Abstract
In biometric recognition applications, the number of training examples per class is limited and consequently the conventional quadratic classifier either performs poorly or cannot be calculated. Other non-conventional quadratic classifiers have been used in limited sample and high dimensional classification problems. In this paper, a new quadratic classifier called Maximum Entropy Covariance Selection (MECS) is presented. This classifier combines the sample group covariance matrices and the pooled covariance matrix under the principle of maximum entropy. This approach is a direct method that not only deals with the singularity and instability of the maximum likelihood covariance estimator, but also does not require an optimisation procedure. In order to evaluate the MECS effectiveness, experiments on face and fingerprint recognition were carried out and compared with other similar classifiers, including the Reguralized Discriminant Analysis (RDA), the Leave-One-Out Covariance estimator (LOOC) and the Simplified Quadratic Discriminant Function (SQDF). In both applications, using the publicly released databases FERET and NIST-4, the MECS classifier achieved the lowest classification error.
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References
J.H. Friedman, “Reguralized Discriminant Analysis”, Journal of the American Statistical Association, vol. 84, no. 405, pp. 165–175, March 1989.
K. Fukunaga, Introduction to Statistical Pattern Recognition, second edition. Boston: Academic Press, 1990.
J.P. Hoffbeck and D.A. Landgrebe, “Covariance Matrix Estimation and Classification With Limited Training Data”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 7, pp. 763–767, July 1996.
R. A. Horn and C.R. Johnson, Matrix Analysis. Cambridge University Press, 1985.
E.T. Jaynes, “On the rationale of maximum-entropy methods”, Proceedings of the IEEE, vol. 70, pp. 939–952, 1982.
A.K. Jain and B. Chandrasekaran, “Dimensionality and Sample Size Considerations in Pattern Recognition Practice”, Handbook of Statistics, P.R. Krishnaiah and L.N. Kanal Eds, vol. 2, pp. 835–855, North Holland, 1982.
S. Omachi, F. Sun, and H. Aso, “A New Approximation Method of the Quadratic Discriminant Function”, SSPR&SPR 2000, Springer-Verlag LNCS 1876, pp. 601–610, 2000.
P. J. Phillips, H. Wechsler, J. Huang and P. Rauss, “The FERET database and evaluation procedure for face recognition algorithms”, Image and Vision Computing Journal, vol. 16, no. 5, pp. 295–306, 1998.
S. Tadjudin and D.A. Landgrebe, “Covariance Estimation With Limited Training Samples”, Transactions on Geoscience and Remote Sensing, vol. 37, no. 4, July 1999.
C. E. Thomaz, D. F. Gillies and R. Q. Feitosa, “Small Sample Problem in Bayes Plug-in Classifier for Image Recognition”, in proceedings of Int’l Conference on Image and Vision Computing New Zealand, pp. 295–300, Dunedin, New Zealand, November 2001.
M. Turk and A. Pentland, “Eigenfaces for Recognition”, Journal of Cognitive Neuroscience, vol. 3, pp. 72–85, 1991.
C. L. Wilson, G. T. Candela, P. J. Grother, C. I. Watson, and R. A. Wilkinson, “Massively Parallel Neural Network Fingerprint Classification System”, Technical Report NIST IR 4880, National Institute of Standards and Technology, July 1992.
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Thomaz, C.E., Gillies, D.F., Feitosa, R.Q. (2002). A New Quadratic Classifier Applied to Biometric Recognition. In: Tistarelli, M., Bigun, J., Jain, A.K. (eds) Biometric Authentication. BioAW 2002. Lecture Notes in Computer Science, vol 2359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47917-1_19
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DOI: https://doi.org/10.1007/3-540-47917-1_19
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