一种基于支持向量机的PCA分析方法

提出一种更简洁的用于主要成分分析 (PCA)及其非线性分析的公式 .给出一个含有规则化项的原始权空间的约束最大优化问题 ,应用核技巧来解决其对偶问题 .该公式同最小二乘支持向量机 (LS SVM )分类器相似 .遵循常规的SVM方法 ,将输入空间的数据映射到高维特征空间 ,然后使用核技巧 ,利用主对偶约束最大优化来解释线性和非线性PCA分析问题 .其优点在于对偶问题适用于高维输入空间 ,而原始问题在N很大时能被更好地解决 .

A PCA analysis method based on support vector machine

A simple formulation for principal component analysis (PCA) and its kernel version was presented. A constrained optimization problem in primal weight space with incorporation of a regularization term was discussed. The dual problem was solved by using the kernel trick. The formulation was made in the same fashion as in the least squares support vector machine (LS SVM) classifiers. The data was mapped from the input space to a high dimensional feature by following the usual SVM methodology and the kernel trick was applied. A solution equivalent to kernel PCA can be obtained from the nonlinear version of the formulation. The dual problem is suit for the light dimensional input space and the primal problem can be solved better when N is bigger.