The parsimonious Gaussian mixture models with partitioned parameters and their application in clustering

Cluster analysis is a method that identifies similar groups of data without any prior knowledge of the relevant groups. One of the most widely used clustering methods is model-based clustering, in which data clustering is performed by fitting a probabilistic model to the data. Mixture of Gaussian distributions is a commonly used model in model-based clustering. Unfortunately, the number of covariance matrices parameters rapidly increases by increasing the number of variables or components in these models. So far, various classes of the parsimonious Gaussian mixture models, by applying various constraints on the covariance matrices, have been introduced to solve this problem. Unfortunately, the number of models in each of these classes is so small such that in practice it does not allow the study and selection of models with any number of parameters, which can vary between the minimum number (one parameter) and the maximum number (no constraints model) of parameters. In this paper, to deal with this problem a family of the parsimonious Gaussian mixture models is introduced. This is done by identifying and determining the appropriate partitions of the variances and correlation coefficients between variables among clusters. We call these models “the parsimonious Gaussian mixture models with partitioned parameters". The generalized Expectation-Conditional Maximization algorithm, by employing the Fisher scoring method within the algorithm, is used to compute the maximum likelihood estimates of parameters. Bayesian information criterion is used for comparing and selecting the best model. Also, the steepest ascent method is adapted to search the best model. Finally, performances of these models are examined on two real datasets and a brief simulation study.