基于岭估计的岭马田系统在复共线性数据中的应用  

The Application of Ridge Mahalanobis-Taguchi System Based on Ridge Estimation in Data with Multicollinearity

作　　者：陶建波[1] 程龙生[1] 

机构地区：[1]南京理工大学经济管理学院,江苏南京210094

出　　处：《数学的实践与认识》2016年第4期109-116,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71271114)

摘　　要：在多变量模式识别领域,变量间经常会存在复共线性,复共线性不仅会影响参数估计的效果,也会使变量的敏感性出现显著异常.马田系统是以马氏距离作为测量尺度的多变量模式识别方法,复共线性会通过马氏距离影响马田系统变量筛选的效果和判别的准确率.基于岭估计提出了一种新的测量尺度—岭马氏距离,利用岭迹法确定岭参数,将其引入马田系统使得马田系统对病态数据具有更好的耐受性.通过案例验证了岭马氏距离可以很好的克服复共线性,并提高马田系统的判别准确率.Multicollinearity is often existed among variables in the area of multi-dimensional pattern recognition, which will affect the performance of parameter estimation, make parameters extremely sensitive on slight variable＇s perturbation. Mahalanobis-Taguchi System （MTS） is a methodology of multi-dimensional pattern recognition whose measure scale is based on the mahalanobis distance（MD）, multicollinearity will affect the performance of variable screening and discrimination accuracy in MTS through MD. This paper analysis the effect of multicollinearity to MD and presents a new measuring scale function-ridge mahalanobis distance （RMD） based on the ridge estimation, the ridge parameter will be determined by the ridge trace. And introduce RMD to MTS which make it more robust to bad data. The case validates that RMD can be very good to overcome multicollinearity and improve the accuracy of MTS.

关 键 词：复共线性 马氏距离 岭估计 马田系统 

分 类 号：O212.1[理学—概率论与数理统计]