Abstract

In this thesis, we propose a novel approach that can be used in modeling non-Gaussian
data using the generalized Gaussian distribution (GGD). The motivation behind this work is the shape flexibility of the GGD because of which it can be applied to model different types of data having well-known marked deviation from the Gaussian shape.

We present the variational expectation-maximization algorithm to evaluate the posterior distribution and Bayes estimators of GGD mixture models. With well defined prior distributions, the lower bound of the variational objective function is constructed. We also present a variational learning framework for the infinite generalized Gaussian mixture (IGGM) to address the model selection problem; i.e., determination of the number of clusters without recourse to the classical selection criteria such that the number of mixture components increases automatically to best model available data accordingly. We incorporate feature selection to consider the features that are most appropriate in constructing an approximate model in terms of clustering accuracy. We finally integrate the Pitman-Yor process into our proposed model for an infinite extension that leads to better performance in the task of background subtraction. Experimental results show the effectiveness of the proposed algorithms.