A hybrid nonlinear classifier based on generalized choquet integrals

Abstract

In this new hybrid model of nonlinear classifier, unlike the classical linear classifier where the feature attributes influence the classifying attribute independently, the interaction among the influences from the feature attributes toward the classifying attribute is described by a signed fuzzy measure. An optimized Choquet integral with respect to an optimized signed fuzzy measure is adopted as a nonlinear projector to map each observation from the sample space onto a one-dimensional space. Thus, combining a criterion concerning the weighted Euclidean distance, the new linear classifier also takes account of the elliptic-clustering character of the classes and, therefore, is much more powerful than some existing classifiers. Such a classifier can be applied to deal with data even having classes with some complex geometrical shapes such as crescent (cashew-shaped) classes. © Springer-Verlag Berlin Heidelberg 2004.