Treatment of a class-in-class modelling problem in chemical pattern recognition

A supervised learning procedure is described for the detection and characterization of classes which overlap or are located within other classes. The UNEQ classifier proposed by Derde and Massart is extended by applying tests for multivariate homogeneity and homoscedasticity, principal components analysis of each class box, and Boolean-type decision rules. The extended algorithm is suitable for class-in-class modelling. The procedure is applied to chemical data for an environmental problem involving an industrial source of emission and its immission effects.