核函数在主成分分析中的应用

Application of Kernel Function in Principal Component Analysis

主成分分析在对线性数据进行降维时非常有效，核函数能够将线性不可分的数据映射到高维希尔伯特空间中可能可分。将核函数应用到主成分分析中成为核主成分分析。从核函数的性质、核函数的参数调整、核函数的构造等方面对核主成分分析进行应用与实现，并结合核Fisher判别分析，对样例数据进行核主成分分析，结论表明，效果良好，但执行速度较慢，需要后续改进。

Principal component analysis is very effective to linear data dimension reduction, kernel function can be mapped to high-dimensional Hilbert space where unclassified data in linear space may be classified.Thus,Kernel principal component analysis （KPCA）is proposed. From the nature,the parameters adjustment and the structure of the kernel function, KPCA is discussed. Connecting with the kernel Fisher discriminant analysis, the conclusion shows that the effect is good, but the execution speed is slower, needs follow-up improvement.