Interactive variable selection (IVS) for PLS. Part 1: Theory and algorithms

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Abstract
A modified PLS algorithm is introduced with the goal of achieving improved prediction ability. The method, denoted IVS‐PLS, is based on dimension‐wise selective reweighting of single elements in the PLS weight vectorw. Cross‐validation, a criterion for the estimation of predictive quality, is used for guiding the selection procedure in the modelling stage. A threshold that controls the size of the selected values inwis put inside a cross‐validation loop. This loop is repeated for each dimension and the results are interpreted graphically. The manipulation ofwleads to rotation of the classical PLS solution. The results of IVS‐PLS are different from simply selectingX‐variables prior to modelling. The theory is explained and the algorithm is demonstrated for a simulated data set with 200 variables and 40 objects, representing a typical spectral calibration situation with four analytes. Improvements of up to 70% in external PRESS over the classical PLS algorithm are shown to be possible.

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