A new convex relaxation for tensor completion

Advances in Neural Information Processing Systems

Volumn , Issue , 2013, Pages

  Romera Paredes, Bernardino ^a   Pontil, Massimiliano ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

TENSORS;

ALTERNATING DIRECTION METHOD OF MULTIPLIERS; CONVEX RELAXATION; ESTIMATION ERRORS; LINEAR MEASUREMENTS; LOW-RANK MATRICES; REAL DATA SETS; TENSOR COMPLETION; TRACE-NORMS;

RELAXATION PROCESSES;

EID: 84898929494     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (27)

1. A. Argyriou, R. Foygel and N. Srebro. Sparse Prediction with the k-Support Norm. Advances in Neural Information Processing Systems 25, pages 1466-1474, 2012.
2. A. Argyriou, C.A. Micchelli, M. Pontil, L. Shen and Y. Xu. Efficient first order methods for linear com- posite regularizers. arXiv:1104.1436, 2011.
3. R. Bhatia. Matrix Analysis. Springer Verlag, 1997.
4. D.P. Bertsekas, J.N. Tsitsiklis. Parallel and Distributed Computation: Numerical Methods. Prentice-Hall, 1989.
5. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1):1-122, 2011.
6. S. Boyd, L. Xiao, A. Mutapcic. Subgradient methods, Stanford University, 2003.
7. P. L. Combettes and J.-C. Pesquet. Proximal splitting methods in signal processing. In Fixed-Point Al-gorithms for Inverse Problems in Science and Engineering (H. H. Bauschke et al. Eds), pages 185-212, Springer, 2011.
8. M. Fazel, H. Hindi, and S. Boyd. A rank minimization heuristic with application to minimum order system approximation. Proc. American Control Conference, Vol. 6, pages 4734-4739, 2001.
9. S. Gandy, B. Recht, I. Yamada. Tensor completion and low-n-rank tensor recovery via convex optimiza- tion. Inverse Problems, 27(2), 2011.
10. G. H. Golub, C. F. Van Loan. Matrix Computations. 3rd Edition. Johns Hopkins University Press, 1996.
11. Z. Harchaoui, M. Douze, M. Paulin, M. Dudik, J. Malick. Large-scale image classification with trace-norm regularization. IEEE Conference on Computer Vision & Pattern Recognition (CVPR), pages 3386-3393, 2012.
12. J-B. Hiriart-Urruty and C. Lemaréchal. Convex Analysis and Minimization Algorithms, Part I. Springer, 1996.
13. J-B. Hiriart-Urruty and C. Lemaréchal. Convex Analysis and Minimization Algorithms, Part II. Springer, 1993.
14. R.A. Horn and C.R. Johnson. Topics in Matrix Analysis. Cambridge University Press, 2005.
15. A. Karatzoglou, X. Amatriain, L. Baltrunas, N. Oliver. Multiverse recommendation: n-dimensional ten-sor factorization for context-aware collaborative filtering. Proc. 4th ACM Conference on Recommender Systems, pages 79-86, 2010.
16. T.G. Kolda and B.W. Bade. Tensor decompositions and applications. SIAM Review, 51(3):455-500, 2009.
17. J. Liu, P. Musialski, P. Wonka, J. Ye. Tensor completion for estimating missing values in visual data. Proc. 12th International Conference on Computer Vision (ICCV), pages 2114-2121, 2009.
18. Y. Nesterov. Gradient methods for minimizing composite objective functions. ECORE Discussion Paper, 2007/96, 2007.
19. B. Recht. A simpler approach to matrix completion. Journal of Machine Learning Research, 12:3413-3430, 2009.
20. B. Romera-Paredes, H. Aung, N. Bianchi-Berthouze and M. Pontil. Multilinear multitask learning. Proc. 30th International Conference on Machine Learning (ICML), pages 1444-1452, 2013.
21. N. Z. Shor. Minimization Methods for Non-differentiable Functions. Springer, 1985.
22. M. Signoretto, Q. Tran Dinh, L. De Lathauwer, J.A.K. Suykens. Learning with tensors: a framework based on convex optimization and spectral regularization. Machine Learning, to appear.
23. M. Signoretto, R. Van de Plas, B. De Moor, J.A.K. Suykens. Tensor versus matrix completion: a com-parison with application to spectral data. IEEE Signal Processing Letters, 18(7):403-406, 2011.
24. N. Srebro, J. Rennie and T. Jaakkola. Maximum margin matrix factorization. Advances in Neural Infor-mation Processing Systems (NIPS) 17, pages 1329-1336, 2005.
25. R. Tomioka, K. Hayashi, H. Kashima, J.S.T. Presto. Estimation of low-rank tensors via convex optimiza-tion. arXiv:1010.0789, 2010.
26. R. Tomioka and T. Suzuki. Convex tensor decomposition via structured Schatten norm regularization. arXiv:1303.6370, 2013.
27. R. Tomioka, T. Suzuki, K. Hayashi, H. Kashima. Statistical performance of convex tensor decomposition. Advances in Neural Information Processing Systems (NIPS) 24, pages 972-980, 2013.