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Enhancing Bilinear Subspace Learning by Element Rearrangement
October 2009 (vol. 31 no. 10)
pp. 1913-1920
ASCII Text
x 
 
Dong Xu, Shuicheng Yan, Stephen Lin, Thomas S. Huang, Shih-Fu Chang, "Enhancing Bilinear Subspace Learning by Element Rearrangement," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 10, pp. 1913-1920, October, 2009.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2009.51,
author = {Dong Xu and Shuicheng Yan and Stephen Lin and Thomas S. Huang and Shih-Fu Chang},
title = {Enhancing Bilinear Subspace Learning by Element Rearrangement},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {31},
number = {10},
issn = {0162-8828},
year = {2009},
pages = {1913-1920},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2009.51},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Enhancing Bilinear Subspace Learning by Element Rearrangement
IS - 10
SN - 0162-8828
SP1913
EP1920
EPD - 1913-1920
A1 - Dong Xu,
A1 - Shuicheng Yan,
A1 - Stephen Lin,
A1 - Thomas S. Huang,
A1 - Shih-Fu Chang,
PY - 2009
KW - Bilinear subspace learning
KW - element rearrangement
KW - earth mover's distance
KW - dimensionality reduction.
VL - 31
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
Dong Xu, Nanyang Technological University, Singapore
Shuicheng Yan, National University of Singapore, Singapore
Stephen Lin, Microsoft Research Asia, Beijing
Thomas S. Huang, University of Illinois at Urbana-Champaign, Urbana
Shih-Fu Chang, Columbia University, New York
The success of bilinear subspace learning heavily depends on reducing correlations among features along rows and columns of the data matrices. In this work, we study the problem of rearranging elements within a matrix in order to maximize these correlations so that information redundancy in matrix data can be more extensively removed by existing bilinear subspace learning algorithms. An efficient iterative algorithm is proposed to tackle this essentially integer programming problem. In each step, the matrix structure is refined with a constrained Earth Mover's Distance procedure that incrementally rearranges matrices to become more similar to their low-rank approximations, which have high correlation among features along rows and columns. In addition, we present two extensions of the algorithm for conducting supervised bilinear subspace learning. Experiments in both unsupervised and supervised bilinear subspace learning demonstrate the effectiveness of our proposed algorithms in improving data compression performance and classification accuracy.

[1] M. Turk and A. Pentland, “Face Recognition Using Eigenfaces,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 586-591, 1991.
[2] P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces versus Fisherfaces: Recognition Using Class Specific Linear Projection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 711-720, July 1997.
[3] M. Vasilescu and D. Terzopoulos, “Multilinear Subspace Analysis for Image Ensembles,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 93-99, 2003.
[4] H. Chen, H. Chang, and T. Liu, “Local Discriminant Embedding and Its Variants,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 846-852, 2005.
[5] G. Dai and D. Yeung, “Tensor Embedding Methods,” Proc. Assoc. for the Advancement of Artificial Intelligence, pp. 330-335, 2006.
[6] D. Tao, X. Li, W. Hu, S.J. Maybank, and X. Wu, “Supervised Tensor Learning,” Proc. IEEE Conf. Data Mining, pp. 450-457, 2005.
[7] D. Tao, X. Li, X. Wu, and S.J. Maybank, “General Tensor Discriminant Analysis and Gabor Features for Gait Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 10, pp. 1700-1715, Oct. 2007.
[8] D. Xu, S. Yan, L. Zhang, H. Zhang, Z. Liu, and H. Shum, “Concurrent Subspace Analysis,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 203-208, 2005.
[9] S. Yan, D. Xu, Q. Yang, L. Zhang, X. Tang, and H. Zhang, “Discriminant Analysis with Tensor Representation,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 526-532, 2005.
[10] J. Yang, D. Zhang, A. Frangi, and J. Yang, “Two-Dimensional pca: A New Approach to Appearance-Based Face Representation and Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 131-137, Jan. 2004.
[11] J. Ye, “Generalized Low Rank Approximations of Matrices,” Machine Learning, vol. 61, pp. 167-191, 2005.
[12] J. Ye, R. Janardan, and Q. Li, “Two-Dimensional Linear Discriminant Analysis,” Advances in Neural Information Processing Systems, pp. 1569-1576, MIT Press, 2004.
[13] E. Simoncelli and B. Olshausen, “Natural Image Statistics and Neural Representation,” Ann. Rev. Neuroscience, vol. 24, pp. 1193-1216, 2001.
[14] G. Nemhauser and L. Wolsey, Integer and Combinatorial Optimization. Wiley, 1988.
[15] Y. Rubner, C. Tomasi, and L. Guibas, “The Earth Mover's Distance as a Metric for Image Retrieval,” Int'l J. Computer Vision, vol. 40, no. 2, pp. 99-121, Nov. 2000.
[16] P. Jensen and J. Bard, Operations Research Models and Methods. John Wiley and Sons, 2003.
[17] S. Yan, D. Xu, B. Zhang, H. Zhang, Q. Yang, and S. Lin, “Graph Embedding and Extensions: A General Framework for Dimensionality Reduction,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 1, pp. 40-51, Jan. 2007.
[18] T. Jebara, “Images as Bags of Pixels,” Proc. IEEE Conf. Computer Vision, pp.265-272, 2003.
[19] T. Jebara, “Convex Invariance Learning,” Proc. Int'l Conf. Artificial Intelligence and Statistics, 2003.
[20] T. Jebara, “Kernelizing Sorting, Permutation and Alignment for Minimum Volume PCA,” Proc. Conf. Learning Theory, 2004.
[21] P. Shivaswamy and T. Jebara, “Permutation Invariant svms,” Proc. Int'l Conf. Machine Learning, 2006.
[22] T. Sim, S. Baker, and M. Bsat, “The CMU Pose, Illumination, and Expression Database,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 12, pp. 1615-1618, Dec. 2003.
[23] P. Phillips, H. Moon, S. Rizvi, and P. Rauss, “The Feret Evaluation Methodology for Face-Recognition Algorithms,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 10, pp. 1090-1104, Oct. 2000.
[24] S. Yan, D. Xu, S. Lin, T. Huang, and S.-F. Chang, “Element Rearrangement for Tensor-Based Subspace Learning,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2007.
[25] X. He, S. Yan, Y. Hu, P. Niyogi, and H. Zhang, “Face Recognition Using Laplacianfaces,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 3, pp. 328-340, Mar. 2005.
[26] J. Munkres, “Algorithms for the Assignment and Transportation Problems,” J. SIAM, vol. 5, no. 1, pp. 32-38, Mar. 1957.

Index Terms:
Bilinear subspace learning, element rearrangement, earth mover's distance, dimensionality reduction.
Citation:
Dong Xu, Shuicheng Yan, Stephen Lin, Thomas S. Huang, Shih-Fu Chang, "Enhancing Bilinear Subspace Learning by Element Rearrangement," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 10, pp. 1913-1920, Oct. 2009, doi:10.1109/TPAMI.2009.51
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