Abstract

Clustering is an important step in data mining, machine learning, computer vision and image processing. It is the process of assigning similar objects to the same subset. Among available clustering techniques, finite mixture models have been remarkably used, since they have the ability to consider prior knowledge about the data. Employing mixture models requires, choosing a standard distribution, determining the number of mixture components and estimating the model parameters. Currently, the combination of Gaussian distribution, as the standard distribution, and Expectation Maximization (EM), as the parameter estimator, has been widely used with mixture models. However, each of these choices has its own limitations. In this thesis, these limitations are discussed and addressed via defining a variational inference framework for finite inverted Dirichlet mixture model, which is able to provide a better capability in modeling multivariate positive data, that appear frequently in many real world applications. Finite inverted Dirichlet mixtures enable us to model high-dimensional, both symmetric and asymmetric data. Compared to the conventional expectation maximization (EM) algorithm, the variational approach has the following advantages: it is computationally more efficient, it converges fast, and is able to estimate the parameters and the number of the mixture model components, automatically and simultaneously. The experimental results validate the presented approach on different synthetic datasets and shows its performance for two interesting and challenging real world applications, namely natural scene categorization and human activity classification.