主成分综合得分法应用于水质评价的不可靠性

The Unreliability of Principal Component Comprehensive Score Method Used in Assessment of Water Quality

针对在主成分分析基础上,以主成分的贡献率作为权重,对各主成分得分进行加权求和计算"综合得分"的方法进行了数学理论求证和实际数据分析,证实了该方法应用于水质评价时具有不可靠性,并明确提出了导致其不可靠性产生的3个缺陷:以贡献率作为权重忽视了主成分对评价目标的实际影响;相关系数矩阵的特征单位向量可以改变方向,导致"综合得分"表达式不唯一;标准化处理可以导致数据失真。

A method which is based on principal component analysis and calculates ＂comprehensive score＂ as weighted sum of principal com- ponents using contributing rates of them as weights, is widely used in assessment of water quality. But through math theory and practical data analysis, it was confirmed that the method is not reliable, and three defects of the method which cause the unreliability were put forward ： actu- al effects of principal components are ignored by taking contributing rates as weight; directions of correlation matrix eigenvectors may change, so expression of ＂comprehensive score＂ is not unique; standardization sometimes distorts the data.