Fuzzy discriminant analysis with outlier detection by genetic algorithm

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 classi.cation error using a genetic algorithm. Euclidean distance is used to measure the similarity between data points and de.ning membership functions. A numerical example is provided for illustration. The numerical example indicates that the classi.cation 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. ? 2003 Elsevier Ltd. All rights reserved.