Nonlinear Spline Kernel-based Partial Least Squares Regression Method and Its Application

Inspired by the traditional Wold's nonlinear PLS algorithm comprises of NIPALS approach and a spline inner function model,a novel nonlinear partial least squares algorithm based on spline kernel(named SK-PLS)is proposed for nonlinear modeling in the presence of multicollinearity.Based on the inner-product kernel spanned by the spline basis functions with infinite number of nodes,this method firstly maps the input data into a high-dimensional feature space,and then calculates a linear PLS model with reformed NIPALS procedure in the feature space and gives a unified framework of traditional PLS "kernel" algorithms in consequence.The linear PLS in the feature space corresponds to a nonlinear PLS in the original input(primal)space.The good approximating property of spline kernel function enhances the generalization ability of the novel model,and two numerical experiments are given to illustrate the feasibility of the proposed method.