基于核函数变换的PLS回归的非线性结构分析

基于核函数变换的PLS非线性回归模型既吸取了核函数能够拟合适应任意连续变化曲线的优点，又借鉴了偏最小二乘回归方法能够有效解决自变量集合高度相关的技术。在本文中针对多元加法模型，从理论和仿真试验的角度分别验证了，对于多个独立自变量对单因变量为非线性关系的数据系统，基于核函数变换的PLS回归方法不仅能够有效实现自变量对因变量的整体预测，而且能够提取各雏自变量对因变量的单独非线性作用特征，从而确定数据系统内部的复杂非线性结构关系，增强了模型的可解释性。

Nonlinear Structure Analysis with Partial Least-squares Regression Based on Kernel Function Transformation

Nonlinear Partial Least-squares Regression Model based on Kernel Transformation not only takes advantages (of the) characters of kernel functions which can fit continuous curves properly, but also brings in Partial Least-squares (Regression) Method which can effectively solve the problem of high correlations in the set of independent variables. In this (paper,) according to additive modeling methods both in theory and simulation, we prove that Nonlinear Partial Least-squares Regression Method based on Kernel Transformation can not only get the exact whole forecasting model,but also successfully extract nonlinear features of each independent variable's effect on the dependent variable when dealing with nonlinear data systems with multi-absolute independent variables for one dependent variable. In this way, we can acquire the complex (nonlinear) structures of the data system and an explainable model.