The main purpose of discriminant analysis is to enable classification of new observations into one of g classes or populations. Discriminant methods suffer when applied to high dimensional data because the sample covariance matrix is singular. In this study, we propose two new discriminant methods for high dimensional data under the multivariate normal population with a block diagonal covariance matrix structure. As the first method, we approximate the sample covariance matrix as a singular matrix based on the idea of reducing the dimensionality of the observations to get a well-conditioned covariance matrix. As the second method, we use a block diagonal sample covariance matrix instead. The performances of these two methods are compared with some of the existing methods in a simulation study. The results show that both proposed methods outperform other comparative methods in various situations. In addition, the two new proposed methods for discriminant analysis are applied to a real dataset.
