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Volumn 63, Issue 20, 2015, Pages 5450-5463

Parallel Algorithms for Constrained Tensor Factorization via Alternating Direction Method of Multipliers

Author keywords

PARAFAC model; parallel algorithms; Tensor decomposition

Indexed keywords

ALGORITHMS; ARRAY PROCESSING; ARTIFICIAL INTELLIGENCE; AUDIO SIGNAL PROCESSING; BIG DATA; CONSTRAINED OPTIMIZATION; FACTORIZATION; LEARNING SYSTEMS; OPTIMIZATION; PARALLEL ALGORITHMS; SCHEDULING ALGORITHMS; SIGNAL PROCESSING; TENSORS;

EID: 84941923446     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2015.2454476     Document Type: Article
Times cited : (94)

References (36)
  • 2
    • 0034250083 scopus 로고    scopus 로고
    • Parallel factor analysis in sensor array processing
    • N. D. Sidiropoulos, R. Bro, and G. Giannakis, "Parallel factor analysis in sensor array processing," IEEE Trans. Signal Process., vol. 48, no. 8, pp. 2377-2388, 2000.
    • (2000) IEEE Trans. Signal Process. , vol.48 , Issue.8 , pp. 2377-2388
    • Sidiropoulos, N.D.1    Bro, R.2    Giannakis, G.3
  • 5
    • 80053092482 scopus 로고    scopus 로고
    • Notes on nonnegative tensor factorization of the spectrogram for audio source separation: Statistical insights and towards self-clustering of the spatial cues
    • Exploring Music Contents, ser. S. Ystad, M. Aramaki, R. Kronland-Martinet, and K. Jensen, Eds. Berlin, Germany: Springer
    • C. Fevotte and A. Ozerov, "Notes on nonnegative tensor factorization of the spectrogram for audio source separation: Statistical insights and towards self-clustering of the spatial cues," in Exploring Music Contents, ser. Lecture Notes in Computer Science, S. Ystad, M. Aramaki, R. Kronland-Martinet, and K. Jensen, Eds. Berlin, Germany: Springer, 2011, vol. 6684, pp. 102-115.
    • (2011) Lecture Notes in Computer Science , vol.6684 , pp. 102-115
    • Fevotte, C.1    Ozerov, A.2
  • 6
    • 84866867881 scopus 로고    scopus 로고
    • Parcube: Sparse parallelizable tensor decompositions
    • ECML/PKDD (1),ser. P. A. Flach, T. D. Bie, and N. Cristianini, Eds. New York, NY, USA: Springer
    • E. E. Papalexakis, C. Faloutsos, and N. D. Sidiropoulos, "Parcube: Sparse parallelizable tensor decompositions," in ECML/PKDD (1),ser. Lecture Notes in Computer Science, P. A. Flach, T. D. Bie, and N. Cristianini, Eds. New York, NY, USA: Springer, 2012, vol. 7523, pp. 521-536.
    • (2012) Lecture Notes in Computer Science , vol.7523 , pp. 521-536
    • Papalexakis, E.E.1    Faloutsos, C.2    Sidiropoulos, N.D.3
  • 7
    • 0000433620 scopus 로고    scopus 로고
    • Least squares regression under unimodality and non-negativity constraints
    • R. Bro and N. D. Sidiropoulos, "Least squares regression under unimodality and non-negativity constraints," J. Chemometrics, vol. 12, pp. 223-247, 1998.
    • (1998) J. Chemometrics , vol.12 , pp. 223-247
    • Bro, R.1    Sidiropoulos, N.D.2
  • 8
    • 85032780162 scopus 로고    scopus 로고
    • Tensor decompositions for signal processing applications: From two-way to multiway component analysis
    • Feb.
    • A. Cichocki, D. Mandic, C. Caiafa, A.-H. Phan, G. Zhou, Q. Zhao, and L. De Lathauwer, "Tensor decompositions for signal processing applications: From two-way to multiway component analysis," IEEE Signal Process. Mag., vol. 32, no. 2, pp. 145-163, Feb. 2014.
    • (2014) IEEE Signal Process. Mag. , vol.32 , Issue.2 , pp. 145-163
    • Cichocki, A.1    Mandic, D.2    Caiafa, C.3    Phan, A.-H.4    Zhou, G.5    Zhao, Q.6    De Lathauwer, L.7
  • 9
    • 0002740437 scopus 로고
    • Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multimodal factor analysis,"
    • R. Harshman, "Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multimodal factor analysis," UCLA Working Papers in Phonetics, vol. 16, pp. 1-84, 1970.
    • (1970) UCLA Working Papers in Phonetics , vol.16 , pp. 1-84
    • Harshman, R.1
  • 10
    • 0002740439 scopus 로고
    • Determination and proof of minimum uniqueness conditions for PARAFAC-1
    • R. Harshman, "Determination and proof of minimum uniqueness conditions for PARAFAC-1," UCLA Working Papers in Phonetics, vol. 22, pp. 111-117, 1972.
    • (1972) UCLA Working Papers in Phonetics , vol.22 , pp. 111-117
    • Harshman, R.1
  • 11
    • 34250499792 scopus 로고
    • Analysis of individual differences in multi-dimensional scaling via an N-way generalization of 'Eckart-Young' decomposition
    • J. Carroll and J. Chang, "Analysis of individual differences in multi-dimensional 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.1    Chang, J.2
  • 12
    • 0013953617 scopus 로고
    • Some mathematical notes on three-mode factor analysis
    • Sep.
    • L. Tucker, "Some mathematical notes on three-mode factor analysis," Psychometrika, vol. 31, no. 3, pp. 279-311, Sep. 1966.
