Classification of repeated measurements using bias corrected Euclidean distance discriminant function

Abstract

This paper introduces a novel approach for approximating misclassification probabilities in Euclidean distance classifier when the group means exhibit a bilinear structure such as in the growth curve model first proposed by Potthoff and Roy (Biometrika 51:313–326, 1964). Initially, by leveraging certain statistical relationships, we establish two general results for the improved Euclidean discriminant function in both weighted and unweighted growth curve mean structures. We derive these approximations for the expected misclassification probabilities with respect to the distribution of the improved Euclidean discriminant function. Additionally, we compare the misclassification probabilities of the improved Euclidean discriminant function, the standard Euclidean discriminant function, and the linear discriminant function. It is important to note that in cases where the mean structure is weighted, a higher number of repeated measurements yields better classification results with the improved Euclidean discriminant function and the standard Euclidean discriminant function, allowing for more information to be acquired, as opposed to the linear discriminant function, which performs well with a smaller number of repeated measurements. Furthermore, we evaluate the accuracy of the suggested approximations by Monte Carlo simulations.