메뉴 건너뛰기




Volumn 33, Issue 1, 2016, Pages 57-77

A Unified Algorithmic Framework for Block-Structured Optimization Involving Big Data: With applications in machine learning and signal processing

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTATIONAL EFFICIENCY; FACTORIZATION; LEARNING SYSTEMS; MATRIX ALGEBRA; MAXIMUM PRINCIPLE; SIGNAL PROCESSING;

EID: 85032750870     PISSN: 10535888     EISSN: None     Source Type: Journal    
DOI: 10.1109/MSP.2015.2481563     Document Type: Article
Times cited : (442)

References (107)
  • 1
    • 85032763936 scopus 로고    scopus 로고
    • Signal processing of social networks: Interactive sensing and learning
    • V. Krishnamurthy, O. Namvar, and M. Hamdi, "Signal processing of social networks: Interactive sensing and learning," Found. Trends Signal Process., vol. 7, nos. 1-2. pp. 1-19, 2014.
    • (2014) Found. Trends Signal Process. , vol.7 , Issue.1-2 , pp. 1-19
    • Krishnamurthy, V.1    Namvar, O.2    Hamdi, M.3
  • 2
    • 85032770798 scopus 로고    scopus 로고
    • Special issue on signal processing for big data
    • Sept.
    • Special Issue on Signal Processing for Big Data, IEEE Signal Processing Mag., vol. 31, no. 5, Sept. 2014.
    • (2014) IEEE Signal Processing Mag. , vol.31 , Issue.5
  • 4
    • 84871946825 scopus 로고    scopus 로고
    • Streaming fragment assignment for real-time analysis of sequencing experiments
    • A. Roberts and L. Pachter, "Streaming fragment assignment for real-time analysis of sequencing experiments," Nat. Methods, vol. 10, no. 1, pp. 71-73, 2013.
    • (2013) Nat. Methods , vol.10 , Issue.1 , pp. 71-73
    • Roberts, A.1    Pachter, L.2
  • 5
    • 84865692149 scopus 로고    scopus 로고
    • Efficiency of coordinate descent methods on huge-scale optimization problems
    • Y. Nesterov, "Efficiency of coordinate descent methods on huge-scale optimization problems," SIAM J. Optim., vol. 22, no. 2, pp. 341-362, 2012.
    • (2012) SIAM J. Optim. , vol.22 , Issue.2 , pp. 341-362
    • Nesterov, Y.1
  • 6
    • 85032752418 scopus 로고    scopus 로고
    • Convex optimization for big data: Scalable, randomized, and parallel algorithms for big data analytics
    • Sept.
    • V. Cevher, S. Becker, and M. Schmidt, "Convex optimization for big data: Scalable, randomized, and parallel algorithms for big data analytics," IEEE Signal Process. Mag., vol. 31, no. 5, pp. 32-43, Sept. 2014.
    • (2014) IEEE Signal Process. Mag. , vol.31 , Issue.5 , pp. 32-43
    • Cevher, V.1    Becker, S.2    Schmidt, M.3
  • 8
    • 84897116612 scopus 로고    scopus 로고
    • Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
    • P. Richtik and M. Tak?, "Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function," Math. Program., vol. 144, no. 1, pp. 1-38, 2014.
    • (2014) Math. Program. , vol.144 , Issue.1 , pp. 1-38
    • Richtik, P.1    Tak, M.2
  • 10
    • 0030105787 scopus 로고    scopus 로고
    • A regularization approach to joint blur identification and image restoration
    • Y.-L. You and M. Kaveh, "A regularization approach to joint blur identification and image restoration," IEEE Trans. Image Processing, vol. 5, no. 3, pp. 416-428, 1996.
    • (1996) IEEE Trans. Image Processing , vol.5 , Issue.3 , pp. 416-428
    • You, Y.-L.1    Kaveh, M.2
  • 11
    • 77950537175 scopus 로고    scopus 로고
    • Regularization paths for generalized linear models via coordinate descent
    • J. Friedman, T. Hastie, and R. Tibshirani, "Regularization paths for generalized linear models via coordinate descent," J. Stat. Softw., vol. 33, no. 1, pp. 1-22, 2010.
