一类基于Askey-Wilson多项式的新核函数

New Class of Kernel Functions Based on Askey-wilson Polynomial

针对核函数缺少统一范式这一问题,以及为进一步提高支持向量机的性能,基于Askey-Wilson多项式提出一类新的支持向量机核函数,即AW核函数,从而为支持向量机核函数提供一种新的选择.首先,基于Askey-Wilson多项式参数的特性对其进行化简,得到除阶数外仅包含一个参数的AW多项式,以避免引入更多的核参数;然后,根据AW多项式的正交特性以及核函数的性质,构建基于AW多项式和RBF核函数的新核函数.实验结果表明,AW核函数能有效提高支持向量机的分类性能.

Aiming at the problem that there is a lack of unity paradigm for kernel function,and to improve the performance of Support Vector M achine（ SVM）,the paper presents a new class of SVM kernel functions based on Askey-Wilson polynomial,w hich is called AW kernel function,so as to provide a new choice for SVM kernel functions. Firstly,the paper simplifies Askey-Wilson polynomial based on its character to get AW polynomial,and AW polynomial only has one parameter besides order,so as to avoid bringing in more kernel parameters. Then,the paper establishes the new kernel function based on the orthogonality of AW polynomial and the property of kernel function. The experimental results show that AW kernel function can effectively improve the classify- cation performance of SVM..