Two class-modelling techniques that give families of class-models and their relation with the structure of the data

In class-modelling problems, which are again becoming increasingly important, there are two parameters to value the quality of the class-model built for a category, namely sensitivity and specificity. Using them as criteria, in this paper, two different approaches to class-modelling problems are presented, approaches that differ from other usual methods in the fact that they provide not just one class-model per category but a set of different class-models that accounts for the possible pairs of sensitivity-specificity values attainable for a given data set. One of the proposals is partial least squares class-modelling (PLS-CM) that, by the joint use of PLS with binary responses and the posterior statistical modelling of the distribution of the computed responses, permits the estimation of the risks related to the decision of assigning a sample into a class, and thus, the values of sensitivity and specificity. The other proposed method, Pareto-optimal front in class-modelling, is an analytical approach posed in a multi-response optimization framework, the one that corresponds to trying to simultaneously maximise the sensitivity and specificity of a class-model. Additionally, the whole family of computed class-models is validated in prediction by using cross-validation, showing the stability of both methods for prediction. The case-studies show the complementariness of both approaches and, in particular, that the joint use of both techniques allows the user to detect possible structures in the data set especially inadequate for PLS. The results, i.e. the whole set of sensitivity-specificity values achievable for a given problem, are graphically represented to improve its study and make it easy to make a decision about the model.