    • (2010) J. Stat. Softw. , vol.33 , Issue.1 , pp. 1-22
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 12
    • 80051739128 scopus 로고    scopus 로고
    • An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel
    • Q. Shi, M. Razaviyayn, Z.-Q. Luo, and C. He, "An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel," IEEE Trans. Signal Processing, vol. 59, no. 9, pp. 4331-4340, 2011.
    • (2011) IEEE Trans. Signal Processing , vol.59 , Issue.9 , pp. 4331-4340
    • Shi, Q.1    Razaviyayn, M.2    Luo, Z.-Q.3    He, C.4
  • 13
    • 84861636156 scopus 로고    scopus 로고
    • Maximum block improvement and polynomial optimization
    • B. Chen, S. He, Z. Li, and S. Zhang, "Maximum block improvement and polynomial optimization," SIAM J. Optim., vol. 22, no. 1, pp. 87-107, 2012.
    • (2012) SIAM J. Optim. , vol.22 , Issue.1 , pp. 87-107
    • Chen, B.1    He, S.2    Li, Z.3    Zhang, S.4
  • 15
    • 85032766524 scopus 로고    scopus 로고
    • Parallel coordinate descent methods for big data optimization
    • to be published
    • P. Richtik and M. Tak?, "Parallel coordinate descent methods for big data optimization," Math. Program., to be published.
    • Math. Program.
    • Richtik, P.1    Tak, M.2
  • 19
    • 84924692154 scopus 로고    scopus 로고
    • Parallel selective algorithms for nonconvex big data optimization
    • F. Facchinei, G. Scutari, and S. Sagratella, "Parallel selective algorithms for nonconvex big data optimization," IEEE Trans. Signal Processing, vol. 63, no. 7, pp. 1874-1889, 2015.
    • (2015) IEEE Trans. Signal Processing , vol.63 , Issue.7 , pp. 1874-1889
    • Facchinei, F.1    Scutari, G.2    Sagratella, S.3
  • 21
    • 84880570485 scopus 로고    scopus 로고
    • A unified convergence analysis of block successive minimization methods for nonsmooth optimization
    • M. Razaviyayn, M. Hong, and Z.-Q. Luo, "A unified convergence analysis of block successive minimization methods for nonsmooth optimization," SIAM J. Optim., vol. 23, no. 2, pp. 1126-1153, 2013.
    • (2013) SIAM J. Optim. , vol.23 , Issue.2 , pp. 1126-1153
    • Razaviyayn, M.1    Hong, M.2    Luo, Z.-Q.3
  • 22
    • 84897534825 scopus 로고    scopus 로고
    • Optimization with first-order surrogate functions
    • J. Mairal, "Optimization with first-order surrogate functions," in Proc. Int. Conf. Machine Learning (ICML), 2013, pp. 783-791.
    • (2013) Proc. Int. Conf. Machine Learning (ICML) , pp. 783-791
    • Mairal, J.1
  • 23
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage-thresholding algorithm for linear inverse problems
    • A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM J. Imaging Sci., vol. 2, no. 1, pp. 183-202, 2009.
    • (2009) SIAM J. Imaging Sci. , vol.2 , Issue.1 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 24
    • 39449126969 scopus 로고    scopus 로고
    • Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
    • M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Top. Signal Processing, vol. 1, no. 4, pp. 586-597, 2007.
    • (2007) IEEE J. Sel. Top. Signal Processing , vol.1 , Issue.4 , pp. 586-597
    • Figueiredo, M.A.T.1    Nowak, R.D.2    Wright, S.J.3
  • 25
    • 84863765049 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • E. Cand? and B. Recht, "Exact matrix completion via convex optimization," Commun. ACM, vol. 55, no. 6, pp. 111-119, 2012.
