摘要
In machines learning problems, Support Vector Machine is a method of classification. For non-linearly separable data, kernel functions are a basic ingredient in the SVM technic. In this paper, we briefly recall some useful results on decomposition of RKHS. Based on orthogonal polynomial theory and Mercer theorem, we construct the high power Legendre polynomial kernel on the cube [-1,1]<sup>d</sup>. Following presentation of the theoretical background of SVM, we evaluate the performance of this kernel on some illustrative examples in comparison with Rbf, linear and polynomial kernels.
In machines learning problems, Support Vector Machine is a method of classification. For non-linearly separable data, kernel functions are a basic ingredient in the SVM technic. In this paper, we briefly recall some useful results on decomposition of RKHS. Based on orthogonal polynomial theory and Mercer theorem, we construct the high power Legendre polynomial kernel on the cube [-1,1]<sup>d</sup>. Following presentation of the theoretical background of SVM, we evaluate the performance of this kernel on some illustrative examples in comparison with Rbf, linear and polynomial kernels.
作者
Habib Rebei
Nouf S. H. Alharbi
Habib Rebei;Nouf S. H. Alharbi(Department of Mathematics, College of Science, Qassim University, Buraydah, Kingdom of Saudi Arabia;Department of Mathematics, College of Science and Arts in Nabhaniya, Qassim University, Buraydah, Kingdom of Saudi Arabia)
