Abstract: This paper presents a kernel-based principal component analysis method，which is mainly used to solve large-scale non-linear feature extraction of data issues.The paper gives a simplified method of calculating the covariance matrix and the derivation process，but also gives a detailed derivation of KPCA method of the process.Finally，the paper uses the nuclear principal component analysis method to analyze the distribution of linear and nonlinear.This method can get better results than the traditional principal component analysis method.

Key words: principal component analysis, kernel function, support vector machine

摘要： 给出一种基于核函数的主成分分析方法，它主要用来解决大规模非线性数据的特征提取问题。文中给出了简化的协方差矩阵的计算方法与推导过程，还给出了KPCA方法的详细推导过程。最后使用核主成分分析的方法分别对线性与非线性分布的数据进行了分析，取得了比传统主成分分析方法更好的结果。

关键词: 主成分分析, 核函数, 支持向量机