    • (2012) Commun ACM , vol.55 , Issue.6 , pp. 111-119
    • Cand, E.1    Recht, B.2
  • 27
    • 84895057098 scopus 로고    scopus 로고
    • Algorithms for nonnegative matrix and tensor factorizations: A unified view based on block coordinate descent framework
    • Feb.
    • J. Kim, Y. He, and H. Park, "Algorithms for nonnegative matrix and tensor factorizations: A unified view based on block coordinate descent framework," J. Glob Optim., vol. 58, no. 2, pp. 285-319, Feb. 2014.
    • (2014) J. Glob Optim. , vol.58 , Issue.2 , pp. 285-319
    • Kim, J.1    He, Y.2    Park, H.3
  • 28
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions and applications
    • T. G. Kolda and B. W. Bader, "Tensor decompositions and applications," SIAM Rev., vol. 51, no. 3, pp. 455-500, 2009.
    • (2009) SIAM Rev. , vol.51 , Issue.3 , pp. 455-500
    • Kolda, T.G.1    Bader, B.W.2
  • 29
    • 84940008519 scopus 로고    scopus 로고
    • Coordinate descent algorithms
    • S. J. Wright, "Coordinate descent algorithms," Math. Program., vol. 151, no. 1, pp. 3-34, 2015.
    • (2015) Math. Program. , vol.151 , Issue.1 , pp. 3-34
    • Wright, S.J.1
  • 30
    • 0002629270 scopus 로고
    • Maximum likelihood from incomplete data via the em algorithm
    • A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. R. Stat. Soc. Series B, vol. 39, no. 1, pp. 1-38, 1977.
    • (1977) J. R. Stat. Soc. Series B , vol.39 , Issue.1 , pp. 1-38
    • Dempster, A.P.1    Laird, N.M.2    Rubin, D.B.3
  • 31
    • 0037686659 scopus 로고    scopus 로고
    • The concave-convex procedure
    • A. L. Yuille and A. Rangarajan, "The concave-convex procedure," Neural Comput., vol. 15, pp. 915-936, 2003.
    • (2003) Neural Comput. , vol.15 , pp. 915-936
    • Yuille, A.L.1    Rangarajan, A.2
  • 33
    • 70449499094 scopus 로고    scopus 로고
    • Monotonic convergence of distributed interference pricing in wireless networks
    • C. Shi, R. A. Berry, and M. L. Honig, "Monotonic convergence of distributed interference pricing in wireless networks," in Proc. IEEE Int. Conf. Symp. Information Theory, 2009, pp. 1619-1623.
    • (2009) Proc. IEEE Int. Conf. Symp. Information Theory , pp. 1619-1623
    • Shi, C.1    Berry, R.A.2    Honig, M.L.3
  • 34
    • 84922919590 scopus 로고    scopus 로고
    • Signal processing and optimal resource allocation for the interference channel
    • New York: Academic
    • M. Hong and Z.-Q. Luo, "Signal processing and optimal resource allocation for the interference channel," in Academic Press Library in Signal Processing. New York: Academic, 2013.
    • (2013) Academic Press Library in Signal Processing
    • Hong, M.1    Luo, Z.-Q.2
  • 35
    • 85032773118 scopus 로고    scopus 로고
    • Decomposition by successive convex approximation: A unifying approach for linear transceiver design in interfering heterogeneous networks
    • to be published
    • M. Hong, Q. Li, and Y.-F. Liu, "Decomposition by successive convex approximation: A unifying approach for linear transceiver design in interfering heterogeneous networks," IEEE Trans. Wireless Commun., to be published.
    • IEEE Trans. Wireless Commun.
    • Hong, M.1    Li, Q.2    Liu, Y.-F.3
  • 36
    • 0035533631 scopus 로고    scopus 로고
    • Convergence of a block coordinate descent method for nondifferentiable minimization
    • P. Tseng, "Convergence of a block coordinate descent method for nondifferentiable minimization," J. Optim. Theory Appl., vol. 103, no. 9, pp. 475-494, 2001.
