A family of regression methods derived from standard PLSR

We present a new regression method derived from standard PLSR which has a geometric point of view and consists of two projections. In the first, scores are obtained after an oblique projection of the spectra onto the loadings. In the second, the vector of response values is projected orthogonally onto the scores. A metric is introduced for the oblique projection and a new algorithm for calculating the loadings into the variable space is proposed. This work also puts forward a new parameter, a vector, whose different values lead to different regression models with their own prediction abilities, and one of them is the exact form of standard PLSR. This method (called vector orientation decided through knowledge assessment, or VODKA regression) is another way to build least squares regressions using only a few latent variables. We propose two Email addresses: [email protected] (Jean-Claude Boulet ), [email protected] (Dominique Bertrand ), [email protected] (Gérard Mazerolles ), [email protected] (Robert Sabatier), [email protected] (Jean-Michel Roger) 1corresponding author 2present address: Data Frame, 25 rue Stendhal, F-44300 Nantes, France Preprint submitted to Chemolab May 29, 2012 Author-produced version of the article published in Chemometrics and Intelligent Laboratory Systems, 2013, 120, 116-125. The original publication is available at http://www.sciencedirect.com DOI : 10.1016/j.chemolab.2012.11.002 ha l-0 07 80 07 6, v er si on 1 23 J an 2 01 3 Author manuscript, published in ""