemmons, R.J.3
  • 36
    • 81755168313 scopus 로고    scopus 로고
    • Dimensionality reduction, classification, and spectral mixture analysis using nonnegative underapproximation
    • N. Gillis, and R. Plemmons Dimensionality reduction, classification, and spectral mixture analysis using nonnegative underapproximation Optical Engineering 50 2011 027001
    • (2011) Optical Engineering , vol.50 , pp. 027001
    • Gillis, N.1    Plemmons, R.2
  • 37
    • 12344317125 scopus 로고    scopus 로고
    • Improving non-negative matrix factorizations through structured initialization
    • DOI 10.1016/j.patcog.2004.02.013, PII S0031320304000937
    • J. Curry, A. Dougherty, and S. Wild Improving non-negative matrix factorizations through structured initialization The Journal of Pattern Recognition 37 11 2004 2217 2232 (Pubitemid 40134553)
    • (2004) Pattern Recognition , vol.37 , Issue.11 , pp. 2217-2232
    • Wild, S.1    Curry, J.2    Dougherty, A.3
  • 38
    • 36749071484 scopus 로고    scopus 로고
    • SVD based initialization: A head start for nonnegative matrix factorization
    • DOI 10.1016/j.patcog.2007.09.010, PII S0031320307004359
    • C. Boutsidis, and E. Gallopoulos SVD based initialization: a head start for nonnegative matrix factorization The Journal of Pattern Recognition 41 2008 1350 1362 (Pubitemid 350212975)
    • (2008) Pattern Recognition , vol.41 , Issue.4 , pp. 1350-1362
    • Boutsidis, C.1    Gallopoulos, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.