    • (2001) J. Optim. Theory Appl. , vol.103 , Issue.9 , pp. 475-494
    • Tseng, P.1
  • 37
    • 0001258795 scopus 로고
    • On search directions for minimization algorithms
    • M. J. D. Powell, "On search directions for minimization algorithms," Math. Program., vol. 4, no. 1, pp. 193-201, 1973.
    • (1973) Math. Program. , vol.4 , Issue.1 , pp. 193-201
    • Powell, M.J.D.1
  • 39
    • 84937977284 scopus 로고    scopus 로고
    • On the complexity analysis of randomized block-coordinate descent methods
    • Aug.
    • Z. Lu and L. Xiao, "On the complexity analysis of randomized block-coordinate descent methods," Math. Program., vol. 152, no. 1, pp. 615-642, Aug. 2015.
    • (2015) Math. Program. , vol.152 , Issue.1 , pp. 615-642
    • Lu, Z.1    Xiao, L.2
  • 40
    • 84892868336 scopus 로고    scopus 로고
    • On the convergence of block coordinate descent type methods
    • A. Beck and L. Tetruashvili, "On the convergence of block coordinate descent type methods," SIAM J. Optim., vol. 23, no. 4, pp. 2037-2060, 2013.
    • (2013) SIAM J. Optim. , vol.23 , Issue.4 , pp. 2037-2060
    • Beck, A.1    Tetruashvili, L.2
  • 41
    • 84925382477 scopus 로고    scopus 로고
    • On the convergence of alternating minimization with applications to iteratively reweighted least squares and decomposition schemes
    • A. Beck, "On the convergence of alternating minimization with applications to iteratively reweighted least squares and decomposition schemes," SIAM J. Optim., vol. 25, no. 1, pp. 185-209, 2015.
    • (2015) SIAM J. Optim. , vol.25 , Issue.1 , pp. 185-209
    • Beck, A.1
  • 43
    • 84877774282 scopus 로고    scopus 로고
    • On the nonasymptotic convergence of cyclic coordinate descent method
    • A. Saha and A. Tewari, "On the nonasymptotic convergence of cyclic coordinate descent method," SIAM J. Optim., vol. 23, no. 1, pp. 576-601, 2013.
    • (2013) SIAM J. Optim. , vol.23 , Issue.1 , pp. 576-601
    • Saha, A.1    Tewari, A.2
  • 45
    • 84903559962 scopus 로고    scopus 로고
    • On the linear convergence of approximate proximal splitting methods for non-smooth convex minimization
    • M. Kadkhodaei, M. Sanjabi, and Z.-Q. Luo, "On the linear convergence of approximate proximal splitting methods for non-smooth convex minimization," J. Oper. Res. Soc. China, vol. 2, no. 2, pp. 123-141, 2014.
    • (2014) J. Oper. Res. Soc. China , vol.2 , Issue.2 , pp. 123-141
    • Kadkhodaei, M.1    Sanjabi, M.2    Luo, Z.-Q.3
  • 46
    • 84885030988 scopus 로고    scopus 로고
    • A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion
    • Y. Xu and W. Yin, "A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion," SIAM J. Imaging Sci., vol. 6, no. 3, pp. 1758-1789, 2013.
    • (2013) SIAM J. Imaging Sci. , vol.6 , Issue.3 , pp. 1758-1789
    • Xu, Y.1    Yin, W.2
  • 47
    • 85032760611 scopus 로고    scopus 로고
    • An accelerated proximal coordinate gradient method and its application to regularized empirical risk minimization
    • to be published
    • Q. Lin, Z. Lu, and L. Xiao, "An accelerated proximal coordinate gradient method and its application to regularized empirical risk minimization," SIAM J. Optim., to be published.
    • SIAM J. Optim.
