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Volumn 37, Issue 9, 2015, Pages 1751-1763

Bayesian CP factorization of incomplete tensors with automatic rank determination

Author keywords

Bayesian inference; image synthesis; tensor completion; Tensor factorization; tensor rank determination

Indexed keywords

BAYESIAN NETWORKS; FACTORIZATION; IMAGE PROCESSING; INFERENCE ENGINES;

EID: 84939249854     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2015.2392756     Document Type: Article
Times cited : (558)

References (44)
  • 1
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions, and applications
    • T. Kolda, and B. 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.1    Bader, B.2
  • 3
    • 67649880294 scopus 로고    scopus 로고
    • Semi-supervised bilinear subspace learning
    • Jul
    • D. Xu, and S. Yan. "Semi-supervised bilinear subspace learning". IEEE Trans. Image Process., vol. 18, no. 7, pp. 1671-1676, Jul. 2009
    • (2009) IEEE Trans. Image Process , vol.18 , Issue.7 , pp. 1671-1676
    • Xu, D.1    Yan, S.2
  • 4
    • 55149087688 scopus 로고    scopus 로고
    • Reconstruction, and recognition of tensor-based objects with concurrent subspaces analysis
    • Jan
    • D. Xu, S. Yan, L. Zhang, S. Lin, H.-J. Zhang, and T. S. Huang. "Reconstruction, and recognition of tensor-based objects with concurrent subspaces analysis". IEEE Trans. Circuits Syst. Video Technol., vol. 18, no. 1, pp. 36-47, Jan. 2008
    • (2008) IEEE Trans. Circuits Syst. Video Technol , vol.18 , Issue.1 , pp. 36-47
    • Xu, D.1    Yan, S.2    Zhang, L.3    Lin, S.4    Zhang, H.-J.5    Huang, T.S.6
  • 5
    • 69549135109 scopus 로고    scopus 로고
    • Enhancing bilinear subspace learning by element rearrangement
    • Oct
    • D. Xu, S. Yan, S. Lin, T. S. Huang, and S.-F. Chang. "Enhancing bilinear subspace learning by element rearrangement". IEEE Trans. Pattern Anal. Mach. Intell., vol. 31, no. 10, pp. 1913-1920, Oct. 2009
    • (2009) IEEE Trans. Pattern Anal. Mach. Intell , vol.31 , Issue.10 , pp. 1913-1920
    • Xu, D.1    Yan, S.2    Lin, S.3    Huang, T.S.4    Chang, S.-F.5
  • 6
    • 0013953617 scopus 로고
    • Some mathematical notes on three-mode factor analysis
    • L. R. Tucker. "Some mathematical notes on three-mode factor analysis". Psychometrika, vol. 31, no. 3, pp. 279-311, 1966
    • (1966) Psychometrika , vol.31 , Issue.3 , pp. 279-311
    • Tucker, L.R.1
  • 7
    • 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 Phonetics, vol. 16, pp. 1-84, 1970
    • (1970) UCLA Working Papers Phonetics , vol.16 , pp. 1-84
    • Harshman, R.A.1
  • 8
    • 0030813663 scopus 로고    scopus 로고
    • Parafac tutorial, and applications
    • R. Bro. "PARAFAC. Tutorial, and applications". Chemom. Intell. Lab. Syst., vol. 38, no. 2, pp. 149-171, 1997
    • (1997) Chemom. Intell. Lab. Syst , vol.38 , Issue.2 , pp. 149-171
    • Bro, R.1
  • 10
    • 79952446596 scopus 로고    scopus 로고
    • Scalable tensor factorizations for incomplete data
    • E. Acar, D. M. Dunlavy, T. G. Kolda, and M. Mørup. "Scalable tensor factorizations for incomplete data". Chemom. Intell. Lab. Syst., vol. 106, no. 1, pp. 41-56, 2011
    • (2011) Chemom. Intell. Lab. Syst , vol.106 , Issue.1 , pp. 41-56
    • Acar, E.1    Dunlavy, D.M.2    Kolda, T.G.3    Mørup, M.4
  • 11
    • 84880828991 scopus 로고    scopus 로고
    • Optimizationbased 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. "Optimizationbased algorithms for tensor decompositions: Canonical polyadic decomposition, decomposition in rank-(lr, lr, 1) terms, and a new generalization". SIAM J. Opt., vol. 23, no. 2, pp. 695-720, 2013
    • (2013) SIAM J. Opt , vol.23 , Issue.2 , pp. 695-720
    • Sorber, L.1    Van Barel, M.2    De Lathauwer, L.3
  • 12
    • 84902838492 scopus 로고    scopus 로고
    • Low-rank tensor completion by Riemannian optimization
    • Jun
    • D. Kressner, M. Steinlechner, and B. Vandereycken. "Low-rank tensor completion by Riemannian optimization". BIT Numer. Math., vol. 54, no. 2, pp. 447-468, Jun. 2014
