Robust Linear Discriminant Rule Using Novel Distance-based Trimming Procedure

Y.S. Pang, N.A. Ahad, S.S. Syed Yahaya and Y.F. Lim

The widely used pattern classification technique, Linear Discriminant Analysis (LDA), creates a classifier to allocate new observations into one of the two known groups based on training sample mean vectors and covariance matrices. The optimality of the classifier’s performance depends on the accuracy of the estimators. The default classical estimators are known to be easily influenced by contaminated data. Nevertheless, the influence of data contamination can be reduced by several approaches including trimming. One of the existing trimming approaches is through distance based trimmed mean, but this approach still has its drawback as it uses the sensitive to contamination classical mean as the location estimator. Thus, to overcome the sensitivity of the location estimator to contamination, distance-based trimmed median is proposed to handle the aforementioned issue. In this paper, three discriminants rules are developed; classical (CLDR), distance based trimmed mean (RLDRM) and distance based trimmed median (RLDRT). CLDR was constructed using classical estimators, while the two robust classifiers constructed using α-trimmed mean and α-trimmed median paired with robust covariance respectively producing RLDRM and RLDRT. Simulation study showed that classifier constructed using CLDR fared the worst as compared to the RLDRT and RLDRM when outliers exist. RLDRT is the best among the investigated rules.

Volume 11 | 05-Special Issue

Pages: 969-978