核函数方法(上)

支撑矢量机的成功引起了人们对核函数方法的兴趣。通过某种非线性变换将输入空间映射到一个高维特征空间，如果在其中应用标准的线性算法时，其分量间的相互作用仅限于内积，则可以利用函数的技术将这种算法转换为原输入空间里的非线性算法。Fisher判别法和主分析法是在模式分类与特征抽取中已经获得广泛应用的传统线性方法，近年出现的基于核函数的Fisher判别（KFD）与基于核函数的主分量分析（KPCA）是它们的非线性推广，其性能更好，适用范围更广，灵活性更高，是值得关注的应用前景看好的新技术。

Kernel-based methods(A)

The appeal of kernel based methods has been arisen in recent years by the success of support vector machines. Any standard linear technique,if applied in an high dimensional feature space resulted from a nonlinear map of the original input space, may be transformed to its nonlinear version in the input space very simply by means of the kernel trick, provided that interactions between the components of the algorithm are limited to dot products. Fisher discriminant and principal component analysis are classical linear techniques widely used in pattern classification and feature extraction. Their corresponding nonlinear versions, the kernel Fisher discriminant(KFD) and kernel principal component analysis(KPCA), have emerged recently with better performance, wider application area and more flexibility, which are new technologies with promising prospects in applications and worthwhile to pay attention to.