摘要
通过对一般多项式回归模型中的信息矩阵A=XTX添加一个正则化因子α,使其变为XTX+αI,适当选取α,达到改善信息矩阵病态的目的;构造出新的正则化多项式回归模型算法,避免了一般回归模型产生的回归系数有很大变化的不适定现象;数值实验表明,新的正则化多项式回归模型在一定程度上起到了稳定回归系数的作用.
A regularization factor α is added into information matrix A=X^τX in general polynomial regression model. Information matrix is changed into X^τX＋αI. The ill-conditioned matrix is improved when α proper is choired. A new regularized polynomial regression model is con- structed, the ill-posed of the regression coefficient has great changes in general polynomial regression model. Numerical experiment shows that the method has played a stabilization of re- gression coefficient to some extent.
出处
《交通科学与工程》
2009年第4期6-10,共5页
Journal of Transport Science and Engineering
基金
湖南省科技厅计划资助项目(2008SK3054)
关键词
正则化
多项式线性回归
不适定
回归系数
变形分析
regularization
polynomial regression
ill-posed
regression coefficient
deformation analysis
