An efficient algorithm to find the MLE of prior probabilities of a mixture in pattern recognition

Abstract

A number of techniques have been proposed to determine the parameters which define the unknown components of a mixture in pattern recognition. The most common method is the maximum likelihood estimation (MLE). A direct ML approach requires solution to maximize the likelihood function of the unknown prior probabilities of classes in a mixture. This is a complicated multiparameter optimization problem. The direct approach tends to be computationally complex and time consuming. In this study, we use the concave property of the Kullback-Leibler information number to derive a simple and accurate algorithm which can find the MLE of the prior probability of each class. The results of a Monte Carlo simulation study with normal and exponential distributions are presented to demonstrate the favorable prior estimation for the algorithm.