    • Lin, Q.1    Lu, Z.2    Xiao, L.3
  • 48
    • 84953234319 scopus 로고    scopus 로고
    • Accelerated, parallel and proximal coordinate descent
    • O. Fercoq and P. Richtik, "Accelerated, parallel and proximal coordinate descent," SIAM J. Optim., vol. 25, no. 4, pp. 1927-2023, 2015.
    • (2015) SIAM J. Optim. , vol.25 , Issue.4 , pp. 1927-2023
    • Fercoq, O.1    Richtik, P.2
  • 49
    • 1342332031 scopus 로고    scopus 로고
    • A tutorial on MM algorithms
    • D. R. Hunter and K. Lange, "A tutorial on MM algorithms," Am. Stat., vol. 58, no. 1, pp. 30-37, 2004.
    • (2004) Am. Stat. , vol.58 , Issue.1 , pp. 30-37
    • Hunter, D.R.1    Lange, K.2
  • 51
    • 0033904057 scopus 로고    scopus 로고
    • On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
    • L. Grippo and M. Sciandrone, "On the convergence of the block nonlinear Gauss-Seidel method under convex constraints," Oper. Res. Lett., vol. 26, no. 3, pp. 127-136, 2000.
    • (2000) Oper. Res. Lett. , vol.26 , Issue.3 , pp. 127-136
    • Grippo, L.1    Sciandrone, M.2
  • 56
    • 80051594038 scopus 로고    scopus 로고
    • Algorithms for nonnegative matrix factorization with the beta-divergence
    • C. F?otte and J. Idier, "Algorithms for nonnegative matrix factorization with the beta-divergence," Neural Comput., vol. 23, no. 3, pp. 1-24, 2011.
    • (2011) Neural Comput. , vol.23 , Issue.3 , pp. 1-24
    • Fotte, C.1    Idier, J.2
  • 57
    • 77949704355 scopus 로고    scopus 로고
    • Iteratively reweighted least squares minimization for sparse recovery
    • I. Daubechies, R. DeVore, M. Fornasier, and C. S. Gunturk, "Iteratively reweighted least squares minimization for sparse recovery," Commun. Pure Appl. Math., vol. 63, no. 1, pp. 1-38, 2010.
    • (2010) Commun. Pure Appl. Math. , vol.63 , Issue.1 , pp. 1-38
    • Daubechies, I.1    DeVore, R.2    Fornasier, M.3    Gunturk, C.S.4
  • 58
    • 40849106459 scopus 로고    scopus 로고
    • Dynamic spectrum management: Complexity and duality
    • Z-.Q. Luo and S. Zhang, "Dynamic spectrum management: Complexity and duality," IEEE J. Sel. Top. Signal Processing, vol. 2, no. 1, pp. 57-73, 2008.
    • (2008) IEEE J. Sel. Top. Signal Processing , vol.2 , Issue.1 , pp. 57-73
    • Luo, Z.-Q.1    Zhang, S.2
  • 60
    • 84890502670 scopus 로고    scopus 로고
    • Joint user grouping and transceiver design in a MIMO interfering broadcast channel
    • Jan.
    • M. Razaviyayn, H. Baligh, A. Callard, and Z.-Q. Luo, "Joint user grouping and transceiver design in a mimo interfering broadcast channel," IEEE Trans. Signal Processing, vol. 62, no. 1, pp. 85-94, Jan. 2014.
    • (2014) IEEE Trans. Signal Processing , vol.62 , Issue.1 , pp. 85-94
    • Razaviyayn, M.1    Baligh, H.2    Callard, A.3    Luo, Z.-Q.4
  • 61
    • 58149123337 scopus 로고    scopus 로고
    • Weighted sum-rate maximization using weighted MMSE for MIMO-BC beamforming design
    • S. S. Christensen, R. Agarwal, E. D. Carvalho, and J. M. Cioffi, "Weighted sum-rate maximization using weighted MMSE for MIMO-BC beamforming design," IEEE Trans. Wireless Commun., vol. 7, no. 12, pp. 4792-4799, 2008.
