Comparison of simple projection methods (OPLS, PLSO, and TP) for separation of predicting and non-predicting information in PLSR and PCR, with focus on DA

Abstract

Orthogonal projections to latent structures (OPLS) and target projection (TP) are two alternative methods for separation of predicting and non-predicting parts of the predictor matrix in partial least squares regression (PLSR), which can also be applied on principal component regression (PCR). An additional new method called PLSO is developed in the paper. In all three methods, the predicting score vector is a scaled version of the fitted response vector. Otherwise, the resulting score and loading vectors are different, although OPLS and TP are identical within similarity transformations. All these relations are here found by simple projections of the fitted predictor matrix from PLSR or PCR, and the similarities and differences are illustrated in discriminant analysis examples.