中文摘要：

考虑软间隔支持向量机中核函数的改进问题．支持向量机通过核函数定义某个非线性变换将空间x等距嵌入到特征空间Z，然后在空间Z中构造分类超平面．核函数在嵌入过程中诱导了放大因子g（x），它描述了向量x映射到空间Z后被放大的程度．因此，考虑构造保形映射h（x）对g（x）进行调整，提高其在支持向量的取值．从而扩大支持向量密集的区域，增大支持向量机对数据的分类间隔使其具有更好的推广能力．

英文摘要：

A method is proposed of modifying a kernel function to improve the performance of a soft margin support vector machine classifier. This is based on the structure of the Riemannian geometry induced by the kernel function. The idea is to enlarge the spatial resolution around the separating boundary surface, by a conformal mapping, such that the separability between classes is increased.