    • (2008) IEEE Trans. Wireless Commun. , vol.7 , Issue.12 , pp. 4792-4799
    • Christensen, S.S.1    Agarwal, R.2    Carvalho, E.D.3    Cioffi, J.M.4
  • 62
    • 84872894843 scopus 로고    scopus 로고
    • Joint base station clustering and beamformer design for partial coordinated transmission in heterogenous networks
    • M. Hong, R. Sun, H. Baligh, and Z.-Q. Luo, "Joint base station clustering and beamformer design for partial coordinated transmission in heterogenous networks," IEEE J. Sel. Areas Commun., vol. 31, no. 2, pp. 226-240, 2013.
    • (2013) IEEE J. Sel. Areas Commun. , vol.31 , Issue.2 , pp. 226-240
    • Hong, M.1    Sun, R.2    Baligh, H.3    Luo, Z.-Q.4
  • 64
    • 79955492074 scopus 로고    scopus 로고
    • Optimal resource allocation for MIMO Ad Hoc Cognitive Radio Networks
    • S.-J. Kim and G. B. Giannakis, "Optimal resource allocation for MIMO Ad Hoc Cognitive Radio Networks," IEEE Trans. Inform. Theory, vol. 57, no. 5, pp. 3117-3131, 2011.
    • (2011) IEEE Trans. Inform. Theory , vol.57 , Issue.5 , pp. 3117-3131
    • Kim, S.-J.1    Giannakis, G.B.2
  • 65
    • 78649755607 scopus 로고    scopus 로고
    • Linear precoding in cooperative MIMO cellular networks with limited coordination clusters
    • C. T. K. Ng and H. Huang, "Linear precoding in cooperative MIMO cellular networks with limited coordination clusters," IEEE J. Sel. Areas Commun., vol. 28, no. 9, pp. 1446-1454, 2010.
    • (2010) IEEE J. Sel. Areas Commun. , vol.28 , Issue.9 , pp. 1446-1454
    • Ng, C.T.K.1    Huang, H.2
  • 66
    • 62349130698 scopus 로고    scopus 로고
    • Ultrafast and memoryefficient alignment of short DNA sequences to the human genome
    • B. Langmead, C. Trapnell, M. Pop, and S. L. Salzberg, "Ultrafast and memoryefficient alignment of short dna sequences to the human genome," Genome Biol., vol. 10, no. 3, pp. R25, 2009.
    • (2009) Genome Biol. , vol.10 , Issue.3 , pp. R25
    • Langmead, B.1    Trapnell, C.2    Pop, M.3    Salzberg, S.L.4
  • 67
    • 67649884743 scopus 로고    scopus 로고
    • Fast and accurate short read alignment with Burrows-Wheeler transform
    • H. Li and R. Durbin, "Fast and accurate short read alignment with Burrows-Wheeler transform," Bioinformatics, vol. 25, no. 14, pp. 1754-1760, 2009.
    • (2009) Bioinformatics , vol.25 , Issue.14 , pp. 1754-1760
    • Li, H.1    Durbin, R.2
  • 69
    • 31844432834 scopus 로고    scopus 로고
    • Non-negative tensor factorization with applications to statistics and computer vision
    • A. Shashua and T. Hazan, "Non-negative tensor factorization with applications to statistics and computer vision," in Proc. 22nd Int. Conf. Machine Learning (ICML), 2005, pp. 792-799.
    • (2005) Proc. 22nd Int. Conf. Machine Learning (ICML) , pp. 792-799
    • Shashua, A.1    Hazan, T.2
  • 70
    • 0036391742 scopus 로고    scopus 로고
    • Application of the three-way decomposition for matrix compression
    • I. Ibraghimov, "Application of the three-way decomposition for matrix compression," Numer. Linear Algebra Appl., vol. 9, no. 6-7, pp. 551-565, 2002.
