基于极小极大估计器的偏最小二乘方法及应用  

Partical least squares method based on mini-max estimator and its application

作　　者：成忠[1] 陈德钊[2] 

机构地区：[1]浙江科技学院生物与化学工程系,浙江杭州310012 [2]浙江大学化学工程与生物工程系,浙江杭州310027

出　　处：《化学工程》2007年第9期29-32,共4页Chemical Engineering(China)

基　　金：国家自然科学基金资助项目(20276063);浙江省重点科技资助项目(2004C21SA120002)

摘　　要：针对多输入多输出化工过程中,自变量间、因变量间均存在较强的相关性,提出了偏最小二乘回归(PLSR)与极小极大估计器相结合的PLS-Minimax算法。该算法先对样本数据进行多因变量的PLSR,以消除变量间的复共线性,建立较为稳健的模型;然后基于多变量残差的协方差矩阵,采用极小极大准则,估计收缩系数矩阵,以修正回归系数矩阵,改善模型的预报性能。将PLS-Minimax算法实际应用于聚合反应过程的建模,效果良好。与已有方法相比,其所建模型的预报精度有显著提高。In order to eliminate the correlation between predictor variables and make full use of information between the correlated responses in multi-input multi-output chemical process, a PLS-Minimax method that combined the partial least squares regression（PLSR） with mini-max estimator was introduced. The PLSR algorithm with multiple responses to samples data was implemented to eliminate the predictor variables correlation and thus building a robust model. Under the mini-max rule, a shrinkage matrix was calculated based on the covariance matrix of the multiple responses errors between the PLS estimators and the responses to improve the model predictive precision by modifying the regression coefficient matrix. Application to the modeling of polymerization reaction process with four responses of the proposed PLS-Minimax method was presented with comparison to the ordinary least regression （OLR）, PLSR and PLS with Curds and Whey estimator（PLS-C＆W）. The results show that PLS-Minimax method not only gains a considerable improvement on predictive accuracy, but also holds on high cross-validation correlative coefficient of the multiple responses.

关 键 词：多因变量 偏最小二乘回归 极小极大估计 预报性能 聚合反应过程 

分 类 号：TQ021.8[化学工程]