核主成分分析法在生态经济可持续发展评价中应用

Application of Kernel Principal Component Analysis in Evaluation of Sustainable Development of Ecological Economy

文章给出了一种非线性主成分评价模型:核主成分分析(KPCA),它将原变量空间通过一个非线性变换映射到高维特征空间F中,在F中进行线性主成分分析,通过核技巧,它只需在原空间进行点积运算,而不必知道映射的具体形式,只要选取适当的核函数和参数,可以使第一主成分的贡献率达到90%,结合安徽省生态经济可持续发展度为例,说明了KPCA应用,计算结果与现实相符,KPCA方法具有实际的应用价值。

A new method for performing a nonlinear form of principal component analysis (PCA) was proposed, with original variable space mapping through a nonlinear transformation in high dimensional feature space. By kernel skills, the contribution of the first component was up to 90%. Kernel principal component analysis (KPCA) was applied to an example of sustainable development of ecological economy in Anhui Province, with result satisfactory to the reality.