X-tended target projection (XTP)-comparison with orthogonal partial least squares (OPLS) and PLS post-processing by similarity transformation (PLS plus ST)

Target projection (TP) also called target rotation (TR) was introduced to facilitate interpretation of latent-variable regression models. Orthogonal partial least squares (OPLS) regression and PLS post-processing by similarity transform (PLS + ST) represent two alternative algorithms for the same purpose. In addition, OPLS and PLS + ST provide components to explain systematic variation in X orthogonal to the response. We show, that for the same number of components, OPLS and PLS + ST provide score and loading vectors for the predictive latent variable that are the same as for TP except for a scaling factor. Furthermore, we show how the TP approach can be extended to become a hybrid of latent-variable (LV) regression and exploratory LV analysis and thus embrace systematic variation in X unrelated to the response. Principal component analysis (PCA) of the residual variation after removal of the target component is here used to extract the orthogonal components, but X-tended TP (XTP) permits other criteria for decomposition of the residual variation. If PCA is used for decomposing the orthogonal variation in XTP, the variance of the major orthogonal components obtained for OPLS and XTP is observed to be almost the same, showing the close relationship between the methods. The XTP approach is tested and compared with OPLS for a three-component mixture analyzed by infrared spectroscopy and a multicomponent mixture measured by near infrared spectroscopy in a reactor. Copyright (C) 2008 John Wiley & Sons, Ltd.