常用核函数的几何度量与几何性质

Geometric Measures and Properties of Commonly Used Kernel Functions

研究核函数的几何度量和几何性质,并给出核函数选择(核选择)的建议.首先通过对核函数所蕴含的几何度量的深入分析,导出了常用的高斯径向基核函数和多项式核函数的黎曼度量、距离度量和角度度量;然后总结了这些几何度量的性质,并进行了数学证明;最后在几何性质的基础上,给出了核选择的一些建议.

The geometric measures and properties of the kernel functions were studied and some suggestions about the selection of kernel functions were presented. By deeply analyzing the geometric measures of the kernel functions, the Riemann measures, distance measures and angle measures of the commonly used Gaussian radial basis kernel function and polynomial kernel function were de- duced at first. Then the properties of these geometric measures were summarized and the mathematical proofs were finished. Finally some suggestions about selection of kernel functions based on the geometric properties were given.