一类新的基于拉盖尔正交多项式的核函数

New set of kernel functions based on Laguerre orthogonal polynomial

基于拉盖尔正交多项式,提出了广义的拉盖尔多项式,由此建立了一类新的核函数—拉盖尔核函数。在双螺旋集和标准UCI数据集上的实验表明,该核函数比常用的核函数(多项式核、高斯径向基核等)具有更强的鲁棒性与更好的泛化性能,而且该核函数的参数仅在自然数中取值,能大大缩短参数优化时间。

This paper introduces generalized Laguerre polynomial based on Laguerre orthogonal polynomial, and derives a new set of kernel function--Laguerre kernel function from generalized Laguerre polynomial. The performance and robustness of the presented kernel are investigated on bi-spiral benchmark data set as well as five data sets from the UCI benchmark repository. The experiment results demonstrate that the presented kernel has better robustness and generalization performance compared with commonly used kernel functions （polynomial kernel and Radial Basis Function etc.）. Moreover, the Laguerre kernel has one parameter which only chooses from natural number, thus parameter optimization is facilitated greatly.