Abstract
A generalized nonlinear classification model based on cross-oriented Choquet integrals is presented. A couple of Choquet integrals are used in this model to achieve the classification boundaries which can classify data in such situation as one class surrounding another one in a high dimensional space. The values of unknown parameters in the generalized model are optimally determined by a genetic algorithm based on a given training data set. Both artificial experiments and real case studies show that this generalized nonlinear classifier based on cross-oriented Choquet integrals improves and extends the functionality of traditional classifier based on one Choquet integral on solving the classification problems of multi-class multi-dimensional situations.
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References
Denneberg, D.: Non-additive Measure and Integral. Kluwer, Boston (1994)
Wang, Z., Klir, G.K.: Fuzzy Measure Theory. Plenum Press, New York (1992)
Murofushi, T., Sugeno, M., Machida, M.: Non monotonic fuzzy measures and the Choquet integral. Fuzzy Sets and Systems 64, 73–86 (1994)
Pap, E.: Null-Additive Set Functions. Kluwer Academic Publisher, Boston (1995)
Xu, K., Wang, Z., Heng, P.-A., Lueng, K.-S.: Classification by nonlinear integrals projections. IEEE Trans. Fuzzy Syst. 11(2), 187–201 (2003)
Wang, Z., Yang, R., Shi, Y.: A new nonlinear classification model based on cross-oriented Choquet integrals. In: Proc. Inter. Conf. Information Science and Technology, Nanjing, China, pp. 176–181 (2011)
Fang, H., Rizzo, M.L., Wang, H., Espy, K.A., Wang, Z.: A new nonlinear classifier with a penalized signed fuzzy measure using effective genetic algorithm. Pattern Recognition 43, 1393–1401 (2010)
Asuncion, A., Newman, D.J.: UCI Machine Learning Repository. University of California, School of Information and Computer Science, Irvine, CA (2007), http://www.ics.uci.edu/~mlearn/MLRepository.html
Wang, Z., Yang, R., Leung, K.S.: Nonlinear Integrals and Their Application on Data Mining. World Scientific, Signapore (2010)
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© 2012 Springer-Verlag Berlin Heidelberg
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Yang, R., Wang, Z. (2012). Generalized Nonlinear Classification Model Based on Cross-Oriented Choquet Integral. In: Perner, P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2012. Lecture Notes in Computer Science(), vol 7376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31537-4_3
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DOI: https://doi.org/10.1007/978-3-642-31537-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31536-7
Online ISBN: 978-3-642-31537-4
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