|
|
|
| Least Squares Support Vector Machine Based on Scaling Kernel Function |
| WU FangFang, ZHAO YinLiang |
| Institute of Neocomputer, Xi’an Jiaotong University, Xi’an 710049 |
|
|
|
|
Abstract The kernel function of support vector machine (SVM) is an important factor to the learning result of SVM. Based on the wavelet decomposition and conditions of the support vector kernel function, a new scaling kernel function for SVM (SSVM) is proposed. This function is not only a kind of horizontal floating orthonormal function, but also can simulate any curve in quadratic continuous integral space, thus it enhances the generalization ability of the SVM. According to the scaling kernel function and the regularization theory, a least squares support vector machine on scaling kernel function (LSSSVM) is proposed to simplify the solving process of SSVM. The LSSSVM is then applied to the regression analysis and classification. Experimental results show that the precision of regression is improved, compared with LSSVM whose kernel function is Gauss function.
|
|
Received: 30 May 2005
|
|
|
|
|
|
[1] Vapnik V N. The Nature of Statistical Learning Theory. New York, USA: Springer-Verlag, 1995
[2] Zhang Xuegong. Introduction to Statistical Learning Theory and Support Vector Machines. Acta Automatica Sinica, 2000, 26(1): 32-42 (in Chinese)
(张学工.关于统计学习理论与支持向量机.自动化学报,2000, 26(1): 32-42)
[3] Burges C J C. A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery, 1998, 2(2): 955-974
[4] Scholkopf B, Sung K K, et al. Comparing Support Vector Machines with Gaussian Kernels to Radical Basis Function Classifiers. IEEE Trans on Signal Processing, 1997, 45(11): 2758-2765
[5] Osum E, Freund R, Girosi F. Training Support Vector Machines: An Application to Face Detection // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. San Juan, USA, 1997: 130-136
[6] Mercer J. Functions of Positive and Negative Type and Their Connection with the Theory of Integral Equations. Philosophical Transactions of the Royal Society of London, 1909, 209: 415-446
[7] Suykens J A K, Vandewalle J. Least Squares Support Vector Machine Classifiers. Neural Processing Letters, 1999, 9(3): 293-300
[8] Burges C J C. Geometry and Invariance in Kernel Based Methods // Scholkopf B, Burges C J C, Snola A J, eds. Advance in Kernel Methods-Support Vector Learning. Cambridge, USA: MIT Press, 1999: 89-116
[9] Smola A J, Schlkopf B, Müller K R. The Connection between Regularization Operators and Support Vector Kernels. Neural Networks, 1998, 11(4): 637-649
[10] Zhang Q, Benveniste A. Wavelet Networks. IEEE Trans on Neural Networks, 1992, 3(6): 889-898 |
|
|
|
2006, Vol. 19 
