Abstract: Kernel function is the core of Support Vector Machines（SVM），and its major role in dealing with non-linear problems，is to study issues from low-dimensional space into a high-dimensional space，so that in the high-dimensional space into a linear problem，kernel function study in Support Vector Machine is essential.This paper first discusses the nature of the kernel function，and then based on Riemannian geometry dependent on the data structure and method，an improved modifying kernel function is proposed，the kernel function is a simple and less calculation method，which conformal factor and support vector irrelevant，compared with previous studies overcomes the impact of support vector’s number and distribution.This kernel function for pattern classification，achieves good results，significantly improves the generalization ability of classification Support Vector Machine.

Key words: Support Vector Machines Classifier（SVMC）, kernel function, Riemannian geometry structure, conformal transformation

摘要： 核函数是支持向量机的核心，它的作用主要体现在处理非线性问题时，将研究问题从低维空间转化成高维空间，使之在高维空间中变成线性问题，核函数的研究在支持向量机中是非常必要的。首先讨论核函数的本质，并且基于黎曼几何结构和数据依赖的方法，提出了一种改进的修正核函数，改进后的核函数形式简单，计算量较低，其中保形因子与支持向量无关，较之于以前的研究克服了支持向量的数目和分布的影响。将该核函数用于模式分类中，取得了良好的效果，显著提高了支持向量分类机的泛化能力。

关键词: 支持向量分类机, 核函数, 黎曼几何结构, 保形变换