PLS and dimension reduction for classification

Barker and Rayens (J Chemometrics 17:166-173, 2003) offered convincing arguments that partial least squares (PLS) is to be preferred over principal components analysis (PCA) when discrimination is the goal and dimension reduction is required, since at least with PLS as the dimension reduction tool, information involving group separation is directly involved in the structure extraction. In this paper the basic results in Barker and Rayens (J Chemometrics 17:166-173, 2003) are reviewed and some of their ideas and comparisons are illustrated on a real data set, something which Barker and Rayens did not do. More importantly, new results are introduced, including a formal proof for the superiority of PLS over PCA in the two-group case, as well as new connections between PLS for discrimination and an extended class of PLS-like techniques known as "oriented PLS" (OrPLS). In the latter case, a particularly simple subclass of OrPLS procedures, when used to achieve the dimension reduction, is shown to always produce a lower misclassification rate than when "ordinary" PLS is used for the same purpose.