Abstract
A critical issue of applying Linear (or Fisher) Discriminant Analysis (LDA) is the singularity and instability of the within-class scatter matrix. In practice, particularly in image recognition applications such as face recognition, there are often a large number of pixels or pre-processed features available, but the total number of training patterns is limited and commonly less than the dimension of the feature space. Hence, a considerable amount of effort has been devoted to the design of Fisher-based methods, for targeting limited sample and high dimensional problems. In this paper, a new Fisher-based method is proposed. It is based on a novel regularisation approach for the within-class scatter matrix. In order to evaluate its effectiveness, experiments on face recognition using the well-known ORL and FERET face databases were carried out and compared with similar methods, such as Fisherfaces, Chen et al.’s, Yu and Yang’s, and Yang and Yang’s LDA-based methods. In both databases, our method improved the LDA classification performance without a PCA intermediate step and using less discriminant features.
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Belhumeur, P.N., Hespanha, J.P., Kriegman, D.J.: Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection. IEEE Trans. Pattern Analysis and Machine Intelligence 19(7), 711–720 (1997)
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)
Friedman, J.H.: Reguralized discriminant analysis. Journal of the American Statistical Association 84(405), 165–175 (1989)
Fukunaga, K.: Introduction to Statistical Pattern Recognition. Academic Press, New York (1990)
Greene, T., Rayens, W.S.: Covariance pooling and stabilization for classification. Computational Statistics & Data Analysis 11, 17–42 (1991)
Jain, A.K., Chandrasekaran, B.: Dimensionality and sample size considerations in pattern recognition practice. In: Krishnaiah, P.R., Kanal, L.N. (eds.) Handbook of Statistics, vol. 2, pp. 835–855. North Holland, Amsterdam (1982)
Liu, K., Cheng, Y., Yang, J.: Algebraic feature extraction for image recognition based on an optimal discriminant criterion. Pattern Recognition 26(6), 903–911 (1993)
Mika, S., Ratsch, G., Weston, J., Scholkopf, B., Muller, K.–R.: Fisher discriminant analysis with kernels. IEEE Neural Networks for Signal Processing IX, 41–48 (1999)
O’Sullivan, F.: A Statistical Perspective on Ill-Posed Inverse Problems. Statistical Science 1, 502–527 (1986)
Rayens, W.S.: A Role for Covariance Stabilization in the Construction of the Classical Mixture Surface. Journal of Chemometrics 4, 159–169 (1990)
Samal, A., Iyengar, P.: Automatic Recognition and Analysis of Human Faces and Facial Expressions: A Survey. Pattern Recognition 25(1), 65–77 (1992)
Swets, D.L., Weng, J.J.: Using Discriminant Eigenfeatures for Image Retrieval. IEEE Trans. Pattern Analysis and Machine Intelligence 18(8), 831–836 (1996)
Thomaz, C.E., Gillies, D.F., Feitosa, R.Q.: A New Quadratic Classifier applied to Biometric Recognition. In: Tistarelli, M., Bigun, J., Jain, A.K. (eds.) ECCV 2002. LNCS, vol. 2359, pp. 186–196. Springer, Heidelberg (2002)
Turk, M., Pentland, A.: Eigenfaces for Recognition. Journal of Cognitive Neuroscience 3, 71–86 (1991)
Yang, J., Yang, J.: Why can LDA be performed in PCA transformed space? Pattern Recognition 36, 563–566 (2003)
Yu, H., Yang, J.: A direct LDA algorithm for high dimensional data – with application to face recognition. Pattern Recognition 34, 2067–2070 (2001)
Zhao, W., Chellappa, R., Krishnaswamy, A.: Discriminant Analysis of Principal Components for Face Recognition. In: Proc. 2nd Int’l. Conference on Automatic Face and Gesture Recognition, pp. 336–341 (1998)
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Thomaz, C.E., Gillies, D.F. (2003). A New Fisher-Based Method Applied to Face Recognition. In: Petkov, N., Westenberg, M.A. (eds) Computer Analysis of Images and Patterns. CAIP 2003. Lecture Notes in Computer Science, vol 2756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45179-2_73
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DOI: https://doi.org/10.1007/978-3-540-45179-2_73
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