Robustness of the Quadratic Discriminant Function to correlated and uncorrelated normal training samples

Abstract

This study investigates the asymptotic performance of the Quadratic Discriminant Function (QDF) under correlated and uncorrelated normal training samples. This paper specifically examines the effect of correlation, uncorrelation considering different sample size ratios, number of variables and varying group centroid separators (Formula presented.) on classification accuracy of the QDF using simulated data from three populations (πi,i=1,2,3). The three populations differs with respect to their mean vector and covariance matrices. The results show the correlated normal distribution exhibits high coefficient of variation as δ increased. The QDF performed better when the training samples were correlated than when they were under uncorrelated normal distribution. The QDF performed better resulting in the reduction in misclassification error rates as group centroid separator increases with non increasing sample size under correlated training samples.