Abstract

Data clustering is a fundamental unsupervised learning approach that impacts several domains such as data mining, computer vision, information retrieval, and pattern recognition. Various clustering techniques have been introduced over the years to discover the patterns. Mixture model is one of the most promising techniques for clustering. The design of mixture models hence involves finding the appropriate parameters and estimating the number of clusters in the data.

The Gaussian mixture model has especially shown good results to tackle this problem. However, the Gaussian assumption is not ideal for modeling asymmetrical data. For achieving an accurate approximation, I investigate the asymmetric Gaussian distribution which is capable of modeling asymmetric data.

A prevalent challenge researchers face when applying mixture models is the correct identification of the adequate number of mixture components to model the data at hand. Hence, in this thesis, I propose statistical algorithms based on asymmetric Gaussian mixture models. I also present novel Bayesian inference frameworks to estimate parameters and learn model structure.

Here, I thoroughly investigate the Bayesian inference framework, including Markov chain Monte Carlo and variational inference approaches, to learn appropriate model structure and precisely estimate parameters. I also incorporate feature selection within the frameworks to choose relevant features set and avoid noisy influence from uninformative features. Furthermore, I investigate nonparametric hierarchical models by introducing Dirichlet process and Pitman-Yor process.