Large margin low rank tensor analysis

Neural Computation

Volumn 26, Issue 4, 2014, Pages 761-780

  Zhong, Guoqiang ^a   Cheriet, Mohamed ^a  

^a Synchromedia Laboratory   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; HUMAN; LEARNING; PATTERN RECOGNITION; RECOGNITION;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; HUMANS; LEARNING; PATTERN RECOGNITION, AUTOMATED; PATTERN RECOGNITION, VISUAL; RECOGNITION (PSYCHOLOGY);

EID: 84896845961     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00570     Document Type: Letter

References (45)

1. Baudat, G., & Anouar, F. (2000). Generalized discriminant analysis using a kernel approach. Neural Computation, 12(10), 2385-2404.
2. Belkin, M., & Niyogi, P. (2003). Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15(6), 1373-1396.
3. Bengio, Y., Lamblin, P., Popovici, D., & Larochelle, H. (2006). Greedy layer-wise training of deep networks. In B. Scḧolkopf, J. C. Platt, & T. Hoffman (Eds.), Advancess in neural information processing systems, 19 (pp. 153-160). Cambridge, MA: MIT Press.
4. Bengio, Y., Paiement, J.-F., Vincent, P., Delalleau, O., Roux, N.L., & Ouimet, M. (2003).Out-of-sample extensions for LLE, isomap, MDS, eigenmaps, and spectral clustering. In S. Thr ̈un, L. K. Saul, & B. Scḧolkopf (Eds.), Advances in neural information processing systems, 16. Cambridge, MA: MIT Press.
5. Bondy, J. A., & Murty, U.S.R. (1976). Graph theory with applications. Amsterdam: North-Holland.
6. Cand'es, E., & Recht, B. (2012). Exact matrix completion via convex optimization. Commun. ACM, 55(6), 111-119.
7. Cand'es, E., & Tao, T. (2010). The power of convex relaxation: Near-optimal matrix completion. IEEE Transactions on Information Theory, 56(5), 2053-2080.
8. Chung, F. R. K. (1997). Spectral graph theory. Providence, RI: AmericanMathematical Society.
9. Cohn, D., Ladner, R., & Waibel, A. (1994). Improving generalization with active learning machine learning. Machine Learning, 15, 201-221.
10. Dai, G., & Yeung, D.-Y. (2006). Tensor embedding methods. In Proceedings of the 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference (pp. 330-335). Cambridge, MA: MIT Press.
11. Daugman, J. G. (1988). Complete discrete 2D Gabor transforms by neural networks for image analysis and compression. IEEE Transactions on Acoustics, Speech and Signal Processing, 36(7), 1169-1179.
12. de Silva, V., & Lim, L.-H. (2008). Tensor rank and the ill-posedness of the best low-rank approximation problem. SIAM J. Matrix Analysis Applications, 30(3), 1084-1127.
13. Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(7), 179-188.
14. Fu, Y., & Huang, T. S. (2008). Image classification using correlation tensor analysis. IEEE Transactions on Image Processing, 17(2), 226-234.
15. Fukunnaga, K. (1991). Introduction to statistical pattern recognition (2nd ed.). Orlando, FL: Academic Press.
16. Grant, M., & Boyd, S. (2008). Graph implementations for nonsmooth convex programs. In V. Blondel, S. Boyd, & H. Kimura (Eds.), Recent advances in learning and control (pp. 95-110). New York: Springer-Verlag.
17. He, X., & Niyogi, P. (2003). Locality preserving projections. In S. Thr ̈un, L. K. Saul,& B. Scḧolkopf (Eds.), Advances in neural information processing systems, 16. Cambridge, MA: MIT Press.
18. Hinton, G. E., Osindero, S., & Teh, Y. W. (2006). A fast learning algorithm for deep belief nets. Neural Computation, 18(7), 1527-1554.
19. Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. Science, 313(5786), 504-507.
20. Jolliffe, I. (2002). Principal component analysis (2nd ed.). New York: Springer.
21. Kolda, T. G., & Bader, B. W. (2009). Tensor decompositions and applications. SIAM Review, 51(3), 455-500.
22. Lawrence, N. D. (2005). Probabilistic non-linear principal component analysis with gaussian process latent variable models. Journal of Machine Learning Research, 6, 1783-1816.
