Bidirectional Discriminant Supervised Locality Preserving Projection for Face Recognition

Authors: Yiqin Lin, Wenbo Li

Abstract:

Dimensionality reduction and feature extraction are of crucial importance for achieving high efficiency in manipulating the high dimensional data. Two-dimensional discriminant locality preserving projection (2D-DLPP) and two-dimensional discriminant supervised LPP (2D-DSLPP) are two effective two-dimensional projection methods for dimensionality reduction and feature extraction of face image matrices. Since 2D-DLPP and 2D-DSLPP preserve the local structure information of the original data and exploit the discriminant information, they usually have good recognition performance. However, 2D-DLPP and 2D-DSLPP only employ single-sided projection, and thus the generated low dimensional data matrices have still many features. In this paper, by combining the discriminant supervised LPP with the bidirectional projection, we propose the bidirectional discriminant supervised LPP (BDSLPP). The left and right projection matrices for BDSLPP can be computed iteratively. Experimental results show that the proposed BDSLPP achieves higher recognition accuracy than 2D-DLPP, 2D-DSLPP, and bidirectional discriminant LPP (BDLPP).

Keywords: Face recognition, dimension reduction, locality preserving projection, discriminant information, bidirectional projection.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3593178

References:

[1] P. Baldi and G. W. Hatfield, DNA Microarrays and Gene Expression: From Experiments to Data Analysis and Modeling, Cambridge, 2002.
[2] P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman, Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection, IEEE Transactions on Pattern Analysis and Machine Intelligence, 19 (1997), pp. 711–720.
[3] C. M. Bishop, Pattern Recognition and Machine Learning, Springer, 2006.
[4] L. Chen, H. M. Liao, M. Ko, J. Lin, and G. Yu, A new LDA-based face recognition system which can solve the small sample size problem, Pattern Recognition, 33 (2000), pp. 1713–1726.
[5] S. B. Chen, H. F. Zhao, M. Kong, and B. Luo, 2D-LPP: a two-dimensional extension of locality preserving projections, Neurocomputing, 70 (2007), pp. 912–921.
[6] W. K. Ching, D. Chu, L. Z. Liao, and X. Wang, Regularized orthogonal linear discriminant analysis, Pattern Recognition, 45 (2012), pp. 2719–2732.
[7] D. Chu and S. T. Goh, A new and fast implementation for null space based linear discriminant analysis, Pattern Recognition, 43 (2010), pp. 1373–1379.
[8] , A new and fast orthogonal linear discriminant analysis on undersampled problems, SIAM Journal on Scientific Computing, 32 (2010), pp. 2274–2297.
[9] D. Chu, S. T. Goh, and Y. S. Hung, Characterization of all solutions for undersampled uncorrelated linear discriminant analysis problems, SIAM Journal on Matrix Analysis and Applications, 32 (2011), pp. 820–844.
[10] D. Q. Dai and P. C. Yuen, Regularized discriminant analysis and its application to face recognition, Pattern Recognition, 36 (2003), pp. 845–847.
[11] R. Q. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, John Wiley and Sons, second ed., 2001.
[12] 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, 97 (2002), pp. 77–87.
[13] J. H. Friedman, Regularized discriminant analysis, Journal of the American Statistical Association, 84 (1989), pp. 165–175.
[14] K. Fukunaga, Introduction to Statistical Pattern Recognition, CA: Academic, San Diego, second ed., 1990.
[15] Y. Guo, T. Hastie, and R. Tibshirani, Regularized linear discriminant analysis and its application in microarray, Biostatistics, 8 (2007), pp. 86–100.
[16] X. He and P. Niyogi, Locality preserving projections, Advances in Neural Information Processing Systems, 16 (2004), pp. 153–160.
[17] , Tensor subspace analysis, Advances in Neural Information Processing Systems, 18 (2005).
[18] P. Howland and H. Park, Generalizing discriminant analysis using the generalized singular value decomposition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 26 (2004), pp. 995–1006.
[19] A. K. JAIN AND R. C. DUBES, Algorithms for Clustering Data, Prentice Hall, 1988.
[20] Z. Jin, J. Y. Yang, Z. S. Hu, and Z. Lou, Face recognition based on the uncorrelated discriminant transformation, Pattern Recognition, 34 (2001), pp. 1405–1416.
[21] G. Kowalski, Information Retrieval Systems: Theory and Implementation, Kluwer Academic Publishers, 1997.
[22] M. Li and B. Z. Yuan, 2D-LDA: a statistical linear discriminant analysis for image matrix, Pattern Recognition Letters, 26 (2005), pp. 527–532.
[23] C. X. Ren and D. Q. Dai, Bilinear lanczos components for fast dimensionality reduction and feature extraction, Pattern Recognition, 43 (2010), pp. 3742–3752.
[24] D. L. Swets and J. Weng, Using discriminant eigenfeatures for image retrieval, IEEE Transactions on Pattern Analysis and Machine Intelligence, 18 (1996), pp. 831–836.
[25] M. Turk and A. Pentland, Eigenfaces for recognition, Journal of Cognitive Neuroscience, 3 (1991), pp. 71–86.
[26] S. J. Wang, C. G. Zhou, N. Zhang, X. J. Peng, Y. H. Chen, and X. Liu, Face recognition using second-order discriminant tensor subspace analysis, Neurocomputing, 74 (2011), pp. 2142–2156.
[27] Y. Xu, G. Feng, and Y. Zhao, One improvement to two-dimensional locality preserving projection method for use with face recognition, Neurocomputing, 73 (2009), pp. 245–249.
[28] J. Yang, D. Zhang, A. F. Frangi, and J. Y. Yang, Two-dimensional PCA: a new approach to appearance-based face representation and recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 26 (2004), pp. 131–137.
[29] J. Ye, Characterization of a family of algorithms for generalized discriminant analysis on undersampled problems, Journal of Machine Learning Research, 6 (2005), pp. 483–502.
[30] , Generalized low rank approximations of matrices, Machine Learning, 61 (2005), pp. 167–191.
[31] J. Ye, R. Janardan, C. H. Park, and H. Park, An optimization criterion for generalized discriminant analysis on undersampled problems, IEEE Transactions on Pattern Analysis and Machine Intelligence, 26 (2004), pp. 982–994.
[32] J. Ye and Q. Li, A two-stage linear discriminant analysis via QR-decomposition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27 (2005), pp. 929–941.
[33] W. Yu, Two-dimensional discriminant locality preserving projections for face recognition, Pattern Recognition Letters, 30 (2009), pp. 1378–1383.
[34] W. Yu, X. Teng, and C. Liu, Face recognition using discriminant locality preserving projections, Image and Vision Computing, 24 (2006), pp. 239–248.
[35] Z. Zheng, F. Yang, and W. Tan, Gabor feature-based face recognition using supervised locality preserving projections, Signal Processing, 87 (2007), pp. 2473–2483.
[36] L. Zhu and S. Zhu, Face recognition based on orthogonal discriminant locality preserving projections, Neurocomputing, 70 (2007), pp. 1543–1546.