Investigation of the optimal number of clusters by the adaptive EM algorithm

Abstract

This paper considers the investigation of the optimal number of clusters for datasets that are modeled as the Gaussian mixture. For that purpose, the adaptive method that is based on a modified Expectation Maximization (EM) algorithm is developed. The modification is conducted within the hidden variable of the standard EM algorithm. Assuming that data are multivariate normally distributed, where each component of the Gaussian mixture corresponds to one cluster, the modification is provided by utilizing the fact that the Mahalanobis distance of samples follows a Chi-square distribution. Besides, the quantity measure is constructed in order to determine number of clusters. The proposed method is presented in several numerical examples.