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| Research on the Properties of Orthogonal Polynomial Kernel Functions |
| TIAN Meng1,2 ,WANG Wen-Jian1 |
1.School of Computer and Information Technology, Shanxi University, Taiyuan 030006
2.School of Science, Shandong University of Technology, Zibo 255049 |
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Abstract The choice of kernel function and its parameters a core problem of support vector machine (SVM). Based on orthogonality and variability of orthogonal polynomial functions, kernel functions are constructed to be used as general kernel functions instead of some common kernels, such as polynomial kernel and Gaussian kernel. Generally, the kernel parameters are chosen only from natural number, which facilitates the kernel parameter tuning. 6 sets of orthogonal polynomial kernel functions based on Chebyshev polynomial, Legendre polynomial, Hermite polynomial, and Laguerre polynomial are discussed. The properties of these kernel functions are studied, and their robustness and generalization performance on some test datasets are compared. The obtained results provides theoretical basis and technical support for SVM classification.
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Received: 22 May 2013
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2014, Vol. 27 
