Nowadays, with the advent of the Internet and the advancement of technology, a large number of data and variables are being produced and collected in many fields. Clustering is one of the useful methods for analyzing data with large number of variables called high-dimensional data. The purpose of clustering methods is identifying homogeneous structures among individuals described by variables. There is usually no description or information about the pattern and structure of the data before clustering, which is a big challenge. One of the most popular and important data clustering approaches is the multivariate model-based clustering approach. The presence of irrelevant variables that do not possess clustering information may obscure the data group structure. Therefore, it is necessary to delete the irrelevant variables by applying variable-selection methods. Given to the importance of this issue, this thesis deals with the problem of variable selection in the framework of model-based clustering approach by applying Gaussian mixture models. For this purpose, three methods of variable selection and their related algorithms are described and studied.
