基于埃尔米特正交多项式,文章提出了向量形式的广义埃尔米特多项式,并由此衍生出一类新的核函数——埃尔米特核函数.该类核函数最大的优势在于其参数仅在自然数中取值,能大大缩短参数优化时间.在鲁棒性与泛化性能方面,文章在双螺旋集和标准UCI数据集上与常用的核函数(多项式核、高斯径向基核等)做了对比试验. Based on Hermite orthogonal polynomials, a generalized Hermite polynomial of vector form is proposed, and a new kind of kernel function, Hermite kernel function, is derived. The biggest advantage of this type of kernel function is that Its parameters are only natural numbers, which can greatly shorten the parameter optimization time.In the aspect of robustness and generalization performance, this paper compares the commonly used kernel functions (polynomial kernel, Gaussian radial basis Nuclear, etc.) made a comparative test.