Sequential Linear Discriminant Analysis in High Dimensions Using Individual Discriminant Functions

Abstract: High dimensional classification has been highlighted for last two decades and much research has been conducted in order to circumvent challenges encountered in high dimensions. While existing methods have focused mainly on developing classification rules assuming independence of covariates or using regularization on the sample covariance matrix or the sample mean vector or among others, we propose a novel approach that employs the "discriminatory power" of each covariate, selects a set of important variables yielding the lowest misclassification rate empirically, and constructs the optimal linear classifier with selected variables. We carry out simulation studies and analyze real data sets to illustrate the performance of our proposed classifier by comparing it with existing classifiers.