O2-PLS, a two-block (X-Y) latent variable regression (LVR) method with an integral OSC filter

The O2-PLS method is derived from the basic partial least squares projections to latent structures (PLS) prediction approach. The importance of the covariation matrix ((YX)-X-T) is pointed out in-relation to both the prediction model and the structured noise in both X and Y. Structured noise in X (or Y) is defined as the systematic variation of X (or Y) not linearly correlated with Y (or X). Examples in spectroscopy include baseline, drift and scatter effects. If structured noise is present in X, the existing latent variable regression (LVR) methods, e.g. PLS, will have weakened score-loading correspondence beyond the first component. This negatively affects the interpretation of model parameters such as scores and loadings. The O2-PLS method models and predicts both X and Y and has an integral orthogonal signal correction (OSC) filter that separates the structured noise in X and Y from their joint X-Y covariation used in the prediction model. This leads to a minimal number of predictive components with full score-loading correspondence and also an opportunity to interpret the structured noise. In both a real and a simulated example, O2-PLS and PLS gave very similar predictions of Y. However, the interpretation of the prediction models was clearly improved with O2-PLS, because structured noise was present. In the NIR example, O2-PLS revealed a strong water peak and baseline offset in the structured noise component. In the simulated example the O2-PLS plot of observed versus predicted Y-scores (u vs u(hat)) showed good predictions. The corresponding loading vectors provided good interpretation of the covarying analytes in X and Y. Copyright (C) 2003 John Wiley Sons, Ltd.