Orthogonal projections to latent structures (O-PLS)

TLDR: In this article, a generic preprocessing method for multivariate data, called orthogonal projections to latent structures (O-PLS), is described, which removes variation from X (descriptor variables) that is not correlated to Y (property variables, e.g. yield, cost or toxicity).

Abstract: A generic preprocessing method for multivariate data, called orthogonal projections to latent structures (O-PLS), is described. O-PLS removes variation from X (descriptor variables) that is not correlated to Y (property variables, e.g. yield, cost or toxicity). In mathematical terms this is equivalent to removing systematic variation in X that is orthogonal to Y. In an earlier paper, Wold et al. (Chemometrics Intell. Lab. Syst. 1998; 44: 175-185) described orthogonal signal correction (OSC). In this paper a method with the same objective but with different means is described. The proposed O-PLS method analyzes the variation explained in each PLS component. The non-correlated systematic variation in X is removed, making interpretation of the resulting PLS model easier and with the additional benefit that the non-correlated variation itself can be analyzed further. As an example, near-infrared (NIR) reflectance spectra of wood chips were analyzed. Applying O-PLS resulted in reduced model complexity with preserved prediction ability, effective removal of non-correlated variation in X and, not least, improved interpretational ability of both correlated and non-correlated variation in the NIR spectra.