The Study Of Some Problems In Partial Least Squares Regression

Partial least squares regression (PLS) is a new multiple statistic data analytical method, it is produced from chemistry field. The outstanding characteristic of PLS is that it can make the multiple linear regression analysis, the principal components analysis and the canonical correlation analysis combined. In the same arithmetic, it can implement modeling, predigesting the data structure and analyzing of the correlation between two gropes of variables at the same time. It brings huge advantage to the multiple linear regression analysis. PLS has particular predominance when deal with the problems that the sample capacity is small, variable dimension is high or badly multiple correlation is existed.But the partial least squares regression models can be expressed by the original variables. The principal components selected by PLS contain all the variables all the same, so it cannot solve the multiple correlation problems completely. Especially when variable dimension is high and the sample capacity is small. In this thesis, we discuss the modification of PLS and explain that the modified PLS can improve the predictive precision by example analysis.There are four parts in this paper. The first chapter introduces the development of PLS and the recent study of modified PLS. In the second section, we discuss the modification of the PLS, meanwhile we show that it can improve the predictive precision by example analysis. In the third section, we discuss the multivariate Partial least squares regression that based on double variable selection, meanwhile we show that it can improve the predictive precision by example analysis. The last part is concerned with the modification of weighted averaged partial least squares regression.