Abstract

In many unsupervised machine learning algorithms where labelling a large quantity of data is unfeasible and time-consuming, mixture models have been frequently employed as a helpful statistical learning method. Among all the proposed mixture models, the finite Gaussian mixture model is probably the most famous and widely used. However, other approaches, such as mixtures of Dirichlet distributions have recently been demonstrated to yield even more promising outcomes, especially for non-Gaussian data. As a result, we chose to work on Shifted-Scaled Dirichlet (SSD) mixture models that are more flexible than Gaussian and Dirichlet mixture models in fitting proportional data. In this thesis, we propose variational Bayesian frameworks for learning SSD mixture models. This learning approach has some advantages over other techniques, such as tractable learning computations, precise approximations, and guaranteed convergence. First, we propose a novel non-parametric method based on a hierarchical Dirichlet process mixture of SSD distributions. Then, we extend it to a hierarchical Pitman-Yor process mixture of SSD distributions. These Bayesian frameworks present several properties that make the learning process more accurate. Also, simultaneous parameter estimation and model selection (model complexity determination) are possible with the suggested methods. Finally, we propose a novel hidden Markov model (HMM) framework in which the emission density for conventional continuous HMMs is a mixture of SSD distributions. Experiments on challenging applications such as activity recognition, texture clustering, traffic sign detection, vehicle detection, and spam email detection show that our suggested models may deliver effective solutions when compared to existing alternatives.