Abstract

Clustering is a foundational paradigm in data mining and pattern recognition, which is aimed at grouping and uncovering meaningful clusters. Clustering techniques are essential for extracting meaningful structure from data across a wide range of scientific domains. One of the main challenges is the clustering of bounded data that may not follow a Gaussian distribution and has an unknown number of clusters. Furthermore, the presence of irrelevant features poses fundamental challenges under the unsupervised learning setting. The aforementioned challenges undermine both cluster quality and obscure the downstream decision-making. This thesis aims to address these challenges by proposing three frameworks that leverage generalizations of the standard Beta distribution. First, we propose a Bayesian Libby-Novick Beta mixture model (BLNBMM) with integrated feature selection. Second, we propose a Variational Infinite Libby-Novick Beta Mixture Model (VILNBMM). Third, we introduce a Neural Variational Inference for Infinite McDonald's Beta Mixture Model (NVI-IMBMM). To enable posterior inference in our proposed models, we develop multiple variational inference (VI) frameworks. These variational inference algorithms recast posterior estimation into the form of an optimization problem. The proposed algorithms were evaluated on different medical imaging datasets. To benchmark our models, we compared them against established probabilistic mixture models. Our experiments showcase that the proposed models can indeed capture complex class distributions in bounded data domains.