【摘要】 针对主成分分析(PCA)在多指标综合评价中非线性分析上的不足,提出了综合评价的核主成分分析(KPCA)方法。利用核函数将原空间映射到高维特征空间,在高维空间进行线性主成分分析;通过对核参数的适当选取,可使得最大特征值的贡献率达到或接近85%,避免了多个主成分的不同组合而导致评价结果不一致。在此基础上,利用最小二乘法建立核主成分回归方程——KPCR,并将其应用于区域经济社会发展综合评价与预测。更多还原

【Abstract】 In view of the drawbacks of principal composition analysis(PCA) used to analyze nonlinear problem in comprehensive evaluation with multiple indicators,kernel principal composition analysis(KPCA) is introduced.By using the kernel functions,one can efficiently calculate principal compositions in high dimensional feature spaces,related in input space by some nonlinear map.By choosing appropriate parameters,the maximum eigenvalue contributes are above or nearly 85%,avoiding the different array as a result of many principal compositions.On the basis of KPCA,a new kernel principal composition regression(KPCR) equation is established by using least squares method,and applied to evaluate and forecast regional economy and social development in practice.更多还原