Research and Application Based on Probability Statistics and Gaussian Mixture Clustering

This paper synthesises the in-depth study and extensive practical application of the principles of probabilistic statistics and the Gaussian mixture clustering (GMM) algorithm with the aim of revealing the powerful efficacy of the algorithm in dealing with complex data structures. By reviewing the theoretical foundations of Gaussian Mixture Models, this study firstly describes their central role in probability density estimation and how efficient learning of model parameters can be achieved by the Expectation Maximisation (EM) algorithm. Further, the thesis provides an in-depth analysis of algorithm performance optimisation strategies, including but not limited to the selection of initialisation methods, the setting of convergence criteria and model selection criteria, to cope with the challenges posed by large-scale datasets and high-dimensional data.