Weighted Scatter-Difference-Based Two DimensionalDiscriminant Analysis for Face Recognition

Affiliation(s)

Laboratory of Conception and Systems, Faculty of Sciences, University of Mohamed V-AGDAL, Rabat, Morocco.

Laboratory of Conception and Systems, Faculty of Sciences, University of Mohamed V-AGDAL, Rabat, Morocco.

ABSTRACT

Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension. It has been used widely in many applications involving high-dimensional data, such as face recognition, image retrieval, etc. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singular. A well-known approach to deal with the singularity problem is to apply an intermediate dimension reduction stage using Principal Component Analysis (PCA) before LDA. The algorithm, called PCA + LDA, is used widely in face recognition. However, PCA + LDA have high costs in time and space, due to the need for an eigen-decomposition involving the scatter matrices. Also, Two Dimensional Linear Discriminant Analysis (2DLDA) implicitly overcomes the singular- ity problem, while achieving efficiency. The difference between 2DLDA and classical LDA lies in the model for data representation. Classical LDA works with vectorized representation of data, while the 2DLDA algorithm works with data in matrix representation. To deal with the singularity problem we propose a new technique coined as the Weighted Scatter-Difference-Based Two Dimensional Discriminant Analysis (WSD2DDA). The algorithm is applied on face recognition and compared with PCA + LDA and 2DLDA. Experiments show that WSD2DDA achieve competitive recognition accuracy, while being much more efficient.

Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension. It has been used widely in many applications involving high-dimensional data, such as face recognition, image retrieval, etc. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singular. A well-known approach to deal with the singularity problem is to apply an intermediate dimension reduction stage using Principal Component Analysis (PCA) before LDA. The algorithm, called PCA + LDA, is used widely in face recognition. However, PCA + LDA have high costs in time and space, due to the need for an eigen-decomposition involving the scatter matrices. Also, Two Dimensional Linear Discriminant Analysis (2DLDA) implicitly overcomes the singular- ity problem, while achieving efficiency. The difference between 2DLDA and classical LDA lies in the model for data representation. Classical LDA works with vectorized representation of data, while the 2DLDA algorithm works with data in matrix representation. To deal with the singularity problem we propose a new technique coined as the Weighted Scatter-Difference-Based Two Dimensional Discriminant Analysis (WSD2DDA). The algorithm is applied on face recognition and compared with PCA + LDA and 2DLDA. Experiments show that WSD2DDA achieve competitive recognition accuracy, while being much more efficient.

Cite this paper

H. Ahmed, M. Jedra and N. Zahid, "Weighted Scatter-Difference-Based Two DimensionalDiscriminant Analysis for Face Recognition,"*Intelligent Information Management*, Vol. 4 No. 4, 2012, pp. 108-114. doi: 10.4236/iim.2012.44017.

H. Ahmed, M. Jedra and N. Zahid, "Weighted Scatter-Difference-Based Two DimensionalDiscriminant Analysis for Face Recognition,"

References

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[7] X. Li, “Weighted Maximum Scatter Difference Based Feature Extraction and Its Application to Face Recognition,” Machine Vision and Applications, Vol. 22, No. 3, 2011, pp. 591-595.

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[13] E. K. Tang, P. N. Suganthan, X. Yao and A. K. Qin, “Linear Dimensionality Reduction Using Relevance Weighted LDA,” Pattern Recognition, Vol. 38, No. 4, 2005, pp. 485-493. doi:10.1016/j.patcog.2004.09.005

[14] K. Chougdali, M. Jedra and N. Zahid, “Kernel Weighted Scatter Difference Discriminant Analysis,” Journal of Image Analysis and Recognition, Vol. 5112, 2008, pp. 977983. doi:10.1007/978-3-540-69812-8_97

[15] W. Zhao, A. Krishnaswamy, R. Chellappa, D. L. Swets and J. Weng, “Discriminant Analysis of Principal Components for Face Recognition-FGR,” International Conference on Automatic Face and Gesture Recognition, 1416 April 1998, pp. 336-341.

[16] W. Zhao, R. Chellappa and N. Nandhakumar, “Emprical performance Analysis of Linear Discriminant, Classifiers,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition, College Park, 23-25 June 1998, pp. 164-169.

[17] W. Zhao, “Subspace Methods in Object/Face Recognition,” International Conference on Neural Networks IEEE, College Park, 1999. pp. 3260-3264.

[18] F. X. Song, D. Zhang, Q. L. Chen and J. Z. Wang, “Face Recognition Based on a Novel Linear Discriminant Criterion,” Pattern Analysis and Applications, Vol. 10, No. 3, 2007, pp. 165-174. doi:10.1007/s10044-006-0057-3

[19] S. L. Guan and X. D. Li, “Improved Maximum Scatter Difference Discriminant Analysis for Face Recognition,” Proceedings of the 2009 International Workshop on Information Security and Application (IWISA 2009), Qingdao, 21-22 November 2009.

[20] M. Addlesee, C. Turner and A. Hopper, “Displaying the Future,” 4th International Scientific Conference on Work with Display Units, Milan, October 1994, Technical Report 94.13http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html

[21] A. S. Georghiades, P. N. Belhumeur and D. J. Kriegman, “From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 23, No. 6, 2001, pp. 643-660. http://cvc.yale.edu/projects/yalefacesB/yalefacesB.html

[22] N. Gourier, D. Hall and J. L. Crowley, “Estimating Face Orientation from Robust Detection of Salient Facial Features.”http://www-prima.inrialpes.fr/perso/Gourier/Pointing04-Gourier.pdf

[23] “Head Pose Image Database,” International Workshop on Visual Observation of Deictic Gestures, Cambridge, 2004.http://www-prima.inrialpes.fr/perso/Gourier/Faces/HPDatabase.html

[1] R. O. Dudo, P. E. Hart and D. Stork, “Pattern Classification,” Wiley, New York, 2000.

