OPLS filtered data can be obtained directly from non-orthogonalized PLS1

The well-known Martens factorization for PLS1 produces a single y-related score, with all subsequent scores being y-unrelated. The X-explanatory value of these y-orthogonal scores can be summarized by a simple expression, which is analogous to the 'P' loading weights in the orthogonalized NIPALS algorithm. This can be used to rearrange the factorization into entirely y-related and y-unrelated parts. Systematic y-unrelated variation can thus be removed from the X data through a single post hoc calculation following conventional PLS, without any recourse to the orthogonal projections to latent structures (OPLS) algorithm. The work presented is consistent with the development by Ergon (PLS post-processing by similarity transformation (PLS + ST): a simple alternative to OPLS. J. Chemom. 2005; 19: 1-4), which shows that conventional PLS and OPLS are equivalent within a similarity transform. Copyright (C) 2009 John Wiley & Sons, Ltd.