Multilinear subspace regression: An orthogonal tensor decomposition approach

Advances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011

Volumn , Issue , 2011, Pages

  Zhao, Qibin ^a   Caiafa, Cesar F ^b   Mandic, Danilo P ^c   Zhang, Liqing ^d   Ball, Tonio ^e   Schulze Bonhage, Andreas ^e   Cichocki, Andrzej ^a  

^a RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

^b CONICET ^*  (Argentina)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

^d SHANGHAI JIAO TONG UNIVERSITY   (China)

^e UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROENCEPHALOGRAPHY; LEAST SQUARES APPROXIMATIONS; LINEAR TRANSFORMATIONS; REGRESSION ANALYSIS; TENSORS; VECTORS;

2D DATUM; DATA REPRESENTATIONS; DECOMPOSITION APPROACH; LATENT VARIABLE; MATRIX; MODEL-BASED OPC; ORTHOGONAL TENSORS; REGRESSION METHOD; REGRESSION MODELLING; TENSOR DECOMPOSITION;

SINGULAR VALUE DECOMPOSITION;

EID: 85162340833     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (23)

1. L. Wolf, H. Jhuang, and T. Hazan. Modeling appearances with low-rank SVM. In IEEE Conference on Computer Vision and Pattern Recognition, pages 1-6. IEEE, 2007.
2. Hamed Pirsiavash, Deva Ramanan, and Charless Fowlkes. Bilinear classifiers for visual recognition. In Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, and A. Culotta, editors, Advances in Neural Information Processing Systems 22, pages 1482-1490. 2009.
3. H. Lu, K.N. Plataniotis, and A.N. Venetsanopoulos. MPCA: Multilinear principal component analysis of tensor objects. IEEE Transactions on Neural Networks, 19(1):18-39, 2008.
4. S. Yan, D. Xu, Q. Yang, L. Zhang, X. Tang, and H.J. Zhang. Multilinear discriminant analysis for face recognition. IEEE Transactions on Image Processing, 16(1):212-220, 2007.
5. D. Tao, X. Li, X. Wu, and S.J. Maybank. General tensor discriminant analysis and Gabor features for gait recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(10):1700-1715, 2007.
6. A.K. Smilde and H.A.L. Kiers. Multiway covariates regression models. Journal of Chemometrics, 13(1):31-48, 1999.
7. X. He, D. Cai, and P. Niyogi. Tensor subspace analysis. Advances in Neural Information Processing Systems, 18:499, 2006.
8. T.G. Kolda and B.W. Bader. Tensor decompositions and applications. SIAM Review, 51(3):455-500, 2009.
9. A. Cichocki, R. Zdunek, A. H. Phan, and S. I. Amari. Nonnegative Matrix and Tensor Factorizations. John Wiley & Sons, 2009.
10. E. Acar, D.M. Dunlavy, T.G. Kolda, and M. Mørup. Scalable tensor factorizations for incomplete data. Chemometrics and Intelligent Laboratory Systems, 2010.
11. R. Bro, R.A. Harshman, N.D. Sidiropoulos, and M.E. Lundy. Modeling multi-way data with linearly dependent loadings. Journal of Chemometrics, 23(7-8):324-340, 2009.
12. S. Wold, M. Sjostroma, and L. Erikssonb. PLS-regression: A basic tool of chemometrics. Chemometrics and Intelligent Laboratory Systems, 58:109-130, 2001.
13. H. Wold. Soft modeling by latent variables: The nonlinear iterative partial least squares approach. Perspectives in probability and statistics, papers in honour of MS Bartlett, pages 520-540, 1975.
14. A. Krishnan, L.J. Williams, A.R. McIntosh, and H. Abdi. Partial least squares (PLS) methods for neuroimaging: A tutorial and review. NeuroImage, 56(2):455-475, 2011.
15. H. Abdi. Partial least squares regression and projection on latent structure regression (PLS Regression). Wiley Interdisciplinary Reviews: Computational Statistics, 2(1):97-106, 2010.
16. R. Rosipal and N. Krämer.Overview and recent advances in partial least squares. In Subspace, Latent Structure and Feature Selection, volume 3940 of Lecture Notes in Computer Science, pages 34-51. Springer, 2006.
17. R. Bro. Multiway calibration. Multilinear PLS. Journal of Chemometrics, 10(1):47-61, 1996.
18. L. De Lathauwer. Decompositions of a higher-order tensor in block terms - Part II: Definitions and uniqueness. SIAM J. Matrix Anal. Appl, 30(3):1033-1066, 2008.
19. L. De Lathauwer, B. De Moor, and J. Vandewalle. A multilinear singular value decomposition. SIAM Journal on Matrix Analysis and Applications, 21(4):1253-1278, 2000.
20. M. Velliste, S. Perel, M.C. Spalding, A.S. Whitford, and A.B. Schwartz. Cortical control of a prosthetic arm for self-feeding. Nature, 453(7198):1098-1101, 2008.
21. Z.C. Chao, Y. Nagasaka, and N. Fujii. Long-term asynchronous decoding of arm motion using electrocorticographic signals in monkeys. Frontiers in Neuroengineering, 3(3), 2010.
22. T. Pistohl, T. Ball, A. Schulze-Bonhage, A. Aertsen, and C. Mehring. Prediction of arm movement trajectories from ECoG-recordings in humans. Journal of Neuroscience Methods, 167(1):105-114, 2008.
23. T.J. Bradberry, R.J. Gentili, and J.L. Contreras-Vidal. Reconstructing three-dimensional hand movements from noninvasive electroencephalographic signals. The Journal of Neuroscience, 30(9):3432, 2010.