    • (1966) Psychometrika , vol.31 , Issue.3 , pp. 279-311
    • Tucker, L.1
  • 13
    • 67349118082 scopus 로고    scopus 로고
    • Decompositions of a higher-order tensor in block terms - Part II: Definitions and uniqueness
    • L. De Lathauwer, "Decompositions of a higher-order tensor in block terms - Part II: Definitions and uniqueness," SIAM J. Matrix Anal. Appl., vol. 30, no. 3, pp. 1033-1066, 2008.
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , Issue.3 , pp. 1033-1066
    • De Lathauwer, L.1
  • 16
    • 30144444694 scopus 로고    scopus 로고
    • A comparison of algorithms for fitting the PARAFAC model
    • G. Tomasi and R. Bro, "A comparison of algorithms for fitting the PARAFAC model," Comput. Statist. Data Anal., vol. 50, no. 7, pp. 1700-1734, 2006.
    • (2006) Comput. Statist. Data Anal. , vol.50 , Issue.7 , pp. 1700-1734
    • Tomasi, G.1    Bro, R.2
  • 17
    • 79951898361 scopus 로고    scopus 로고
    • A scalable optimization approach for fitting canonical tensor decompositions
    • [Online]. Available
    • E. Acar, D. M. Dunlavy, and T. G. Kolda, "A scalable optimization approach for fitting canonical tensor decompositions," J. Chemometrics vol. 25, no. 2, pp. 67-86, 2011 [Online]. Available: http://dx.doi.org/10.1002/cem.1335
    • (2011) J. Chemometrics , vol.25 , Issue.2 , pp. 67-86
    • Acar, E.1    Dunlavy, D.M.2    Kolda, T.G.3
  • 18
    • 84880828991 scopus 로고    scopus 로고
    • Optimization-based algorithms for tensor decompositions: Canonical polyadic decomposition, decomposition in rank-(lr, lr 1) terms, and a new generalization
    • L. Sorber, M. van Barel, and L. De Lathauwer, "Optimization-based algorithms for tensor decompositions: Canonical polyadic decomposition, decomposition in rank-(lr, lr 1) terms, and a new generalization," SIAM J. Optim., vol. 23, no. 2, pp. 695-720, 2013.
    • (2013) SIAM J. Optim. , vol.23 , Issue.2 , pp. 695-720
    • Sorber, L.1    Van Barel, M.2    De Lathauwer, L.3
  • 20
    • 37549003336 scopus 로고    scopus 로고
    • Mapreduce: Simplified data processing on large clusters
    • J. Dean and S. Ghemawat, "Mapreduce: simplified data processing on large clusters," Commun. ACM, vol. 51, no. 1, pp. 107-113, 2008.
    • (2008) Commun. ACM , vol.51 , Issue.1 , pp. 107-113
    • Dean, J.1    Ghemawat, S.2
  • 23
    • 85032751899 scopus 로고    scopus 로고
    • Parallel randomly compressed cubes: A scalable distributed architecture for big tensor decomposition
    • Sep.
    • N. D. Sidiropoulos, E. E. Papalexakis, and C. Faloutsos, "Parallel randomly compressed cubes: A scalable distributed architecture for big tensor decomposition," IEEE Signal Process. Mag., vol. 31, no. 5, pp. 57-70, Sep. 2014.
    • (2014) IEEE Signal Process. Mag. , vol.31 , Issue.5 , pp. 57-70
    • Sidiropoulos, N.D.1    Papalexakis, E.E.2    Faloutsos, C.3
  • 26
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction Method of Multipliers
    • Jan. [Online]. Available
    • 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, Jan. 2011 [Online]. Available: http://dx.doi.org/10.1561/2200000016
    • (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
  • 27
    • 49749096526 scopus 로고    scopus 로고
    • Efficient MATLAB computations with sparse and factored tensors
    • [Online]. Available
    • B. W. Bader and T. G. Kolda, "Efficient MATLAB computations with sparse and factored tensors," SIAM J. Scientif. Comput. vol. 30, no. 1, pp. 205-231, 2008 [Online]. Available: http://dx.doi.org/10.1137/060676489
    • (2008) SIAM J. Scientif. Comput. , vol.30 , Issue.1 , pp. 205-231
    • Bader, B.W.1    Kolda, T.G.2
  • 28
    • 67049173946 scopus 로고    scopus 로고
    • Scalable tensor decompositions for multi-aspect data mining
    • T. G. Kolda and J. Sun, "Scalable tensor decompositions for multi-aspect data mining," in Proc. IEEE ICDM, 2008, pp. 363-372.
    • Proc. IEEE ICDM, 2008 , pp. 363-372
    • Kolda, T.G.1    Sun, J.2
  • 29
    • 77956050441 scopus 로고    scopus 로고
    • Jan. [Online]. Available
    • B. W. Bader et al., Matlab Tensor Toolbox. ver. 2.5, Jan. 2012 [Online]. Available: http://www.sandia.gov/tgkolda/TensorToolbox/
    • (2012) Matlab Tensor Toolbox. Ver. 2.5
    • Bader, B.W.1
  • 31
    • 84862791611 scopus 로고    scopus 로고
    • An alternating direction algorithm for matrix completion with nonnegative factors
    • Y. Xu, W. Yin, Z. Wen, and Y. Zhang, "An alternating direction algorithm for matrix completion with nonnegative factors," Frontiers Math. China, vol. 51, no. 2, pp. 365-384, 2010.
    • (2010) Frontiers Math. China , vol.51 , Issue.2 , pp. 365-384
    • Xu, Y.1    Yin, W.2    Wen, Z.3    Zhang, Y.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.