Some theoretical properties of the O‐PLS method

Abstract

AbstractThe objective of this paper is to present new properties of the orthogonal projections to latent structures (O‐PLS) method developed by Trygg and Wold (J. Chemometrics 2002; 16: 119–128). The original orthogonal signal correction (OSC) filter of Wold et al. (Chemometrics Intell. Lab. Syst. 1998; 44: 175–185) removes systematic variation from X that is unrelated to Y. O‐PLS is a more restrictive OSC filter. O‐PLS removes only systematic variation in X explained in each PLS component that is not correlated with Y. O‐PLS is a slight modification of the NIPALS PLS algorithm, which should make O‐PLS a generally applicable preprocessing and filtering method. The computation of the O‐PLS components under the constraint of being correlated with one PLS component imposes particular properties on the space spanned by the O‐PLS components. This paper is divided into two main sections. First we give an application of O‐PLS on near‐infrared reflectance spectra of soil samples, showing some graphical properties. Then we give the mathematical justifications of these properties. Copyright © 2004 John Wiley & Sons, Ltd.