Abstract
A method for the linear discrimination of two classes is presented. It maximizes the Patrick-Fisher (PF) distance between the projected class-conditional densities. Since the PF distance is a highly nonlinear function, we propose a method, which searches for the directions corresponding to several large local maxima of the PF distance. Its novelty lies in a neural network transformation of the data along a found direction into data with deflated maxima of the PF distance and iteration to obtain the next direction. A simulation study indicates that the method has the potential to find the global maximum of the PF distance.
This work has been partially supported by the Paul Ivanier Center for Robotics and Production Management, Ben Gurion University of the Negev, Israel
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M.E. Aladjem, “Multiclass discriminant mappings”, Signal Processing, vol.35, pp.1–18, 1994.
M.E. Aladjem, “Linear discriminant analysis for two-classes via removal of classification structure”, IEEE Trans. Pattern Anal. Mach. Intell., vol. 19, pp. 187–192, 1997.
M.E. Aladjem, “Nonparametric discriminant analysis via recursive optimization of Patrick-Fisher distance”, IEEE Trans. on Syst., Man, Cybern., vol.28B, pp.292–299, 1998.
M.E.Aladjem, “Training of an ML neural network for classification via recursive reduction of the class separation”, 14th Int. Conf. on Pattern Recognition, Brisbane, Queensland, Australia, 17–20 August, 1998 (in press).
C.M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press Inc., New York, 1995.
P.A. Devijver and J. Kittler, Pattern Recognition: A Statistical Approach, Prentice-Hall International, Inc., London,1982.
J.H. Friedman, “Exploratory projection pursuit”, Journal of the American Statistical Association, vol. 82, pp.249–266, 1987.
P.J. Huber, “Projected pursuit”, including Discussions, The Annals of Statistics, vol. 13, pp. 435–525, 1985.
T. Lissack and K. Fu, “Error estimation in pattern recognition via Lα-distance between posterior density functions”, IEEE Trans. Inf. Theory, vol.IT-22, pp.34–45, 1976.
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© 1998 Springer-Verlag Berlin Heidelberg
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Aladjem, M. (1998). Linear discriminant analysis for two classes via recursive neural network reduction of the class separation. In: Amin, A., Dori, D., Pudil, P., Freeman, H. (eds) Advances in Pattern Recognition. SSPR /SPR 1998. Lecture Notes in Computer Science, vol 1451. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033302
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DOI: https://doi.org/10.1007/BFb0033302
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