Handling Variables, via Inversion of Partial Least Squares Models for Class-Modelling, to Bring Defective Items to Non-Defective Ones

Abstract

In the context of binary class-modelling techniques, the paper presents the computation in the input space of linear boundaries of a class-model constructed with given values of sensitivity and specificity. This is done by inversion of a decision threshold, set with these values of sensitivity and specificity, in the probabilistic class-models computed by means of PLS-CM (Partial Least Squares for Class-Modelling). The characterization of the boundary hyperplanes, in the latent space (space spanned by the selected latent variables of the fitted PLS model) or in the input space, makes it possible to calculate directions that can be followed to move objects toward the class-model of interest. Different points computed along these directions will show how to modify the input variables (provided they can be manipulated) so that, eventually, a computed ‘object’ would be inside the class-model, in terms of the prediction with the PLS model. When the class of interest is that of “adequate” objects, as for example in some process control or product formulation, the proposed procedure helps in answering the question about how to modify the input variables so that a defective object would be inside the class-model of the adequate (non-defective) ones. This is the situation illustrated with some examples, taken from the literature when modelling the class of adequate objects.