This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Correlation Metric for Generalized Feature Extraction
December 2008 (vol. 30 no. 12)
pp. 2229-2235
Yun Fu, University of Illinois at Urbana-Champaign, Urbana
Shuicheng Yan, National University of Singapore, Singapore
Thomas S. Huang, University of Illinois at Urbana-Champaign, Urbana
Beyond linear and kernel-based feature extraction, we propose in this paper the generalized feature extraction formulation based on the so-called Graph Embedding framework. Two novel correlation metric based algorithms are presented based on this formulation. Correlation Embedding Analysis (CEA), which incorporates both correlational mapping and discriminating analysis, boosts the discriminating power by mapping data from a high-dimensional hypersphere onto another low-dimensional hypersphere and preserving the intrinsic neighbor relations with local graph modeling. Correlational Principal Component Analysis (CPCA) generalizes the conventional Principal Component Analysis (PCA) algorithm to the case with data distributed on a high-dimensional hypersphere. Their advantages stem from two facts: 1) tailored to normalized data, which are often the outputs from the data preprocessing step, and 2) directly designed with correlation metric, which shows to be generally better than Euclidean distance for classification purpose. Extensive comparisons with existing algorithms on visual classification experiments demonstrate the effectiveness of the proposed methods.

[1] Pattern Classification, second ed., R.O. Duda, P.E. Hart, and D.G. Stork, eds. Wiley-Interscience, 2000.
[2] Handbook of Face Recognition, S.Z. Li and A.K. Jain, eds. Springer, 2005.
[3] Y. Fu, S. Yan, and T.S. Huang, “Classification and Feature Extraction by Simplexization,” IEEE Trans. Information Forensics and Security, vol. 3, no. 1, pp. 91-100, 2008.
[4] M.A. Turk and A.P. Pentland, “Face Recognition Using Eigenfaces,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 586-591, 1991.
[5] P.N. Belhumeur, J.P. Hespanha, and D.J. 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.
[6] M.-H. Yang, “Kernel Eigenfaces versus Kernel Fisherfaces: Face Recognition Using Kernel Methods,” Proc. Fifth IEEE Conf. Automatic Face and Gesture Recognition, pp. 215-220, 2002.
[7] B. Moghaddam and A. Pentland, “Probabilistic Visual Learning for Object Representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 696-710, July 1997.
[8] B. Moghaddam, T. Jebara, and A. Pentland, “Bayesian Face Recognition,” Pattern Recognition, vol. 33, no. 11, pp. 1771-1782, 2000.
[9] Z. Li, W. Liu, D. Lin, and X. Tang, “Nonparametric Subspace Analysis for Face Recognition,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 961-966, 2005.
[10] A. Weingessel and K. Hornik, “Local PCA Algorithms,” IEEE Trans. Neural Networks, vol. 11, no. 6, pp. 1242-1250, 2000.
[11] L. Saul and S. Roweis, “Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds,” J. Machine Learning Research, vol. 4, pp.119-155, 2003.
[12] J. Ham, D.D. Lee, S. Mika, and B. Schölkopf, “A Kernel View of the Dimensionality Reduction of Manifolds,” Proc. 21st Int'l Conf. Machine Learning, pp. 369-376, 2004.
[13] S. Roweis and L. Saul, “Nonlinear Dimensionality Reduction by Locally Linear Embedding,” Science, vol. 290, no. 5500, pp. 2323-2326, 2000.
[14] J.B. Tenenbaum, V. de Silva, and J.C. Langford, “A Global Geometric Framework for Nonlinear Dimensionality Reduction,” Science, vol. 290, no. 5500, pp. 2319-2323, 2000.
[15] M. Belkin and P. Niyogi, “Laplacian Eigenmaps for Dimensionality Reduction and Data Representation,” Neural Computation, vol. 15, no. 6, pp. 1373-1396, 2003.
[16] K. Weinberger and L. Saul, “Unsupervised Learning of Image Manifolds by Semidefinite Programming,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 988-995, 2004.
[17] Y. Bengio, J.F. Paiement, P. Vincent, O. Delalleau, N. Roux, and M. Ouimet, “Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering,” Advances in Neural Information Processing Systems, 2004.
[18] S. Yan, D. Xu, B. Zhang, H.-J. 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.
[19] X. He, S. Yan, Y. Hu, P. Niyogi, and H.-J. Zhang, “Face Recognition Using Laplacianfaces,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 3, pp. 328-340, Mar. 2005.
[20] H.-T. Chen, H.-W. Chang, and T.-L. Liu, “Local Discriminant Embedding and Its Variants,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 846-853, 2005.
