Compression into two-component PLS factorizations

Abstract

Partial least squares regression (PLSR) often requires more than two components also in the case of a scalar response variable. As shown in papers on orthogonal signal correction (OSC), it is possible to reduce the number of components, resulting in easier data interpretation. In this paper it is shown how all scalar response PLSR models can be reduced to two-component models with the same structure and giving exactly the same estimator as the original model using many components. This is done by use of a direct and very simple algorithm based on a two-dimensional subspace in the loading weight space. The resulting model may be transformed into different realizations for different purposes, e.g. latent variable profile estimation, process monitoring, fault detection, etc., as discussed in the paper.