The Study Of Partial Least Square Nonlinear Model And Recursive Algorithm

Partial least squares regression algorithm establishes regression models by extracting orthogonal components. PLS can efficiently deal with problem of many variables and collinearity between the independent variables, moderate amounts of missing data, low observation/variable ratio, which the ordinary least squares can not solve. After several decades of development, PLS is widely used in chemistry, chemical engineering, economics, environment, food and other fields.This paper mainly includes two parts contents and researches. The first part is about study of PLS nonlinear regression algorithm. In this part, INLR(Implicit Nonlinear variable regression) algorithm is introduced for its simple and having good predictive ability when system presence polynomial relations. INLR algorithm extend X with the quadratic or cubic terms and cross terms of components are implicitly included in the model of extended X, then we can implement the PLS algorithm to establish model, but the extended X may includes non-correlated variation. INLR algorithm will extract more components as a result of non-correlated variation to y. Interpretations of model will get bad, when the number of component is increasing. The paper adopt OPLS(orthogonal projections to latent structure) to solve that problem. OPLS method analyzes the variation explained in PLS component and removes non-correlated variation in X. The improved algorithm is called OPLS-INLR. The advantages of OPLS-INLR algorithm are proved by simulation experiment. The result illustrates OPLS-INLR retain the ability prediction of INLR and improve the interpretation of model. The two part of this paper is PLS recursive algorithm study. Classical PLS recursive algorithm study continuous dependent variables, this paper mainly research recursive algorithm of category dependent variable. The based on KL-PLS(kernel logistic partial least square) non-linear recursive algorithm is proposed. The predictive accuracy of KL-PLS nonlinear recursive algorithm is superior to logistic recursive algorithm, PLS logistic recursive algorithm and KL-PLS algorithm through analysis of red wine quality data.