[2] K. Fukunage, “Introduction to Statistical Pattren Classification,” Academic Press, San Diego, 1990.

[3] P. N. Belhumeour, J. P. Hespanha and D. J. Kriegman. “Eiegnfaces vs Fisherfaces: Recognition Using Class Specific Linear Projection,” IEEE Transactions on Pattren Analysis and Machine Intelligence, Vol. 19, No. 7, 1997, pp. 711-720. doi:10.1109/34.598228

[4] D. L. Swets and J. Y. Weng, “Using Discriminant Eigenfeatures for Image Retrieval,” IEEE Transaction on Pattren Analysis and Machine Intelligence, Vol. 18, No. 8, 1996, pp. 831-836.

[5] S. Dudoit, J. Fridlyand and T. P. Speed, “Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data,” Journal of the American Statistical Association, Vol. 97, No. 457, 2002, pp. 77-87. doi:10.1198/016214502753479248

[6] W. J. Krzanowski, P. Jonathan, W. V. McCarthy and M. R. Thomas, “Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data,” Applied Statistics, Vol. 44, No. 1, 1995, pp. 101-115. doi:10.2307/2986198

[7] X. Li, “Weighted Maximum Scatter Difference Based Feature Extraction and Its Application to Face Recognition,” Machine Vision and Applications, Vol. 22, No. 3, 2011, pp. 591-595.

[8] J. Yang and D. Zhang, “Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26, No. 1, 2004, pp. 131137. doi:10.1109/TPAMI.2004.1261097

[9] J. Yang and J. Y. Yang, “Form Image Vector to Matrix: A Straightforward Image Projection Technique-IMPCA vs PCA,” Pattern Recognition, Vol. 35, No. 9, 2002, pp. 1997-1999. doi:10.1016/S0031-3203(02)00040-7

[10] J. Ye, R. Janardan and Q. Li, “Two Dimensional Linear Discriminant Analysis,” Proceedings Neural Information Processing Systems (NIPS), 2004, pp. 1569-1576.

[11] J. Ye, “Generalized Low Rank Approximations of Matrices,” The Twenty-First International Conference on Machine Learning, Banff, Vol. 69, 2004, p. 112.

[12] M. Li and B. Yuang, “2D-LDA: A Novel Statistical Linear Discriminant Analysis for Image Matrix,” Pattern Recognition Letters, Vol. 26, No. 5, 2005, pp. 527-532.doi:10.1016/j.patrec.2004.09.007

[13] E. K. Tang, P. N. Suganthan, X. Yao and A. K. Qin, “Linear Dimensionality Reduction Using Relevance Weighted LDA,” Pattern Recognition, Vol. 38, No. 4, 2005, pp. 485-493. doi:10.1016/j.patcog.2004.09.005

[14] K. Chougdali, M. Jedra and N. Zahid, “Kernel Weighted Scatter Difference Discriminant Analysis,” Journal of Image Analysis and Recognition, Vol. 5112, 2008, pp. 977983. doi:10.1007/978-3-540-69812-8_97

[15] W. Zhao, A. Krishnaswamy, R. Chellappa, D. L. Swets and J. Weng, “Discriminant Analysis of Principal Components for Face Recognition-FGR,” International Conference on Automatic Face and Gesture Recognition, 1416 April 1998, pp. 336-341.

[16] W. Zhao, R. Chellappa and N. Nandhakumar, “Emprical performance Analysis of Linear Discriminant, Classifiers,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition, College Park, 23-25 June 1998, pp. 164-169.

[17] W. Zhao, “Subspace Methods in Object/Face Recognition,” International Conference on Neural Networks IEEE, College Park, 1999. pp. 3260-3264.

[18] F. X. Song, D. Zhang, Q. L. Chen and J. Z. Wang, “Face Recognition Based on a Novel Linear Discriminant Criterion,” Pattern Analysis and Applications, Vol. 10, No. 3, 2007, pp. 165-174. doi:10.1007/s10044-006-0057-3

[19] S. L. Guan and X. D. Li, “Improved Maximum Scatter Difference Discriminant Analysis for Face Recognition,” Proceedings of the 2009 International Workshop on Information Security and Application (IWISA 2009), Qingdao, 21-22 November 2009.

[20] M. Addlesee, C. Turner and A. Hopper, “Displaying the Future,” 4th International Scientific Conference on Work with Display Units, Milan, October 1994, Technical Report 94.13http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html

[21] A. S. Georghiades, P. N. Belhumeur and D. J. Kriegman, “From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 23, No. 6, 2001, pp. 643-660. http://cvc.yale.edu/projects/yalefacesB/yalefacesB.html

[22] N. Gourier, D. Hall and J. L. Crowley, “Estimating Face Orientation from Robust Detection of Salient Facial Features.”http://www-prima.inrialpes.fr/perso/Gourier/Pointing04-Gourier.pdf

[23] “Head Pose Image Database,” International Workshop on Visual Observation of Deictic Gestures, Cambridge, 2004.http://www-prima.inrialpes.fr/perso/Gourier/Faces/HPDatabase.html