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Extracting the optimal dimensionality for local tensor discriminant analysis. (English) Zbl 1159.68545
Summary: Supervised dimensionality reduction with tensor representation has attracted great interest in recent years. It has been successfully applied to problems with tensor data, such as image and video recognition tasks. However, in the tensor-based methods, how to select the suitable dimensions is a very important problem. Since the number of possible dimension combinations exponentially increases with respect to the order of tensor, manually selecting the suitable dimensions becomes an impossible task in the case of high-order tensor. In this paper, we aim at solving this important problem and propose an algorithm to extract the optimal dimensionality for local tensor discriminant analysis. Experimental results on a toy example and real-world data validate the effectiveness of the proposed method.

68T10 Pattern recognition, speech recognition
COIL-20; MA Toolbox
Full Text: DOI
[1] Fukunaga, K., Introduction to statistical pattern recognition, (1990), Academic Press Boston, MA · Zbl 0711.62052
[2] Belhumeur, P.N.; Hespanha, J.P.; Kriegman, D.J., Eigenfaces vs fisherfaces: recognition using class specific linear projection, IEEE trans. pattern anal. Mach. intell., 19, 7, 711-720, (1997)
[3] Chen, L.; Liao, H.; Ko, M.; Lin, J.; Yu, G., A new LDA based face recognition system which can solve the small sample size problem, Pattern recognition, 33, 10, 1713-1726, (2000)
[4] Yu, H.; Yang, J., A direct LDA algorithm for high-dimensional data—with application to face recognition, Pattern recognition, 34, 2067-2070, (2001) · Zbl 0993.68091
[5] Liu, J.; Chen, S., Discriminant common vectors versus neighbourhood components analysis and laplacianfaces: a comparative study in small sample size problem, Image vision comput., 24, 3, 249-262, (2006)
[6] Liu, J.; Chen, S.; Tan, X., A study on three linear discriminant analysis based methods in small sample size problem, Pattern recognition, 41, 1, 102-116, (2008) · Zbl 1119.68180
[7] J. Ye, R. Janardan, Q. Li, Two-dimensional linear discriminant analysis, NIPS, 2004.
[8] J. Ye, Generalized low rank approximations of matrices, ICML, 2004.
[9] S. Yan, D. Xu, Q. Yang, L. Zhang, X. Tang, H. Zhang, Discriminant analysis with tensor representation, CVPR, 2005, pp. 526-532.
[10] X. He, D. Cai, P. Niyogi, Tensor subspace analysis, NIPS, 2005.
[11] Tao, D.; Li, X.; Wu, X.; Maybank, S.J., General tensor discriminant analysis and Gabor features for gait recognition, IEEE trans. pattern anal. Mach. intell., 29, 10, 1700-1715, (2007)
[12] Bressan, M.; Vitrià, J., Nonparametric discriminant analysis and nearest neighbor classification, Pattern recognition lett., 24, 15, 2743-2749, (2003)
[13] S. Yan, D. Xu, B. Zhang, H. Zhang, Graph embedding: a general framework for dimensionality reduction, CVPR, 2005, pp. 830-837.
[14] M. Sugiyama, Local Fisher discriminant analysis for supervised dimensionality reduction, ICML, 2006, pp. 905-912.
[15] H.-T. Chen, H.-W. Chang, T.-L. Liu, Local discriminant embedding and its variants, CVPR, 2005, pp. 846-853.
[16] F. Nie, S. Xiang, C. Zhang, Neighborhood minmax projections, IJCAI, 2007, pp. 993-998.
[17] W. Zhang, X. Xue, Z. Sun, Y.-F. Guo, H. Lu, Optimal dimensionality of metric space for classification, ICML, 2007, pp. 1135-1142.
[18] F. Nie, S. Xiang, Y. Song, C. Zhang, Optimal dimensionality discriminant analysis and its application to image recognition, CVPR, 2007.
[19] L.D. Lathauwer, Signal processing based on multilinear algebra, Ph.D. Thesis, Faculteit der Toegepaste Wetenschappen, Katholieke Universiteit Leuven, 1997.
[20] He, X.F.; Yan, S.C.; Hu, Y.X.; Niyogi, P.; Zhang, H.J., Face recognition using laplacianfaces, IEEE trans. pattern anal. Mach. intell., 27, 3, 328-340, (2005)
[21] Golub, G.H.; van Loan, C.F., Matrix computations, (1996), The Johns Hopkins University Press Baltimore, MD, USA · Zbl 0865.65009
[22] H. Li, T. Jiang, K. Zhang, Efficient and robust feature extraction by maximum margin criterion, NIPS, 2003.
[23] D.B. Graham, N.M. Allinson, Characterizing virtual eigensignatures for general purpose face recognition, in: Face Recognition: From Theory to Applications, NATO ASI Series F, Computer and Systems Sciences.
[24] S.A. Nene, S.K. Nayar, H. Murase, Columbia object image library (COIL-20), Technical Report CUCS-005-96, Columbia University, 1996.
[25] ISMIR audio description contest \(\langle\)http://ismir2004.ismir.net/genre_contest/index.htm⟩, 2004.
[26] E. Pampalk, A matlab toolbox to compute similarity from audio, ISMIR, 2004.
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