偏最小二乘回归模型内涵分析方法研究

偏最小二乘回归是一种新型的多元分析方法。它可以在自变量多重相关的条件下，有效地构造出对系统解释性最强的子空间，进行发建模，使模型的精度和可靠性得到很大的提高。本文提出采用因素分析方法，对偏最小二乘回归的最优子空间进行正交变换。这种变换方法对偏最小二乘回归的模型结果没有任何影响，却可以使最优子空间的实际含义得到更好的解释。案例研究表明，经过正交变换后，原始变量被分为若干变量组，每个变量组分别对应于最

Identification of Optimal Subspace from PLS Regression

Partial least squares regression, a novel approach for multivariate analysis, is widely used for modeling a multi collinear variable data set, with improved model accuracy and reliability based on building a subspace with most explanatory ability to the data set. In this paper the factor analysis method is presented to transform orthogonally the optimal subspace, which is obtained from partial least squares regression. The transformation can identify each factor in a meaningful way but does not change the results of partial least squares regression model. Therefore, the physical meaning of the optimal subspace of partial least squares regression can be illustrated. A case study demonstrates that the original variable set is divided into several variable groups after the orthogonal transform, each of which is corresponding to a new factor in the subspace such that its explanatory ability is improved.