Variable selection in partial least squares with the weighted variable contribution to the first singular value of the covariance matrix

The selection of informative variables in partial least squares (PLS) is important in process analytical technology (PAT) applications in the pharmaceutical industry, for example, the calibration of spectrometers. In the past, numerous approaches have been proposed to select the variables in partial least squares. In this work, a new variable selection method for PLS with the weighted variable contribution (PLS-WVC) to the first singular value of the covariance matrix for each PLS component is proposed. Several variants of PLS-WVC with different weighting factors are proposed. One variant of PLS-WVC is equivalent to the PLS with variable importance in projection (PLS-VIP). However, the variants with the correlation between X γ w γ and Y γ q γ as the weighting factor are preferred based on the results of the simulation cases studies. The proposed PLS-WVCs are integrated with interval PLS (iPLS) further to select the informative wavelength intervals for spectroscopic modelling. The utility of the proposed WVC based variable selection methods in PLS is demonstrated with the real spectral data sets.