    • (2002) Numer. Linear Algebra Appl. , vol.9 , Issue.6-7 , pp. 551-565
    • Ibraghimov, I.1
  • 71
    • 0001424792 scopus 로고
    • Tensor rank is NP-complete
    • J. H?tad, "Tensor rank is NP-complete," J. Algorithms, vol. 11, no. 4, pp. 644-654, 1990.
    • (1990) J. Algorithms , vol.11 , Issue.4 , pp. 644-654
    • Htad, J.1
  • 72
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via an N-way generalization of 'Eckart-Young' decomposition
    • J. D. Carroll and J. J. Chang, "Analysis of individual differences in multidimensional scaling via an N-way generalization of 'Eckart-Young' decomposition," Psychometrika, vol. 35, no. 3, pp. 283-319, 1970.
    • (1970) Psychometrika , vol.35 , Issue.3 , pp. 283-319
    • Carroll, J.D.1    Chang, J.J.2
  • 73
    • 0002740437 scopus 로고
    • Foundations of the parafac procedure: Models and conditions for an explanatory" multimodal factor analysis
    • R. A. Harshman, "Foundations of the parafac procedure: Models and conditions for an "explanatory" multimodal factor analysis," UCLA Working Papers in Phonetics, 16, pp. 1-84, 1970.
    • (1970) UCLA Working Papers in Phonetics , vol.16 , pp. 1-84
    • Harshman, R.A.1
  • 75
    • 84886522651 scopus 로고    scopus 로고
    • Rank regularization and Bayesian inference for tensor completion and extrapolation
    • J. A. Bazerque, G. Mateos, and G. B. Giannakis, "Rank regularization and Bayesian inference for tensor completion and extrapolation," IEEE Trans. Signal Processing, vol. 61, no. 21-24, pp. 5689-5703, 2013.
    • (2013) IEEE Trans. Signal Processing , vol.61 , Issue.21-24 , pp. 5689-5703
    • Bazerque, J.A.1    Mateos, G.2    Giannakis, G.B.3
  • 76
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • D. L. Donoho, "Compressed sensing," IEEE Trans. Inform. Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.L.1
  • 77
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • E. J. Cand?, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inform. Theory, vol. 52, no. 2, pp. 489-509, 2006.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.2 , pp. 489-509
    • Cand, E.J.1    Romberg, J.2    Tao, T.3
  • 80
    • 33750383209 scopus 로고    scopus 로고
    • K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation
    • M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation," IEEE Trans. Signal Processing, vol. 54, no. 11, pp. 4311-4322, 2006.
    • (2006) IEEE Trans. Signal Processing , vol.54 , Issue.11 , pp. 4311-4322
    • Aharon, M.1    Elad, M.2    Bruckstein, A.3
  • 82
    • 80054768348 scopus 로고    scopus 로고
    • Penalized classification using Fisher's linear discriminant
    • D. M. Witten and R. Tibshirani, "Penalized classification using Fisher's linear discriminant," J. R. Stat. Soc. Series B (Stat. Methodol.), vol. 73, no. 5, pp. 753-772, 2011.
    • (2011) J. R. Stat. Soc. Series B (Stat. Methodol.) , vol.73 , Issue.5 , pp. 753-772
    • Witten, D.M.1    Tibshirani, R.2
  • 84
    • 84898983087 scopus 로고    scopus 로고
    • Stochastic majorization-minimization algorithms for large-scale optimization
    • J. Mairal, "Stochastic majorization-minimization algorithms for large-scale optimization," in Proc. Advances in Neural Information Processing Systems, 2013, pp. 2283-2291.
    • (2013) Proc. Advances in Neural Information Processing Systems , pp. 2283-2291
    • Mairal, J.1
  • 86
    • 76749107542 scopus 로고    scopus 로고
    • Online learning for matrix factorization and sparse coding
    • Jan.
    • J. Mairal, F. Bach, J. Ponce, and G. Sapiro, "Online learning for matrix factorization and sparse coding," J. Mach. Learn. Res., vol. 11, pp. 19-60, Jan. 2010.
