Robust Fuzzy Discriminant Analysis in Presence of Outliers by Genetic Algorithms

Abstract

This paper studies a robust fuzzy discriminant analysis (RFDA) to deal with outliers in the crisp data. The difference between RFDA and classic fuzzy discriminant anlaysis (FDA), which is based on the distance, is that RFDA uses robust distance to measure the similarity between data points. The performance of RFDA is evaluated by a simulation study. The data are generated by using theMonte Carlosimulation technique. The data are arbitrarily set to 2, 3, and 4 groups with the sample size of 30 each. In each group, there are 3 and 10 independent variables and there are 1 and 3 outliers. The genetic algorithm implement by MATLAB version 6.5 is used with 100 runs for each setting condition. Based on the mean of apparent error rates and correct identification rates of outliers, the results reveal that RFDA is more satisfactory for group classification and outlier detection than the FDA.