PLS Typological Regression: Algorithmic, Classification and Validation Issues

Classification, within a PLS regression framework, is classically meant in the sense of the SIMCA methodology, i.e. as the assignment of statistical units to a-priori defined classes. As a matter of fact, PLS components are built with the double objective of describing the set of explanatory variables while predicting the set of response variables. Taking into account this objective, a classification algorithm is developed that allows to build typologies of statistical units whose different local PLS models have an intrinsic explanatory power higher than the initial global PLS model. The typology induced by the algorithm may undergo a non parametric validation procedure based on bootstrap. Finally, the definition of a compromise model is investigated.