基于样条变换的非线性PLSR方法及应用

针对样本数据多呈现非线性和小样本的特点,为提高此类样本数据回归预测的有效性和精度,根据偏最小二乘回归(PLSR)方法原理、样务插值原理和拟线性化思想,提出基于三次B样条变换的非线性PLSR模型及其实现方法.分析了进行有效变换和成分提取的条件,给出了应用该方法的具体步骤.最后通过对非线性函数回归预测仿真和军用运输机采购价格回归预测实例,以及与BP神经网络模型结果的比较,表明了该方法的有效性和实用性.

Nonlinear PLSR method and its application based on spline transform

Sample data are usually small quantity and nonlinearity.In order to enhance the precision and validity of regression and forecast about such sample data,the nonlinear PLSR model and its implementation based on cubic B-spline transform are proposed,according to the theory of partial least-square regression(PLSR),spline interpolation theory and linearization idea.The conditions of effective transform and component computering are analysed,and the detailed steps of the method are given.Finally,the method is applied to nonlinear function regression simulation and military aircraft acquisition cost instance,and is compared with neural networks.Results show the validity and practicability of the proposed method.