    • (2014) BIT Numer. Math , vol.54 , Issue.2 , pp. 447-468
    • Kressner, D.1    Steinlechner, M.2    Vandereycken, B.3
  • 13
    • 84870175618 scopus 로고    scopus 로고
    • Tensor completion for estimating missing values in visual data
    • Jan
    • J. Liu, P. Musialski, P. Wonka, and J. Ye. "Tensor completion for estimating missing values in visual data". IEEE Trans. Pattern Anal. Mach. Intell., vol. 35, no. 1, pp. 208-220, Jan. 2013
    • (2013) IEEE Trans. Pattern Anal. Mach. Intell , vol.35 , Issue.1 , pp. 208-220
    • Liu, J.1    Musialski, P.2    Wonka, P.3    Ye, J.4
  • 14
    • 84894640150 scopus 로고    scopus 로고
    • Learning with tensors: A framework based on convex optimization, and spectral regularization
    • M. Signoretto, Q. T. Dinh, L. De Lathauwer, and J. A. Suykens. "Learning with tensors: A framework based on convex optimization, and spectral regularization". Mach. Learn., pp. 1-49, 2013
    • Mach. Learn , vol.2013 , pp. 1-49
    • Signoretto, M.1    Dinh, Q.T.2    De Lathauwer, L.3    Suykens, J.A.4
  • 15
    • 80055061162 scopus 로고    scopus 로고
    • Composite splitting algorithms for convex optimization
    • J. Huang, S. Zhang, H. Li, and D. Metaxas. "Composite splitting algorithms for convex optimization". Comput. Vis. Image Understanding, vol. 115, no. 12, pp. 1610-1622, 2011
    • (2011) Comput. Vis. Image Understanding , vol.115 , Issue.12 , pp. 1610-1622
    • Huang, J.1    Zhang, S.2    Li, H.3    Metaxas, D.4
  • 16
    • 79551661156 scopus 로고    scopus 로고
    • Tensor completion, and lown-rank tensor recovery via convex optimization
    • S. Gandy, B. Recht, and I. Yamada. "Tensor completion, and lown-rank tensor recovery via convex optimization". Inverse Probl., vol. 27, no. 2, p. 025010, 2011
    • (2011) Inverse Probl , vol.27 , Issue.2 , pp. 025010
    • Gandy, S.1    Recht, B.2    Yamada, I.3
  • 17
    • 84894556521 scopus 로고    scopus 로고
    • Tensor completion via a multi-linear low-n-rank factorization model
    • H. Tan, B. Cheng, W. Wang, Y.-J. Zhang, and B. Ran. "Tensor completion via a multi-linear low-n-rank factorization model". Neurocomputing, vol. 133, pp. 161-169, 2014
    • Neurocomputing , vol.133 , Issue.2014 , pp. 161-169
    • Tan, H.1    Cheng, B.2    Wang, W.3    Zhang, Y.-J.4    Ran, B.5
  • 18
    • 84896845961 scopus 로고    scopus 로고
    • Large margin low rank tensor analysis
    • G. Zhong, and M. Cheriet. "Large margin low rank tensor analysis". Neural Comput., vol. 26, no. 4, pp. 761-780, 2014
    • (2014) Neural Comput , vol.26 , Issue.4 , pp. 761-780
    • Zhong, G.1    Cheriet, M.2
  • 20
    • 84894544955 scopus 로고    scopus 로고
    • Simultaneous tensor decomposition, and completion using factor priors
    • Mar
    • Y.-L. Chen, C.-T. Hsu, and H.-Y. Liao. "Simultaneous tensor decomposition, and completion using factor priors". IEEE Trans. Pattern Anal. Mach. Intell., vol. 36, no. 3, pp. 577-591, Mar. 2014
    • (2014) IEEE Trans. Pattern Anal. Mach. Intell , vol.36 , Issue.3 , pp. 577-591
    • Chen, Y.-L.1    Hsu, C.-T.2    Liao, H.-Y.3
  • 21
    • 84864537879 scopus 로고    scopus 로고
    • Tensor factorization using auxiliary information
    • A. Narita, K. Hayashi, R. Tomioka, and H. Kashima. "Tensor factorization using auxiliary information". Data Min. Knowl. Discov., vol. 25, no. 2, pp. 298-324, 2012
    • (2012) Data Min. Knowl. Discov , vol.25 , Issue.2 , pp. 298-324
    • Narita, A.1    Hayashi, K.2    Tomioka, R.3    Kashima, H.4
  • 22
    • 0001424792 scopus 로고
    • Tensor rank is NP-complete
    • J. Ha stad. "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
  • 25
    • 55349142218 scopus 로고    scopus 로고
    • Tensor rank, and the ill-posedness of the best low-rank approximation problem
    • V. De Silva, and L.-H. Lim. "Tensor rank, and the ill-posedness of the best low-rank approximation problem". SIAM J. Matrix Anal. Appl., vol. 30, no. 3, pp. 1084-1127, 2008
    • (2008) SIAM J. Matrix Anal. Appl , vol.30 , Issue.3 , pp. 1084-1127
