Robust Linear Discriminant Analysis with Highest Breakdown Point Estimator

Abstract

Linear Discriminant Analysis (LDA) is a supervised classification technique concerned with the relationship between a categorical variable and a set of interrelated variables. The main objective of LDA is to create a rule to distinguish between populations and allocating future observations to previously defined populations. The LDA yields optimal discriminant rule between two or more groups under the assumptions of normality and homoscedasticity. Nevertheless, the classical estimates, sample mean and sample covariance matrix, are highly affected when the ideal conditions are violated. To abate these problems, a new robust LDA rule using high breakdown point estimators has been proposed in this article. A winsorized approach used to estimate the location measure while the multiplication of Spearman’s rho and the rescaled median absolute deviation were used to estimate the scatter measure to replace the sample mean and sample covariance matrix, respectively. Simulation and real data study were conducted to evaluate the performance of the proposed model measured in terms of misclassification error rates. The computational results showed that the proposed LDA is always better than the classical LDA and were comparable with the existing robust LDAs.