Fuzzy discriminant analysis with outlier detection by genetic algorithm

Authors:
Chang-Chun Lin;An-Pin Chen
Affiliations:
Department of Information Management, Kun-Shan University of Technology, 949. Da-Wan Road, Yung-Kang, Tainan 710, Taiwan, ROC;Institute of Information Management, National Chiao-Tung University, Hsinchu 300, Taiwan, ROC
Venue:
Computers and Operations Research
Year:
2004

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Abstract

This paper proposes a method for performing fuzzy multiple discriminant analysis on groups of crisp data and determining the membership function of each group by minimizing the classification error using a genetic algorithm. Euclidean distance is used to measure the similarity between data points and defining membership functions. A numerical example is provided for illustration. The numerical example indicates that the classification obtained by fuzzy discriminant analysis is more satisfactory than that obtained by crisp discriminant analysis and is less fuzzy than that obtained by fuzzy cluster analysis. Moreover, the proposed fuzzy discriminant analysis is also a good approach to identifying outliers, of which the degree of membership to each group is zero.