A family of regression methods derived from standard PLSR
The standard PLSR is presented from a geometric point of view consisting of two projections. In the first, the 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 the calculation of the loadings into the variables space is proposed. This work also develops a new parameter, a vector, whose different values lead to different regression models with their own abilities of prediction; one of them is the exact form of the standard PLSR. Two applications are described to illustrate the performance of the proposed method called VODKA regression, which is also a way to build least square regressions by introducing additional knowledge into the models. (C) 2012 Elsevier B.V. All rights reserved.
regression plsr projection oblique orthogonal metric calibration