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 19-60
    • Mairal, J.1    Bach, F.2    Ponce, J.3    Sapiro, G.4
  • 87
    • 85032752034 scopus 로고    scopus 로고
    • Stochastic approximation vis-a-vis online learning for big data analytics
    • K. Slavakis, S.-J. Kim, G. Mateos, and G. B. Giannakis, "Stochastic approximation vis-a-vis online learning for big data analytics," IEEE Signal Processing Mag., vol. 31, no. 6, pp. 124-129, 2014.
    • (2014) IEEE Signal Processing Mag. , vol.31 , Issue.6 , pp. 124-129
    • Slavakis, K.1    Kim, S.-J.2    Mateos, G.3    Giannakis, G.B.4
  • 88
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction method of multipliers
    • S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, "Distributed optimization and statistical learning via the alternating direction method of multipliers," Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1-122, 2011.
    • (2011) Found. Trends Mach. Learn. , vol.3 , Issue.1 , pp. 1-122
    • Boyd, S.1    Parikh, N.2    Chu, E.3    Peleato, B.4    Eckstein, J.5
  • 94
    • 84970028395 scopus 로고    scopus 로고
    • An asynchronous distributed proximal method for composite convex optimization
    • N. S. Aybat, G. Iyengar, and Z. Wang, "An asynchronous distributed proximal method for composite convex optimization," in Proc. 32th Int. Conf. Machine Learning (ICML), 2015, pp. 2454-2462.
    • (2015) Proc. 32th Int. Conf. Machine Learning (ICML) , pp. 2454-2462
    • Aybat, N.S.1    Iyengar, G.2    Wang, Z.3
  • 96
    • 84867028133 scopus 로고    scopus 로고
    • Gurobi Optimization Inc.
    • Gurobi Optimization, Inc. Gurobi Optimizer Reference Manual, 2013. [Online]. Available: http://www.gurobi.com/documentation/6.0/refman/
    • (2013) Gurobi Optimizer Reference Manual
  • 97
    • 0023421620 scopus 로고
    • Relaxation methods for network flow problems with convex arc costs
    • Sept.
    • D. P. Bertsekas, P. Hosein, and P. Tseng, "Relaxation methods for network flow problems with convex arc costs," SIAM J. Control Optim., vol. 25, no. 5, pp. 1219-1243, Sept. 1987.
    • (1987) SIAM J. Control Optim. , vol.25 , Issue.5 , pp. 1219-1243
    • Bertsekas, D.P.1    Hosein, P.2    Tseng, P.3
  • 98
    • 34547453958 scopus 로고
    • A general inner approximation algorithm for nonconvex mathematical programs
    • B. R. Marks and G. P. Wright, "A general inner approximation algorithm for nonconvex mathematical programs," Oper. Res., vol. 26, no. 4, pp. 681-683, 1978.
    • (1978) Oper. Res. , vol.26 , Issue.4 , pp. 681-683
    • Marks, B.R.1    Wright, G.P.2
  • 100
    • 84893409470 scopus 로고    scopus 로고
    • Decomposition by partial linearization: Parallel optimization of multi-agent systems
    • G. Scutari, F. Facchinei, P. Song, D. P. Palomar, and J.-S. Pang, "Decomposition by partial linearization: Parallel optimization of multi-agent systems," IEEE Trans. Signal Processing, vol. 63, no. 3, pp. 641-656, 2014.
    • (2014) IEEE Trans. Signal Processing , vol.63 , Issue.3 , pp. 641-656
    • Scutari, G.1    Facchinei, F.2    Song, P.3    Palomar, D.P.4    Pang, J.-S.5
  • 102
    • 84879800501 scopus 로고    scopus 로고
    • Gradient methods for minimizing composite functions
    • Yu. Nesterov, "Gradient methods for minimizing composite functions," Math. Program., vol. 140, no. 1, pp. 125-161, 2013.
    • (2013) Math. Program. , vol.140 , Issue.1 , pp. 125-161
    • Nesterov, Yu.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.