23. LeCun, Y., Bottou, L., Bengio, Y., & Haffner, P. (2001). Gradient-based learning applied to document recognition. In S. Haykin & B. Kosko (Eds.), Intelligent signal processing (pp. 306-351). Piscataway, NJ: IEEE Press.
24. Lee, D. D.,&Seung, H. S. (1999). Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755), 788-791.
25. Liu, Y., Liu, Y., & Chan, K. C. C. (2010). Tensor distance based multilinear localitypreserved maximum information embedding. IEEE Transactions on Neural Networks, 21(11), 1848-1854.
26. Liu, J., Liu, J., Wonka, P., & Ye, J. (2012). Sparse non-negative tensor factorization using columnwise coordinate descent. Pattern Recognition, 45(1), 649-656.
27. Ma, S., Goldfarb, D., & Chen, L. (2011). Fixed point and Bregman iterative methods for matrix rank minimization. Math. Program., 128(1-2), 321-353.
28. Northcott, D. G. (1984). Multilinear algebra. Cambridge: Cambridge University Press.
29. Pan, S. J., & Yang, Q. (2010). A survey on transfer learning. IEEE Trans. Knowl. Data Eng., 22(10), 1345-1359.
30. Rosch, E. (1973). Natural categories. Cognitive Psychol., 4, 328-350.
31. Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323-2326.
32. Scḧolkopf, B., Smola, A. J., & M̈ Uller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299-1319.
33. Seung, H. S.,&Lee, D. D. (2000). The manifold ways of perception. Science, 290(5500), 2268-2269.
34. Sugiyama, M. (2007). Dimensionality reduction of multimodal labeled data by local fisher discriminant analysis. Journal of Machine Learning Research, 8, 1027-1061.
35. Tao, D., Li, X., Wu, X., & Maybank, S. J. (2007). General tensor discriminant analysis and Gabor features for gait recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(10), 1700-1715.
36. Tenenbaum, J. B., de Silva, V.,&Langford, J. C. (2000).Aglobal geometric framework for nonlinear dimensionality reduction. Science, 290(5500), 2319-2323.
37. Tenenbaum, J. B., Kemp, C., Griffiths, T. L., & Goodman, N. D. (2011). How to grow a mind: Statistics, structure, and abstraction. Science, 331(6022), 1279-1285.
38. van der Maaten, L., & Hinton, G. E. (2008). Visualizing data using t-SNE. Journal of Machine Learning Research, 9, 2579-2605.
39. Vincent, P., Larochelle, H., Lajoie, I., Bengio, Y., & Manzagol, P.-A. (2010). Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion. Journal of Machine Learning Research, 11, 3371-3408.
40. Wang, H., Yan, S., Huang, T. S., & Tang, X. (2007). A convengent solution to tensor subspace learning. In Proceedings of the 20th International Joint Conference on Artificial Intelligence. San Francisco: Morgan Kaufmann.
41. Weinberger, K. Q., Blitzer, J., & Saul, L. K. (2005). Distance metric learning for large margin nearest neighbor Classification. In Y. Weis, B. Scḧolkopf, & J. Platt (Eds.), Advances in neural information processing systems, 18. Cambridge, MA: MIT Press.
42. Yan, S., Xu, D., Zhang, B., Zhang, H.-J., Yang, Q., & Lin, S. (2007). Graph embedding and extensions: A general framework for dimensionality reduction. IEEE Trans. Pattern Anal. Mach. Intell., 29(1), 40-51.
43. Yang, J., Zhang, D., Frangi, A. F., & Yang, J.-Y. (2004). Two-dimensional PCA: A new approach to appearance-based face representation and recognition. IEEE Trans. Pattern Anal. Mach. Intell., 26(1), 131-137.
44. Ye, J., Janardan, R., & Li, Q. (2004). Two-dimensional linear discriminant analysis. In L. Saul, Y. Weiss, & L. Bottou (Eds.), Advances in neural information processing systems, 17. Cambridge, MA: MIT Press.
45. Zhong, G., Li, W.-J., Yeung, D.-Y., Hou, X., & Liu, C.-L. (2010). Gaussian process latent random field. In Proceedings of the 24th AAAI Conference on Artificial Intelligence. Cambridge, MA: MIT Press.