publication . Preprint . Article . 2016

Efficient tensor completion: Low-rank tensor train

Johann Bengua;
Open Access English
  • Published: 06 Jan 2016
Comment: 11 pages, 9 figures
ACM Computing Classification System: MathematicsofComputing_NUMERICALANALYSIS
free text keywords: Computer Science - Numerical Analysis
32 references, page 1 of 3

[1] T. G. Kolda and B. W. Bader, “Tensor decompositions and applications,” SIAM Review, vol. 51, no. 3, pp. 455-500, 2009.

[2] M. Vasilescu and D. Terzopoulos, “Multilinear subspace analysis of image ensembles,” in 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2003. Proceedings. Institute of Electrical & Electronics Engineers (IEEE), 2003. [OpenAIRE]

[3] J.-T. Sun, H.-J. Zeng, H. Liu, Y. Lu, and Z. Chen, “Cubesvd: A novel approach to personalized web search,” in Proceedings of the 14th International Conference on World Wide Web, ser. WWW '05. New York, NY, USA: ACM, 2005, pp. 382-390. [OpenAIRE]

[4] T. Franz, A. Schultz, S. Sizov, and S. Staab, “Triplerank: Ranking semantic web data by tensor decomposition,” in The Semantic Web - ISWC 2009, ser. Lecture Notes in Computer Science, A. Bernstein, D. Karger, T. Heath, L. Feigenbaum, D. Maynard, E. Motta, and K. Thirunarayan, Eds. Springer Berlin Heidelberg, 2009, vol. 5823, pp. 213-228.

[5] J. 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.

[6] R. A. Harshman, “Foundations of the PARAFAC procedure: Models and conditions for an“ explanatory” multi-modal factor analysis,” UCLA Working Papers in Phonetics, vol. 16, no. 1, p. 84, 1970.

[7] L. R. Tucker, “Some mathematical notes on three-mode factor analysis,” Psychometrika, vol. 31, no. 3, pp. 279-311, Sep 1966.

[8] I. V. Oseledets, “Tensor-Train Decomposition,” SIAM J. Sci. Comput., vol. 33, no. 5, pp. 2295-2317, Jan 2011.

[9] M. Fannes, B. Nachtergaele, and R. Werner, “Finitely correlated states on quantum spin chains,” Communications in Mathematical Physics, vol. 144, no. 3, pp. 443-490, 1992. [OpenAIRE]

[10] A. Klmper, A. Schadschneider, and J. Zittartz, “Matrix product ground states for one-dimensional spin-1 quantum antiferromagnets,” EPL (Europhysics Letters), vol. 24, no. 4, p. 293, 1993. [Online]. Available: [OpenAIRE]

[11] D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, “Matrix product state representations,” Quantum Info. Comput., vol. 7, no. 5, pp. 401-430, 2007.

[12] J.-F. Cai, E. J. Cande`s, and Z. Shen, “A Singular Value Thresholding Algorithm for Matrix Completion,” SIAM J. Optim., vol. 20, no. 4, pp. 1956-1982, Jan 2010.

[13] S. Ma, D. Goldfarb, and L. Chen, “Fixed point and Bregman iterative methods for matrix rank minimization,” Mathematical Programming, vol. 128, no. 1-2, pp. 321-353, Sep 2009.

[14] B. Recht, M. Fazel, and P. A. Parrilo, “Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization,” SIAM Rev., vol. 52, no. 3, pp. 471-501, Jan 2010.

[15] J. Liu, P. Musialski, P. Wonka, and J. Ye, “Tensor completion for estimating missing values in visual data,” Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 35, no. 1, pp. 208-220, Jan 2013.

32 references, page 1 of 3
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue