病态加权总体最小二乘靶向病灶的正则化方法

Target Focus Regularization as Compared with Ill-Posed Weighted Total Least Square

病态EIV模型的病灶源于设计矩阵的部分数据列之间存在复共线性关系。针对病灶特点制定正则化策略,在克服病态性的同时尽量减小正则化过程所引起的副作用,提出靶向病灶的正则化方法。通过数值试验,与总体最小二乘方法、病态总体正则化方法等进行比较,结果表明靶向病灶的正则化方法最优。

Usually in ill-posed error-in-variable models,only part of columns in the design matrix possess multicollinearity.This is where the model focuses.According to the focus characteristics,the corresponding regularization strategy is made,which can overcome the ill-posed effects and minimize side effects caused by the process of regularization at the same time.We propose target focus regularization as opposed to the ill-posed error-in-variable model.Numerical experiments show the proposed regularized total least-squares solution method performs better than others.