Detailed Clustering Based on Gaussian Mixture Models

Abstract

The work is devoted to the application of models of Gaussian Mixture Models (GMM) and Deep Gaussian Mixture Models (DGMM) for solving clustering problems. Besides the brief review of clustering algorithms and such algorithms classification is presented. Examples of probability densities functions (PDF) for GMM and DGMM are presented. Firstly the only one-parameter systems are considered. Then the models are generalized to apply it for clustering two- and more parameters data. However the basic research deals with 2D-data. The dataset included National Hockey League (NHL) and Continental Hockey League (KHL) statistics. Some teams were divided to three groups: leaders, middle-table teams and outsiders. So it was necessary to cluster all teams in this 3 groups and deep clustering was aided to divide all teams in six groups given the championship. So important parameters for clustering are goals scored and wins in season. It is shown that a two-layer deep model has more options for clustering compared to a single-layer. A comparative analysis of the operation of clustering algorithms based on such models for the statistics of hockey championships has been performed. Thus the DGMM allows one’s to make deep clustering not only dividing to 3 table-place groups but also to determine championship.