Abstract

This thesis proposes a set of innovative clustering techniques that lever- age finite and infinite mixture models to analyze medical data and images of cells. The proposed approaches are designed to improve the accuracy and efficiency of clustering in these domains. These models utilize a flexible distribution, the Libby-Novick Beta distribution, to better model data with varying shapes due to an additional shape parameter compared to the con- ventional Beta distribution. In this study, our initial approach involves the use of deterministic learning techniques, with a focus on maximum likelihood using the expectation-maximization approach. To achieve accurate data rep- resentation in unsupervised learning, it is crucial to determine the optimal number of clusters. So, we expand the minimum message length (MML) principle to ascertain the number of clusters in Libby-Novick Beta mixtures. In order to overcome the challenge of estimating the number of mixture components, we extend our finite mixture model to an infinite one. Nonparametric Bayesian techniques can effectively capture data distribution with an unknown number of components. This approach is useful for complex data sets and can lead to more accurate predictions and better decision-making. Our models are evaluated for different medical applications throughout the entire process, and they consistently show superior performance over traditional alternatives. This study reveals the significance of the Libby-Novick Beta distribution and the recommended mixture models in converting medical data into practical insights. This conversion aids healthcare professionals in making more accurate decisions, thereby advancing the overall healthcare field.