Abstract
The kernel function of support vector machine (SVM) is an important factor for the learning result of SVM. Based on the wavelet decomposition and conditions of the support vector kernel function, Gaussian wavelet kernel function set for SVM is proposed. Each one of these kernel functions is a kind of orthonormal function, and it can simulate almost any curve in quadratic continuous integral space, thus it enhances the generalization ability of the SVM. According to the wavelet kernel function and the regularization theory, Least squares support vector machine on Gaussian wavelet kernel function set (LS-GWSVM) is proposed to greatly simplify the solving process of GWSVM. The LS-GWSVM is then applied to the regression analysis and classifying. Experiment results show that the regression’s precision is improved by LS-GWSVM, compared with LS-SVM whose kernel function is Gaussian function.
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References
Vapnik, V.: The Nature of Statistical Learning Theory, pp. 1–175. Springer, Heidelberg (1995)
Burges, C.J.C.: A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery 2(2), 955–974 (1998)
Edgar, O., Robert, F., Federico, G.: Training Support Vector Machines: An Application to Face Detection. In: IEEE Conference on Computer Vision and Pattern Recognition, San Juan, Puerto Rico, pp. 130–136 (1997)
Mercer, J.: Function of Positive and Negative Type and Their Connection with The Theory of Integral Equations. Philosophical Transactions of The Royal Society of London: A 209, 415–446 (1909)
Suykens, J.A.K., Vandewalle, J.: Least Squares Support Vector Machine Classifiers. Neural Processing Letter 9(3), 293–300 (1999)
Burges, C.J.C.: Geometry and Invariance in Kernel Based Methods [A]. In: Advance in Kernel Methods-Support Vector Learning[C], pp. 89–116. MIT Press, Cambridge (1999)
Smola, A., Schölkopf, B., Müller, K.R.: The Connection between Regularization Operators and Support Vector Kernels. IEEE Trans. on Neural Networks 11(4), 637–649 (1998)
Zhang, L., Zhou, W.D., Jiao, L.C.: Wavelet Support Vector Machines. IEEE Transaction on Systems, Man, and Cybernetics, Part B: Cybernetics 34, 34–39 (2004)
Wu, F.F., Zhao, Y.L.: Least Squares Littlewood-Paley Wavelet Support Vector Machine. In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds.) MICAI 2005. LNCS (LNAI), vol. 3789, pp. 462–472. Springer, Heidelberg (2005)
Zhang, Q., Benveniste, A.: Wavelet Networks. IEEE Trans. on Neural Networks 3(6), 889–898 (1992)
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© 2006 Springer-Verlag Berlin Heidelberg
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Wu, F., Zhao, Y. (2006). Least Squares Support Vector Machine on Gaussian Wavelet Kernel Function Set. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_137
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DOI: https://doi.org/10.1007/11759966_137
Publisher Name: Springer, Berlin, Heidelberg
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