    • De Silva, V.1    Lim, L.-H.2
  • 26
    • 84887356726 scopus 로고    scopus 로고
    • Tensor rank, invariants, inequalities, and applications
    • E. S. Allman, P. D. Jarvis, J. A. Rhodes, and J. G. Sumner. "Tensor rank, invariants, inequalities, and applications". SIAM J. Matrix Anal. Appl., vol. 34, no. 3, pp. 1014-1045, 2013
    • (2013) SIAM J. Matrix Anal. Appl , vol.34 , Issue.3 , pp. 1014-1045
    • Allman, E.S.1    Jarvis, P.D.2    Rhodes, J.A.3    Sumner, J.G.4
  • 28
    • 56449131205 scopus 로고    scopus 로고
    • Bayesian probabilistic matrix factorization using markov chain monte carlo
    • R. Salakhutdinov, and A. Mnih. "Bayesian probabilistic matrix factorization using Markov chain Monte Carlo". in Proc. 25th Int. Conf. Mach. Learn., 2008, pp. 880-887
    • (2008) Proc. 25th Int. Conf. Mach. Learn , pp. 880-887
    • Salakhutdinov, R.1    Mnih, A.2
  • 29
  • 30
    • 48249140327 scopus 로고    scopus 로고
    • Variational Bayesian approach to movie rating prediction
    • Y. J. Lim, and Y. W. Teh. "Variational Bayesian approach to movie rating prediction". in Proc. KDD Cup Workshop, 2007, pp. 15-21
    • (2007) Proc. KDD Cup Workshop , pp. 15-21
    • Lim, Y.J.1    Teh, Y.W.2
  • 33
    • 84862293016 scopus 로고    scopus 로고
    • Probabilistic models for incomplete multi-dimensional arrays
    • W. Chu, and Z. Ghahramani. "Probabilistic models for incomplete multi-dimensional arrays". in JMLR Workshop Conf. Proc., 2009, vol. 5, pp. 89-96
    • (2009) JMLR Workshop Conf. Proc , vol.5 , pp. 89-96
    • Chu, W.1    Ghahramani, Z.2
  • 34
    • 84867411640 scopus 로고    scopus 로고
    • Probabilistic latent tensor factorization model for link pattern prediction in multirelational networks
    • S. Gao, L. Denoyer, P. Gallinari, and J. GUO. "Probabilistic latent tensor factorization model for link pattern prediction in multirelational networks". J. China Univ. Posts Telecommun., vol. 19, pp. 172-181, 2012
    • (2012) J. China Univ. Posts Telecommun , vol.19 , pp. 172-181
    • Gao, S.1    Denoyer, L.2    Gallinari, P.3    Guo, J.4
  • 35
    • 80052121737 scopus 로고    scopus 로고
    • Temporal collaborative filtering with Bayesian probabilistic tensor factorization
    • L. Xiong, X. Chen, T.-K. Huang, J. Schneider, and J. G. Carbonell. "Temporal collaborative filtering with Bayesian probabilistic tensor factorization". in Proc. SIAM Data Min., 2010, vol. 2010
    • (2010) Proc. SIAM Data Min , vol.2010
    • Xiong, L.1    Chen, X.2    Huang, T.-K.3    Schneider, J.4    Carbonell, J.G.5
  • 37
    • 84867120756 scopus 로고    scopus 로고
    • Infinite Tucker decomposition: Nonparametric Bayesian models for multiway data analysis
    • Z. Xu, F. Yan, and A. Qi. "Infinite Tucker decomposition: Nonparametric Bayesian models for multiway data analysis". in Proc. 29th Int. Conf. Mach. Lear., 2012, pp. 1023-1030
    • (2012) Proc. 29th Int. Conf. Mach. Lear , pp. 1023-1030
    • Xu, Z.1    Yan, F.2    Qi, A.3
  • 38
    • 0000335983 scopus 로고    scopus 로고
    • Bayesian methods for backpropagation networks
    • New York, NY, USA Springer
    • D. J. MacKay. "Bayesian methods for backpropagation networks". in Models of Neural Networks III. New York, NY, USA: Springer, 1996, pp. 211-254
    • (1996) Models of Neural Networks III , pp. 211-254
    • MacKay, D.J.1
  • 39
    • 0001224048 scopus 로고    scopus 로고
    • Sparse bayesian learning, and the relevance vector machine
    • M. E. Tipping. "Sparse Bayesian learning, and the relevance vector machine". J. Mach. Learn. Res., vol. 1, pp. 211-244, 2001
    • (2001) J. Mach. Learn. Res , vol.1 , pp. 211-244
    • Tipping, M.E.1
  • 41
    • 21844450606 scopus 로고    scopus 로고
    • Variational message passing
    • J. M. Winn, and C. M. Bishop. "Variational message passing". J. Mach. Learn. Res., vol. 6, pp. 661-694, 2005
    • (2005) J. Mach. Learn. Res , vol.6 , pp. 661-694
    • Winn, J.M.1    Bishop, C.M.2


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