[21] J. Yang, S. Yan, Y. Fu, X. Li, and T.S. Huang, “Non-Negative Graph Embedding,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2008.
[22] D. Cai, X. He, J. Han, and H.-J. Zhang, “Orthogonal Laplacianfaces for Face Recognition,” IEEE Trans. Image Processing, vol. 15, no. 11, pp. 3608-3614, 2006.
[23] S. Yan, H.-J. Zhang, Y. Hu, B. Zhang, and Q. Cheng, “Discriminant Analysis on Embedded Manifold,” Proc. Eighth European Conf. Computer Vision, pp.121-132, 2004.
[24] D. Cai, X. He, and J. Han, “Spectral Regression for Efficient Regularized Subspace Learning,” Proc. 11th IEEE Conf. Computer Vision, 2007.
[25] M.-H. Yang, “Extended Isomap for Pattern Classification,” Proc. 18th Nat'l Conf. Artificial Intelligence, pp. 224-229, 2002.
[26] Y. Fu, M. Liu, and T.S. Huang, “Conformal Embedding Analysis with Local Graph Modeling on the Unit Hypersphere,” Proc. IEEE CVPR First Workshop Component Analysis, 2007.
[27] Correlation Pattern Recognition, B.V.K.V. Kumar, A. Mahalanobis, and R.D.Juday, eds. Cambridge Univ. Press, 2006.
[28] Y. Ma, S. Lao, E. Takikawa, and M. Kawade, “Discriminant Analysis in Correlation Similarity Measure Space,” Proc. 24th Int'l Conf. Machine Learning, vol. 227, pp. 577-584, 2007.
[29] T. Kim, J. Kittler, and R. Cippola, “Discriminative Learning and Recognition of Image Set Classes Using Canonical Correlations,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 6, pp. 1005-1018, June 2007.
[30] A. Graf, A. Smola, and S. Borer, “Classification in a Normalized Feature Space Using Support Vector Machines,” IEEE Trans. Neural Network, vol. 14, no. 3, pp. 597-605, 2003.
[31] A. Banerjee, I. Dhillon, J. Ghosh, and S. Sra, “Clustering on the Unit Hypersphere Using von Mises-Fisher Distributions,” J. Machine Learning Research, vol. 6, pp. 1345-1382, 2005.
[32] Y. Fu and T.S. Huang, “Correlation Embedding Analysis,” Proc. IEEE Int'l Conf. Image Processing, 2008.
[33] 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.
[34] F. Rapisarda, D. Brigo, and F. Mercurio, “Parameterizing Correlations: A Geometric Interpretation,” IMA J. Management Math., vol. 18, no. 1, pp. 55-73, 2007.
[35] M. Eisen, P. Spellman, P. Brown, and D. Botstein, “Cluster Analysis and Display of Genome-Wide Expression Patterns,” Proc. Nat'l Academy of Sciences of the USA, vol. 95, pp. 14863-14868, 1998.
[36] D. Lin, S. Yan, and X. Tang, “Comparative Study: Face Recognition on Unspecific Persons Using Linear Subspace Methods,” Proc. IEEE Int'l Conf. Image Processing, vol. 3, pp. 764-767, 2005.
[37] Y. Fu and T.S. Huang, “Image Classification Using Correlation Tensor Analysis,” IEEE Trans. Image Processing, vol. 17, no. 2, pp. 226-234, 2008.
[38] D. Cai, X. He, K. Zhou, J. Han, and H. Bao, “Locality Sensitive Discriminant Analysis,” Proc. 20th Int'l Joint Conf. Artificial Intelligence, pp. 708-713, 2007.
[39] 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.
[40] A. Georghiades, P. Belhumeur, and D. Kriegman, “From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 643-660, June 2001.
[41] K. Lee, J. Ho, and D. Kriegman, “Acquiring Linear Subspaces for Face Recognition under Variable Lighting,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 5, pp. 684-698, May 2005.
[42] D. Tao, X. Li, W. Hu, S.J. Maybank, and X. Wu, “Supervised Tensor Learning,” Knowledge and Information Systems, vol. 13, no. 1, pp. 1-42, 2007.

Index Terms:
Machine learning, Face and gesture recognition, Geometric
Citation:
Yun Fu, Shuicheng Yan, Thomas S. Huang, "Correlation Metric for Generalized Feature Extraction," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 12, pp. 2229-2235, Dec. 2008, doi:10.1109/TPAMI.2008.154
Usage of this product signifies your acceptance of the Terms of Use.