Improved variable reduction in Partial Least Squares modelling by global-minimum error reproducible Uninformative-Variable Elimination

The well-known Uninformative-Variable Elimination for Partial Least Squares, denoted as UVE-PLS, is not reproducible regarding the selected variables. Additionally, in UVE, variables are selected in the first minimum of the graph of the root mean squared error of cross validation ( RMSECV ) against the number of retained variables. This results mostly in rather large numbers of selected variables. Therefore, there is a need for a new and reproducible UVE method with better selective and preferably also better predictive abilities. Consequently, the Global-Minimum Error Reproducible Uninformative-Variable Elimination method, denoted as GME-RUVE, is proposed and tested. In the GME-RUVE method, main characteristics of two existing methods, i.e. Jack-knife-based Partial Least Squares Regression (JK-PLSR) and Global-Minimum Error Uninformative-Variable Elimination (GME-UVE), are combined. JK-PLSR can be considered as a reproducible version of the original UVE method. In GME-RUVE, as in the JK-PLSR method, no artificial random variables are added to the X matrix, and firstly the significance of the PLS regression coefficients is determined from jack-knifing. Secondly, as in the GME-UVE method, either the global minimum or the critical RMSECV is used for the selection of the variables. The performance of the new GME-RUVE method is investigated using four datasets with multivariate profiles, i.e. either simulated profiles, NIR spectra or theoretical molecular descriptor profiles, resulting in 12 profile-response ( X - y ) combinations. The predictive performance of GME-RUVE, using the global RMSECV minimum and both the selective and predictive performances of GME-RUVE, using the critical RMSECV , are significantly better than both those of the JK-PLSR method, using the first local RMSECV minimum , and of the existing UVE method. The selective and predictive performances of the new GME-RUVE method are also much better than those of the existing GME-UVE method. Moreover, variables selected by the above GME-RUVE method have a chemical meaning. • A new and reproducible UVE method for PLS1, called GME-RUVE, is proposed. • Variable set is selected at the global minimum or at the critical RMSECV. • GME-RUVE has better selective and predictive abilities than JK-PLSR, UVE and GME-UVE. • Variables selected by GME-RUVE have a chemical meaning.