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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Devijver, P.A., Kittler, J.: Pattern Recognition: A Statistical Approach. Prentice Hall, Englewood Cliffs (1982)
Grabisch, M., Nicolas, J.M.: Classification by fuzzy integral: Performance and tests. Fuzzy Sets and Systems 65, 255–271 (1994)
Mikenina, L., Zimmermann, H.: Improved feature selection and classification by the 2-additive fuzzy measure. Fuzzy Sets and Systems 107, 197–218 (1999)
Murofushi, T., Sugeno, M.: An interpretation of fuzzy measure and the Choquet integral as an integral with respect to a fuzzy measure. Fuzzy Sets and Systems 29, 201–227 (1989)
Wang, W., Wang, Z., Klir, G.J.: Genetic algorithm for determining fuzzy measures from data. Journal of Intelligent and Fuzzy Systems 6, 171–183 (1998)
Wang, Z.: A new genetic algorithm for nonlinear multiregressions based on generalized Choquet integrals. In: Proc. FUZZ-IEEE, pp. 819–821 (2003)
Wang, Z.: Convergence theorems for sequences of Choquet integrals. Int. J. General Systems 26, 133–143 (1997)
Wang, Z., Klir, G.J.: Fuzzy Measure Theory. Plenum, New York (1992)
Wang, Z., Leung, K.S., Wang, J.: A genetic algorithm for determining nonadditive set functions in information fusion. Fuzzy Sets and Systems 102, 463–469 (1999)
Weiss, S.M., Kapouleas, I.: An empirical comparison of pattern recognition, neural nets, and machine learning classification methods. In: Proc. 11th IJCAI, pp. 781–787 (1989)
Xu, K., Wang, Z., Heng, P.A., Leung, K.S.: Using generalized Choquet integrals in projection pursuit based classification. In: Proc. IFSA/NAFIPS, pp. 506–511 (2001)
Xu, K., Wang, Z., Leung, K.S.: Classification by nonlinear integral projections. IEEE T. Fuzzy Systems 11(2), 187–201 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, Z., Guo, HF., Shi, Y., Leung, KS. (2004). A Hybrid Nonlinear Classifier Based on Generalized Choquet Integrals. In: Shi, Y., Xu, W., Chen, Z. (eds) Data Mining and Knowledge Management. CASDMKM 2004. Lecture Notes in Computer Science(), vol 3327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30537-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-30537-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23987-1
Online ISBN: 978-3-540-30537-8
eBook Packages: Computer ScienceComputer Science (R0)