Statistical Approaches for Binary and Categorical Data Modeling

Nowadays a massive amount of data is generated as the development of technology and services has accelerated. Therefore, the demand for data clustering in order to gain knowledge has increased in many sectors such as medical sciences, risk assessment and product sales. Moreover, binary data has been widely used in various applications including market basket data and text documents analysis. While applying classic widely used k-means method is inappropriate to cluster binary data, we propose an improvement of K-medoids algorithm using binary similarity measures instead of Euclidean distance which is generally deployed in clustering algorithms. In addition to K-medoids clustering method, agglomerative hierarchical clustering methods based on Gaussian probability models have recently shown to be efficient in different applications. However, the emerging of pattern recognition applications where the features are binary or integer-valued demand extending research efforts to such data types. We propose a hierarchical clustering framework for clustering categorical data based on Multinomial and Bernoulli mixture models. We have compared two widely used density-based distances, namely; Bhattacharyya and Kullback-Leibler. The merits of our proposed clustering frameworks have been shown through extensive experiments on clustering text, binary images categorization and images categorization. The development of generative/discriminative approaches for classifying different kinds of data has attracted scholars’ attention. Considering the strengths and weaknesses of both approaches, several hybrid learning approaches which combined the desirable properties of both have been developed. Our contribution is to combine Support Vector Machines (SVMs) and Bernoulli mixture model in order to classify binary data. We propose using Bernoulli mixture model for generating probabilistic kernels for SVM based on information divergence. These kernels make intelligent use of unlabeled binary data to achieve good data discrimination. We evaluate the proposed hybrid learning approach by classifying binary and texture images

High-dimensional Sparse Count Data Clustering Using Finite Mixture Models

Due to the massive amount of available digital data, automating its analysis and modeling for different purposes and applications has become an urgent need. One of the most challenging tasks in machine learning is clustering, which is defined as the process of assigning observations sharing similar characteristics to subgroups. Such a task is significant, especially in implementing complex algorithms to deal with high-dimensional data. Thus, the advancement of computational power in statistical-based approaches is increasingly becoming an interesting and attractive research domain. Among the successful methods, mixture models have been widely acknowledged and successfully applied in numerous fields as they have been providing a convenient yet flexible formal setting for unsupervised and semi-supervised learning. An essential problem with these approaches is to develop a probabilistic model that represents the data well by taking into account its nature. Count data are widely used in machine learning and computer vision applications where an object, e.g., a text document or an image, can be represented by a vector corresponding to the appearance frequencies of words or visual words, respectively. Thus, they usually suffer from the well-known curse of dimensionality as objects are represented with high-dimensional and sparse vectors, i.e., a few thousand dimensions with a sparsity of 95 to 99%, which decline the performance of clustering algorithms dramatically. Moreover, count data systematically exhibit the burstiness and overdispersion phenomena, which both cannot be handled with a generic multinomial distribution, typically used to model count data, due to its dependency assumption. This thesis is constructed around six related manuscripts, in which we propose several approaches for high-dimensional sparse count data clustering via various mixture models based on hierarchical Bayesian modeling frameworks that have the ability to model the dependency of repetitive word occurrences. In such frameworks, a suitable distribution is used to introduce the prior information into the construction of the statistical model, based on a conjugate distribution to the multinomial, e.g. the Dirichlet, generalized Dirichlet, and the Beta-Liouville, which has numerous computational advantages. Thus, we proposed a novel model that we call the Multinomial Scaled Dirichlet (MSD) based on using the scaled Dirichlet as a prior to the multinomial to allow more modeling flexibility. Although these frameworks can model burstiness and overdispersion well, they share similar disadvantages making their estimation procedure is very inefficient when the collection size is large. To handle high-dimensionality, we considered two approaches. First, we derived close approximations to the distributions in a hierarchical structure to bring them to the exponential-family form aiming to combine the flexibility and efficiency of these models with the desirable statistical and computational properties of the exponential family of distributions, including sufficiency, which reduce the complexity and computational efforts especially for sparse and high-dimensional data. Second, we proposed a model-based unsupervised feature selection approach for count data to overcome several issues that may be caused by the high dimensionality of the feature space, such as over-fitting, low efficiency, and poor performance. Furthermore, we handled two significant aspects of mixture based clustering methods, namely, parameters estimation and performing model selection. We considered the Expectation-Maximization (EM) algorithm, which is a broadly applicable iterative algorithm for estimating the mixture model parameters, with incorporating several techniques to avoid its initialization dependency and poor local maxima. For model selection, we investigated different approaches to find the optimal number of components based on the Minimum Message Length (MML) philosophy. The effectiveness of our approaches is evaluated using challenging real-life applications, such as sentiment analysis, hate speech detection on Twitter, topic novelty detection, human interaction recognition in films and TV shows, facial expression recognition, face identification, and age estimation