A Proposed Non-Normal Classification Groups in Discriminant Analysis

Abstract

The paper tackles the problem of supervised classification of an object to one of two classification groups when one or both groups are not normal. The usual way to address this problem is through linear (quadratic) discriminant analysis where the populations are usually assumed normal. We proposed a median-based disciminant analysis (MDA) and demonstrated that it is superior to the usual LDA in terms of the high probability of correct classification (or low misclassification probability) when one or both groups are not normal. In the multivariate case, we proposed a Multivariate Median-Based Discriminant Rule (MMDA) and a Hyperplane-Based Discriminant Rule (HDA) as alternatives to the linear discriminant analysis procedure (LDA). Results in the multivariate case show the superiority of both approaches when the populations are not normal (highly skewed) or when the means of the two populations are close to each other. Applications in the field of Biological Diversity are suggested to illustrate the potential use of the new procedures for discrimination.