Selection of principal variables through a modified Gram–Schmidt process with and without supervision

In various situations requiring empirical model building from highly multivariate measurements, modelling based on partial least squares regression (PLSR) may often provide efficient low-dimensional solutions. unsupervised situations, the same be true for principal component analysis (PCA). both cases, however, it is also of interest to identify subsets measured variables useful obtaining sparser but still comparable models without significant loss information and performance. present paper, we propose a voting approach sparse overall maximisation variance analogous PCA similar alternative deriving influenced closely related PLSR method. Both cases yield pivoting strategies modified Gram–Schmidt process its corresponding (partial) QR-factorisation underlying data matrix manage variable selection process. The proposed methods include score loading plot possibilities that are acknowledged providing interpretations PLS in chemometric applications.