主成分分析法在环境评价中的应用辨析

Discrimination on Application of Principal Component Analysis in Environmental Assessment

摘要: 主成分分析法在环境评价中已被广泛应用，以水环境质量评价为例，探讨该方法应用于环境评价的可行性。结果表明，在不少情形下主成分分析法在环境评价中的应用明显有误。从物理意义和操作流程两个方面分析错误原因，得出以下结论：1) 主成分分析实质主要做协方差的数值分析，综合评价则是对评价体系的价值判断，当围绕指标体系的协方差所得数值差异不构成对该体系价值判断时，强行应用主成分分析法进行环境价值评价是一种错误的做法；2) 方差贡献率只代表指标体系的方差信息，而非全部信息，仅依据方差贡献率的大小判断信息量载荷大小的观点不妥，仅根据方差贡献率的大小甄选指标可能会造成重要指标被错误剔除；不能简单拿方差贡献率作为价值高低的评价尺度，在综合评价中，将方差贡献率作为各指标的权重系数不恰当；3) 主成分分析法本身是个好的数学方法，但不能盲目引申该数学方法的物理意义，当且仅当评价指标体系中各个指标的协方差所得数值差异构成对其所评价事物的价值判断时，才可能可以采用主成分分析法进行价值评价，具体何时恰当，何时不恰当，必须具体问题具体分析，难以简单下结论。

Abstract: Principal component analysis (PCA) has been widely applied to environmental assessment. Taking the water environmental quality assessment as an example, whether the method can be applied to environmental quality assessment has been discussed. And the results showed that it was obviously wrong in many cases. We analyze the reasons why it was wrong in these cases from two aspects including the physical meanings and operation process of PCA, The conclusions were as follows: 1) PCA is a Mathematics method about numerical analysis of covariance essentially, but comprehensive evaluation is the judgment of the value of the evaluation system. When the numerical difference has not constituted value judgments on the comprehensive evaluation, it is wrong to apply PCA to environmental valuation forcibly. 2) The variance contribution rate only represents the variance information of the index system, not all of the information. It may cause the removal of the important index, if researchers select important indexes only according to variance contribution rate. We must consider other factors to select important index, such as, Natural and Geographical conditions, Social and Economic status and so on. So it can not be taken as a mainly yardstick to judge whether the value is high or low, and also, it is not appropriate to regard the variance contribution and the weight coefficient as the same in comprehensive evaluation. 3) PCA is a good mathematical method which has physical meaning itself, but we can’t quote its physical meaning blindly. Whether a method could be applied to environmental quality assessment or not, if and only if the numerical difference of the evaluation index system constitutes on the value differ of things being evaluated. Specifically speaking, it is difficult to get a simple conclusion of when it is appropriate or not. We must make a detail analysis according to concrete problems.