基于径向基函数的非线性岭回归方法及仿真研究

Nonlinear Ridge Regression Modeling Method Based on Radial Basis Function and Its Simulation Research

提出了一种基于径向基函数的非线性岭回归建模方法(RBF-RR),该方法的核心是先通过RBF的转换实现输入样本的非线性映射,然后用岭回归方法进行线性建模,并采用了一种效果较好的基于广义交叉有效性(GCV)的逐步估计法来确定岭参数k;该建模方法的优点在于:径向基函数的引入赋予岭回归方法非线性功能,同时岭回归方法又可以消除使用RBF进行非线性处理后RBF输出之间潜在的复共线性。通过仿真研究表明:使用RBF-RR建立的模型具有较好的稳定性和预测精度。

A nonlinear ridge regression modeling method based on Radial Basis Function was put forward, and the kernel of this modeling method is, firstly Radial Basis Function is used to realize the nonlinear mapping of input, and then a linear model using Ridge Regression is built, meanwhile, a re-estimation formula based on the Generalized Cross Validation（GCV） is adopted to calculate the ridge parameter k .The advantages of this modeling method is that the introduction of the RBF gives the Ridge Regression a nonlinear ability and the RR can also eliminate latent multicollinearity after the nonlinear process using the RBE The simulation research shows that the model built up by RBF-RR has good modeling stability and prediction ability.