Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach

Robust linear discriminant analysis (RLDA) methods are becoming the better choice for classification problems as compared to the classical linear discriminant analysis (LDA) due to their ability in circumventing outliers issue. Classical LDA relies on the usual location and scale estimators which are the sample mean and covariance matrix. The sensitivity of these estimators towards outliers will jeopardize the classification process. To alleviate the issue, robust estimators of location and covariance are proposed. Thus, in this study, two RLDA for two groups classification were modified using two highly robust location estimators namely Modified One-Step M-estimator (MOM) and Winsorized Modified One-Step M-estimator (WMOM). Integrated with a
highly robust scale estimator, Qn, in the trimming criteria of MOM and WMOM, two new RLDA were developed known as RLDAMQ and RLDAWMQ respectively. In the computation of the new RLDA, the usual mean is replaced by MOM-Qn and
WMOM-Qn accordingly. The performance of the new RLDA were tested on simulated as well as real data and then compared against the classical LDA. For simulated data, several variables were manipulated to create various conditions that
always occur in real life. The variables were homogeneity of covariance (equal and unequal), samples (balanced and unbalanced), dimension of variables, and the percentage of contamination. In general, the results show that the performance of the new RLDA are more favorable than the classical LDA in terms of average
misclassification error for contaminated data, although the new RLDA have the shortcoming of requiring more computational time. RLDAMQ works best under balanced sample sizes while RLDAWMQ surpasses the others under unbalanced sample
sizes. When real financial data were considered, RLDAMQ shows capability in handling outliers with lowest misclassification error. As a conclusion, this research has achieved its primary objective which is to develop new RLDA for two groups classification of multivariate data in the presence of outliers.