• O2-PLS;
  • O-PLS;
  • latent variable regression;
  • structured noise;
  • score–loading correspondence;
  • model interpretation


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 (YTX) 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 components. In the simulated example the O2-PLS plot of observed versus predicted Y-scores (u vs uhat) showed good predictions. The corresponding loading vectors provided good interpretation of the covarying analytes in X and Y. Copyright © 2003 John Wiley & Sons, Ltd.