Winsorization on linear discriminant analysis

Abstract

Linear discriminant analysis (LDA) is a widely used multivariate technique for pattern classification. LDA creates an equation which can minimize the possibility of misclassifying observations into their corresponding populations. The main objective of LDA is to classify multivariate data into different populations on the basis of a training sample with known group memberships. Under ideal conditions that is when the distribution is normal and variances are equal (homoscedasticity), LDA performs optimally. Nevertheless, the classical estimates, sample mean and sample covariance, are highly affected when the ideal conditions are violated. To alleviate these problems, a new robust LDA model using winsorized approach to estimate the location measure to replace the sample mean was introduced in this study. Meanwhile, for the robust covariance, the product of Spearman’s rho and the rescaled median absolute deviation was used as the substitute for the classical covariance. The optimality of the proposed model in terms of misclassification error rate was evaluated through simulation and real data application. The results revealed that the misclassification error rate of the proposed model were always better than the classical LDA and were comparable with the existing robust LDA under contamination. In contrast, in terms of computational time, classical LDA provide the shortest time followed by the proposed model and the existing robust LDA.