Fisher’s Linear Discriminant Classifier And Rank Transformation Approach To Discriminant Analysis

Abstract

Discriminant analysis is a multivariate statistical technique used primarily for obtaining a linear function of p variables which maximizes the distance between centroids or midpoints of multivariate distributions of k groups. Linear discriminant analysis was performed using the fisher’s technique which was also derived. Test for differences in the means for the two groups and their variance covariance matrices were discussed. A major shortcoming of the fisher’s linear discriminant analysis is that if normality assumption does not hold, the optimal property is lost. This paper compared Fisher’s linear discriminant analysis and the rank transformation approach. This was illustrated by performing discriminant analysis on the data and discriminant analysis on the ranks.  If the population is not normal, the effectiveness of this method is enhanced by using the ranks of the original data rather than the data themselves. The results obtained indicate that the two methods perform equally well but the rank transformation is a better alternative to the Fisher’s discriminant  technique  for distributions of small samples and non-normal data.

Keywords Fisher’s Linear Discriminant Analysis, Rank transformation, Classification, Apparent Error Rate.