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Volumn 7, Issue 2, 2012, Pages 365-384

An alternating direction algorithm for matrix completion with nonnegative factors

Author keywords

alternating direction method; hyperspectral unmixing; matrix completion; nonnegative matrix factorization

Indexed keywords


EID: 84862791611     PISSN: 16733452     EISSN: 16733576     Source Type: Journal    
DOI: 10.1007/s11464-012-0194-5     Document Type: Article
Times cited : (316)

References (34)
  • 3
    • 33746874045 scopus 로고    scopus 로고
    • Semidefinite programming based algorithms for sensor network localization
    • Biswas P, Lian T C, Wang T C, Ye Y. Semidefinite programming based algorithms for sensor network localization. ACM Trans Sensor Networks, 2006, 2(2): 188-220.
    • (2006) ACM Trans Sensor Networks , vol.2 , Issue.2 , pp. 188-220
    • Biswas, P.1    Lian, T.C.2    Wang, T.C.3    Ye, Y.4
  • 4
    • 77951291046 scopus 로고    scopus 로고
    • A singular value thresholding algorithm for matrix completion export
    • Cai J F, Candes E J, Shen Z. A singular value thresholding algorithm for matrix completion export. SIAM J Optim, 2010, 20: 1956-1982.
    • (2010) SIAM J Optim , vol.20 , pp. 1956-1982
    • Cai, J.F.1    Candes, E.J.2    Shen, Z.3
  • 5
    • 79960675858 scopus 로고    scopus 로고
    • Robust principal component analysis?
    • Cand'es E J, Li X, Ma Y, Wright J. Robust principal component analysis? J ACM, 2011, 58(3): 11.
    • (2011) J ACM , vol.58 , Issue.3 , pp. 11
    • Cand'es, E.J.1    Li, X.2    Ma, Y.3    Wright, J.4
  • 6
    • 71049116435 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • Cand'es E J, Recht B. Exact matrix completion via convex optimization. Found Comput Math, 2009, 9(6): 717-772.
    • (2009) Found Comput Math , vol.9 , Issue.6 , pp. 717-772
    • Cand'es, E.J.1    Recht, B.2
  • 7
    • 77951528523 scopus 로고    scopus 로고
    • The power of convex relaxation: Near-optimal matrix completion
    • Cand'es E J, Tao T. The power of convex relaxation: Near-optimal matrix completion. IEEE Trans Inform Theory, 2010, 56(5): 2053-2080.
    • (2010) IEEE Trans Inform Theory , vol.56 , Issue.5 , pp. 2053-2080
    • Cand'es, E.J.1    Tao, T.2
  • 11
    • 0002211517 scopus 로고
    • A dual algorithm for the solution of nonlinear variational problems via finite element approximation
    • Gabay D, Mercier B. A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput Math Appl, 1976, 2(1): 17-40.
    • (1976) Comput Math Appl , vol.2 , Issue.1 , pp. 17-40
    • Gabay, D.1    Mercier, B.2
  • 12
    • 0016536442 scopus 로고
    • Sur lapproximation par elements finis dordre un, et la resolution par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires
    • Glowinski R, Marrocco A. Sur lapproximation par elements finis dordre un, et la resolution par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires. Rev Francaise dAut Inf Rech Oper, 1975, 41-76.
    • (1975) Rev Francaise dAut Inf Rech Oper , pp. 41-76
    • Glowinski, R.1    Marrocco, A.2
  • 13
    • 84976668719 scopus 로고
    • Using collaborative filtering to weave an information tapestry
    • Goldberg D, Nichols D, Oki B M, Terry D. Using collaborative filtering to weave an information tapestry. Commun ACM, 1992, 35(12): 61-70.
    • (1992) Commun ACM , vol.35 , Issue.12 , pp. 61-70
    • Goldberg, D.1    Nichols, D.2    Oki, B.M.3    Terry, D.4
  • 14
    • 77949594951 scopus 로고    scopus 로고
    • In: Proceedings of 47th Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois
