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

Approximate Bayesian Inference for Count Data Modeling

Bayesian inference allows to make conclusions based on some antecedents that depend on prior knowledge. It additionally allows to quantify uncertainty, which is important in Machine Learning in order to make better predictions and model interpretability. However, in real applications, we often deal with complicated models for which is unfeasible to perform full Bayesian inference. This thesis explores the use of approximate Bayesian inference for count data modeling using Expectation Propagation and Stochastic Expectation Propagation. In Chapter 2, we develop an expectation propagation approach to learn an EDCM finite mixture model. The EDCM distribution is an exponential approximation to the widely used Dirichlet Compound distribution and has shown to offer excellent modeling capabilities in the case of sparse count data. Chapter 3 develops an efficient generative mixture model of EMSD distributions. We use Stochastic Expectation Propagation, which reduces memory consumption, important characteristic when making inference in large datasets. Finally, Chapter 4 develops a probabilistic topic model using the generalized Dirichlet distribution (LGDA) in order to capture topic correlation while maintaining conjugacy. We make use of Expectation Propagation to approximate the posterior, resulting in a model that achieves more accurate inference compared to variational inference. We show that latent topics can be used as a proxy for improving supervised tasks

Statistical Analysis of Spherical Data: Clustering, Feature Selection and Applications

In the light of interdisciplinary applications, data to be studied and analyzed have witnessed a growth in volume and change in their intrinsic structure and type. In other words, in practice the diversity of resources generating objects have imposed several challenges for decision maker to determine informative data in terms of time, model capability, scalability and knowledge discovery. Thus, it is highly desirable to be able to extract patterns of interest that support the decision of data management. Clustering, among other machine learning approaches, is an important data engineering technique that empowers the automatic discovery of similar object’s clusters and the consequent assignment of new unseen objects to appropriate clusters. In this context, the majority of current research does not completely address the true structure and nature of data for particular application at hand. In contrast to most previous research, our proposed work focuses on the modeling and classification of spherical data that are naturally generated in many data mining and knowledge discovery applications. Thus, in this thesis we propose several estimation and feature selection frameworks based on Langevin distribution which are devoted to spherical patterns in offline and online settings. In this thesis, we first formulate a unified probabilistic framework, where we build probabilistic kernels based on Fisher score and information divergences from finite Langevin mixture for Support Vector Machine. We are motivated by the fact that the blending of generative and discriminative approaches has prevailed by exploring and adopting distinct characteristic of each approach toward constructing a complementary system combining the best of both. Due to the high demand to construct compact and accurate statistical models that are automatically adjustable to dynamic changes, next in this thesis, we propose probabilistic frameworks for high-dimensional spherical data modeling based on finite Langevin mixtures that allow simultaneous clustering and feature selection in offline and online settings. To this end, we adopted finite mixture models which have long been heavily relied on deterministic learning approaches such as maximum likelihood estimation. Despite their successful utilization in wide spectrum of areas, these approaches have several drawbacks as we will discuss in this thesis. An alternative approach is the adoption of Bayesian inference that naturally addresses data uncertainty while ensuring good generalization. To address this issue, we also propose a Bayesian approach for finite Langevin mixture model estimation and selection. When data change dynamically and grow drastically, finite mixture is not always a feasible solution. In contrast with previous approaches, which suppose an unknown finite number of mixture components, we finally propose a nonparametric Bayesian approach which assumes an infinite number of components. We further enhance our model by simultaneously detecting informative features in the process of clustering. Through extensive empirical experiments, we demonstrate the merits of the proposed learning frameworks on diverse high dimensional datasets and challenging real-world applications

Novel Mixture Allocation Models for Topic Learning

Unsupervised learning has been an interesting area of research in recent years. Novel algorithms are being built on the basis of unsupervised learning methodologies to solve many real world problems. Topic modelling is one such fascinating methodology that identifies patterns as topics within data. Introduction of latent Dirichlet Allocation (LDA) has bolstered research on topic modelling approaches with modifications specific to the application. However, the basic assumption of a Dirichlet prior in LDA for topic proportions, might not be applicable in certain real world scenarios. Hence, in this thesis we explore the use of generalized Dirichlet (GD) and Beta-Liouville (BL) as alternative priors for topic proportions. In addition, we assume a mixture of distributions over topic proportions which provides better fit to the data. In order to accommodate application of the resulting models to real-time streaming data, we also provide an online learning solution for the models. A supervised version of the learning framework is also provided and is shown to be advantageous when labelled data are available. There is a slight chance that the topics thus derived may not be that accurate. In order to alleviate this problem, we integrate an interactive approach which uses inputs from the user to improve the quality of identified topics. We have also tweaked our models to be applied for interesting applications such as parallel topics extraction from multilingual texts and content based recommendation systems proving the adaptability of our proposed models. In the case of multilingual topic extraction, we use global topic proportions sampled from a Dirichlet process (DP) to tackle the problem and in the case of recommendation systems, we use the co-occurrences of words to our advantage. For inference, we use a variational approach which makes computation of variational solutions easier. The applications we validated our models with, show the efficiency of proposed models