Probability Base Classification Technique: A Preliminary Study for Two Groups

Abstract

The conventional Fisher linear classification technique to perform classification for two groups problem is strictly developed based on the within group sample mean vectors and within group sample variance covariance matrices. A comparable classification procedure that incorporate the within group probabilities is considered. The conventional procedure based on the Fisher’s technique assumed equality of the within group probabilities as such the computational procedure negate the within groups probabilities to solve classification problems. The new approach is a modification of the coefficient of the Fisher’s technique by applying the within group probability for the respective groups to solve classification problems.The classification performance of these techniques is investigated based on generated contaminated normal data set using homoscedastic and heteroscedastic variance covariance matrices for various sample sizes and dimensions. The comparative performance of these procedures are investigated by comparing the mean probabilities of correct classification based on the contaminated date set with the mean of the optimal probability computed from the uncontaminated data set. The comparative classification performance revealed that both techniques perform comparable. Though, the Monte Carlo simulation indicate that as the proportion of contamination increases, the probability base approach perform better for homoscedastic covariance matrices, on the other hand, the Fisher’s technique outperformed the probability base procedure for heteroscedastic covariance matrices. The comparative analysis indicate that the probability base approach performed comparable with the conventional procedure. The implication of this procedure indicate that classification problems can be solved by incorporating the respective within group probabilities to develop the classification model.

Keywords: Classification, Homoscedastic and Heteroscedastic Covariance Matrices, Mean Probability