    • Goldfarb D, Ma S, Wen Z. Solving low-rank matrix completion problems efficiently. In: Proceedings of 47th Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois. 2009.
    • (2009) Solving low-rank matrix completion problems efficiently
    • Goldfarb, D.1    Ma, S.2    Wen, Z.3
  • 15
    • 0033904057 scopus 로고    scopus 로고
    • On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
    • Grippo L, Sciandrone M. On the convergence of the block nonlinear Gauss-Seidel method under convex constraints. Oper Res Lett, 2000, 26(3): 127-136.
    • (2000) Oper Res Lett , vol.26 , Issue.3 , pp. 127-136
    • Grippo, L.1    Sciandrone, M.2
  • 16
    • 69649095451 scopus 로고    scopus 로고
    • 1-minimization: methodology and convergence
    • 1-minimization: methodology and convergence. SIAM J Optim, 2008, 19(3): 1107-1130.
    • (2008) SIAM J Optim , vol.19 , Issue.3 , pp. 1107-1130
    • Hale, E.T.1    Yin, W.2    Zhang, Y.3
  • 17
    • 0014604308 scopus 로고
    • Multiplier and gradient methods
    • Hestenes M R. Multiplier and gradient methods. J Optim Theory Appl, 1969, 4(5): 303-320.
    • (1969) J Optim Theory Appl , vol.4 , Issue.5 , pp. 303-320
    • Hestenes, M.R.1
  • 18
    • 0033592606 scopus 로고    scopus 로고
    • Learning the parts of objects by non-negative matrix factorization
    • Lee D D, Seung H S. Learning the parts of objects by non-negative matrix factorization. Nature, 1999, 401(6755): 788-791.
    • (1999) Nature , vol.401 , Issue.6755 , pp. 788-791
    • Lee, D.D.1    Seung, H.S.2
  • 19
    • 84898964201 scopus 로고    scopus 로고
    • Algorithms for non-negative matrix factorization
    • Lee D D, Seung H S. Algorithms for non-negative matrix factorization. Adv Neural Inf Process Syst, 2001, 13: 556-562.
    • (2001) Adv Neural Inf Process Syst , vol.13 , pp. 556-562
    • Lee, D.D.1    Seung, H.S.2
  • 20
    • 72549110327 scopus 로고    scopus 로고
    • Interior-point method for nuclear norm approximation with application to system identification
    • Liu Z, Vandenberghe L. Interior-point method for nuclear norm approximation with application to system identification. SIAM J Matrix Anal Appl, 2009, 31(3): 1235-1256.
    • (2009) SIAM J Matrix Anal Appl , vol.31 , Issue.3 , pp. 1235-1256
    • Liu, Z.1    Vandenberghe, L.2
  • 21
    • 79957957723 scopus 로고    scopus 로고
    • Fixed point and Bregman iterative methods for matrix rank minimization
    • Ma S, Goldfarb D, Chen L. Fixed point and Bregman iterative methods for matrix rank minimization. Math Program, Ser A, 2011, 128(1-2): 321-353.
    • (2011) Math Program, Ser A , vol.128 , Issue.1-2 , pp. 321-353
    • Ma, S.1    Goldfarb, D.2    Chen, L.3
  • 22
    • 0030954231 scopus 로고    scopus 로고
    • Least squares formulation of robust non-negative factor analysis
    • Paatero P. Least squares formulation of robust non-negative factor analysis. Chemometrics Intell Lab Syst, 1997, 37(1): 23-35.
    • (1997) Chemometrics Intell Lab Syst , vol.37 , Issue.1 , pp. 23-35
    • Paatero, P.1
  • 23
    • 0033275630 scopus 로고    scopus 로고
    • The multilinear engine: A table-driven, least squares program for solving multilinear problems, including the n-way parallel factor analysis model
    • Paatero P. The multilinear engine: A table-driven, least squares program for solving multilinear problems, including the n-way parallel factor analysis model. J Comput Graph Statist, 1999, 8(4): 854-888.
    • (1999) J Comput Graph Statist , vol.8 , Issue.4 , pp. 854-888
    • Paatero, P.1
  • 24
    • 0028561099 scopus 로고
    • Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values
    • Paatero P, Tapper U. Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics, 1994, 5(2): 111-126.
    • (1994) Environmetrics , vol.5 , Issue.2 , pp. 111-126
    • Paatero, P.1    Tapper, U.2
  • 25
    • 0002380692 scopus 로고
    • A method for nonlinear constraints in minimization problems
    • R. Fletcher (Ed.), New York: Academic Press
    • Powell M J D. A method for nonlinear constraints in minimization problems. In: Fletcher R, ed. Optimization. New York: Academic Press, 1969, 283-298.
    • (1969) Optimization , pp. 283-298
    • Powell, M.J.D.1
  • 26
    • 78549288866 scopus 로고    scopus 로고
    • Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
    • Recht B, Fazel M, Parrilo P A. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Review, 2010, 52(3): 471-501.
    • (2010) SIAM Review , vol.52 , Issue.3 , pp. 471-501
    • Recht, B.1    Fazel, M.2    Parrilo, P.A.3
  • 27
    • 34250427726 scopus 로고
    • The multiplier method of Hestenes and Powell applied to convex programming
    • Rockafellar R T. The multiplier method of Hestenes and Powell applied to convex programming. J Optim Theory Appl, 1973, 12(6): 555-562.
    • (1973) J Optim Theory Appl , vol.12 , Issue.6 , pp. 555-562
    • Rockafellar, R.T.1
  • 28
    • 85012251675 scopus 로고    scopus 로고
    • A new alternating minimization algorithm for total variation image reconstruction
    • Wang Y, Yang J, Yin W, Zhang Y. A new alternating minimization algorithm for total variation image reconstruction. SIAM J Imaging Sci, 2008, 1(3): 248-272.
    • (2008) SIAM J Imaging Sci , vol.1 , Issue.3 , pp. 248-272
    • Wang, Y.1    Yang, J.2    Yin, W.3    Zhang, Y.4
  • 29
    • 79952297247 scopus 로고    scopus 로고
    • Alternating direction augmented Lagrangian methods for semidefinite programming
    • Wen Z, Goldfarb D, Yin W. Alternating direction augmented Lagrangian methods for semidefinite programming. Math Program Comput, 2010, 2(3-4): 203-230.
    • (2010) Math Program Comput , vol.2 , Issue.3-4 , pp. 203-230
    • Wen, Z.1    Goldfarb, D.2    Yin, W.3
  • 30
    • 79951629197 scopus 로고    scopus 로고
    • Solving a low-rank factorization model for matrix completion by a non-linear successive over-relaxation algorithm
    • Wen Z, Yin W, Zhang Y. Solving a low-rank factorization model for matrix completion by a non-linear successive over-relaxation algorithm. Rice Univ CAAM Technical Report TR 10-07, 2010.
    • (2010) Rice Univ CAAM Technical Report TR 10-07
    • Wen, Z.1    Yin, W.2    Zhang, Y.3
  • 31
    • 84877286728 scopus 로고    scopus 로고
    • Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization
    • (to appear)
    • Yang J, Yuan X. Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization. Math Comp (to appear).
    • Math Comp
    • Yang, J.1    Yuan, X.2
  • 32
    • 76149100480 scopus 로고    scopus 로고
    • An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise
    • Yang J, Zhang Y, Yin W. An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise. SIAM J Sci Comput, 2008, 31: 2842-2865.
    • (2008) SIAM J Sci Comput , vol.31 , pp. 2842-2865
    • Yang, J.1    Zhang, Y.2    Yin, W.3
  • 34
    • 84862797996 scopus 로고    scopus 로고
    • An alternating direction algorithm for nonnegative matrix factorization
    • Zhang Y. An alternating direction algorithm for nonnegative matrix factorization. Rice Technical Report TR 10-03, 2010.
    • (2010) Rice Technical Report TR 10-03
    • Zhang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.