Abstract
Previously, a novel classifier called Kernel-based Nonlinear Discriminator (KND) was proposed to discriminate a pattern class from other classes by minimizing mean effect of the latter. To consider the effect of the target class, this paper introduces an oblique projection algorithm to determine the coefficients of a KND so that it is extended to a new version called extended KND (eKND). In eKND construction, the desired output vector of the target class is obliquely projected onto the relevant subspace along the subspace related to other classes. In addition, a simple technique is proposed to calculate the associated oblique projection operator. Experimental results on handwritten digit recognition show that the algorithm performes better than a KND classifier and some other commonly used classifiers.
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References
M. A. Kraaijveld, A Parzen classifier with an improved robustness against deviations between training and test data, Pattern Recognition Letters, 17(1996)7, 679–689.
C. Cortes, V. Vapnik, Support-vector networks, Machine Learning, 20(1995)3, 273–297.
B. Y. Liu, A kernel-based nonlinear discriminator with closed-form solution, Proc. IEEE Int. Conf. Neural Network and Signal Processing, Nanjing, China, 2003, 41–44.
T. Poggio, F. Girosi, Networks for approximation and learning, Proc. IEEE, 78(1990) 9, 1481–1479.
H. Ogawa, Neural network learning, generalization and over-learning, Proc. Int. Conf. Intelligent Information Processing & System (Supplemental volume), Beijing, China, 1992, 1–6.
B. Y. Liu, H. Ogawa, An equivalent form of S-L projection learning, J. Electronic Science and Technology of China, 1(2003)1, 6–11.
R. Schatten, Norm Ideals of Completely Continuous Operators, Berlin: Springer-Verlag, 1960, 7–10.
B. Y. Liu, J. Zhang, Partial oblique projection learning for optimal generalization, J. Electronic Science and Technology of China, 2(2004)1, 63–68.
A. Albert, Regression and the Moor-Penrose Pseudoinverse, New York: Academic Press, 1972, 20–30.
S. Kayalar, H. L. Weiner, Oblique projection: Formulas, algorithms, and error bounds, Math. Control Signals Systems, 2(1989), 33–45.
A. K. Jain, R. P. W. Duin, J.C. Mao, Statistical pattern recognition: A review, IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(2000)1, 4–37.
K. Tsuda, Subspace classifier in the Hilbert space, Pattern Recognition Letters, 20(1999)5, 513–519.
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Supported by the key project of Chinese Ministry of Education (No. 1051150).
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Liu, B., Zhang, J. Oblique projection realization of a Kernel-based Nonlinear Discriminator. J. of Electron.(China) 23, 94–98 (2006). https://doi.org/10.1007/s11767-004-0036-z
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DOI: https://doi.org/10.1007/s11767-004-0036-z