A hybrid nonlinear classifier based on generalized choquet integrals

Authors:
Zhenyuan Wang;Hai-Feng Guo;Yong Shi;Kwong-Sak Leung
Affiliations:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE;Department of Computer Science, University of Nebraska at Omaha, Omaha, NE;Department of Information Systems and Quantitative Analysis, University of Nebraska at Omaha, Omaha, NE;Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong
Venue:
CASDMKM'04 Proceedings of the 2004 Chinese academy of sciences conference on Data Mining and Knowledge Management
Year:
2004

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Abstract

In this new hybrid model ofnonlinear 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.