Abstract

Multimedia contents are mostly described in discrete forms, so analyzing discrete data becomes an important task in many image processing and computer vision applications. One of the most used approaches for discrete data modeling is the finite mixture of multinomial distributions, considering that the events to model are independent. It, however, fails to capture the true nature in the case of sparse data and leads generally to poor biased estimates. Different smoothing techniques that reflect prior background knowledge are proposed to overcome this issue. Generalized Dirichlet distribution has suitable covariance structure, so it offers flexibility in parameter estimation; therefore, it has become a favorable choice as a prior. This specific choice, however, has its problems mainly in the estimation of the parameters, which appears to be a laborious task and can deteriorate the estimates accuracy when we consider the maximum likelihood (ML) approach.

In this thesis, we propose an unsupervised statistical approach to learn structures of this kind of data. The central ingredient in our model is the introduction of the generalized Dirichlet distribution mixture as a prior to the multinomial. An estimation algorithm for the parameters based on leave-one-out (LOO) likelihood and empirical Bayesian inference is developed. This estimation algorithm can be viewed as a hybrid expectation-maximization (EM) which alternates EM iterations with Newton-Raphson iterations using the Hessian matrix. We also propose the use of our model as a parametric basis for support vector machines (SVM) within a hybrid Generative/discriminative framework. Through a series of experiments involving scene modeling and classification using visual words and color texture modeling, we show the efficiency of the proposed approaches.