Bounded Support Finite Mixtures for Multidimensional Data Modeling and Clustering

Data is ever increasing with today’s many technological advances in terms of both quantity and dimensions. Such inflation has posed various challenges in statistical and data analysis methods and hence requires the development of new powerful models for transforming the data into useful information. Therefore, it was necessary to explore and develop new ideas and techniques to keep pace with challenging learning applications in data analysis, modeling and pattern recognition. Finite mixture models have received considerable attention due to their ability to effectively and efficiently model high dimensional data. In mixtures, choice of distribution is a critical issue and it has been observed that in many real life applications, data exist in a bounded support region, whereas distributions adopted to model the data lie in unbounded support regions. Therefore, it was proposed to define bounded support distributions in mixtures and introduce a modified procedure for parameters estimation by considering the bounded support of underlying distributions. The main goal of this thesis is to introduce bounded support mixtures, their parameters estimation, automatic determination of number of mixture components and application of mixtures in feature extraction techniques to overall improve the learning pipeline. Five different unbounded support distributions are selected for applying the idea of bounded support mixtures and modified parameters estimation using maximum likelihood via Expectation-Maximization (EM). Probability density functions selected for this thesis include Gaussian, Laplace, generalized Gaussian, asymmetric Gaussian and asymmetric generalized Gaussian distributions, which are chosen due to their flexibility and broad applications in speech and image processing. The proposed bounded support mixtures are applied in various speech and images datasets to create leaning applications to demonstrate the effectiveness of proposed approach. Mixtures of bounded Gaussian and bounded Laplace are also applied in feature extraction and data representation techniques, which further improves the learning and modeling capability of underlying models. The proposed feature representation via bounded support mixtures is applied in both speech and images datasets to examine its performance. Automatic selection of number of mixture components is very important in clustering and parameter learning is highly dependent on model selection and it is proposed for mixture of bounded Gaussian and bounded asymmetric generalized Gaussian using minimum message length. Proposed model selection criterion and parameter learning are simultaneously applied in speech and images datasets for both models to examine the model selection performance in clustering

Features for matching people in different views

There have been significant advances in the computer vision field during the last decade. During this period, many methods have been developed that have been successful in solving challenging problems including Face Detection, Object Recognition and 3D Scene Reconstruction. The solutions developed by computer vision researchers have been widely adopted and used in many real-life applications such as those faced in the medical and security industry. Among the different branches of computer vision, Object Recognition has been an area that has advanced rapidly in recent years. The successful introduction of approaches such as feature extraction and description has been an important factor in the growth of this area. In recent years, researchers have attempted to use these approaches and apply them to other problems such as Content Based Image Retrieval and Tracking. In this work, we present a novel system that finds correspondences between people seen in different images. Unlike other approaches that rely on a video stream to track the movement of people between images, here we present a feature-based approach where we locate a target’s new location in an image, based only on its visual appearance. Our proposed system comprises three steps. In the first step, a set of features is extracted from the target’s appearance. A novel algorithm is developed that allows extraction of features from a target that is particularly suitable to the modelling task. In the second step, each feature is characterised using a combined colour and texture descriptor. Inclusion of information relating to both colour and texture of a feature add to the descriptor’s distinctiveness. Finally, the target’s appearance and pose is modelled as a collection of such features and descriptors. This collection is then used as a template that allows us to search for a similar combination of features in other images that correspond to the target’s new location. We have demonstrated the effectiveness of our system in locating a target’s new position in an image, despite differences in viewpoint, scale or elapsed time between the images. The characterisation of a target as a collection of features also allows our system to robustly deal with the partial occlusion of the target

Pixel Value Graphical Password Scheme: K-Means as Graphical Password Fault Tolerance

Pixel value access control (PVAC) was introduced to deliver a secure and simple graphical password method where it requires users to load their image as their password. PVAC extracts the image to obtain a three-octet 8-bits Red-Green-Blue (RGB) value as its password to authenticate a user. The pixel value must be matched with the record stored in the database or otherwise, the user is failed to authenticate. However, users which prefer to store images on cloud storage would unintentionally alter and as well as the pixel value due to media compression and caused faulty pixels. Thus, the K-Means clustering algorithm is adapted to fix the issue where the faulty pixel value would be recognized as having the same pixel value cluster as the original. However, most of K-Means algorithm works were mainly developed for content-based image retrieval (CBIR) which having opposite characteristics from PVAC. Thus, this study was aimed to investigate the crucial criteria of PVAC and its compatibility with the K-Means algorithm for the problem. The theoretical analysis is used for this study where the suitable characteristics of K-Means are analyze based on PVAC requirements. The compliance analysis might become a referencing work for digital image clustering techniques adaptation on security system such as image filtering, image recognition, and object detection since most of image clustering works was focused on less sensitive image retrieval

Variational Approaches For Learning Finite Scaled Dirichlet Mixture Models

With a massive amount of data created on a daily basis, the ubiquitous demand for data analysis is undisputed. Recent development of technology has made machine learning techniques applicable to various problems. Particularly, we emphasize on cluster analysis, an important aspect of data analysis. Recent works with excellent results on the aforementioned task using finite mixture models have motivated us to further explore their extents with different applications. In other words, the main idea of mixture model is that the observations are generated from a mixture of components, in each of which the probability distribution should provide strong flexibility in order to fit numerous types of data. Indeed, the Dirichlet family of distributions has been known to achieve better clustering performances than those of Gaussian when the data are clearly non-Gaussian, especially proportional data.  Thus, we introduce several variational approaches for finite Scaled Dirichlet mixture models. The proposed algorithms guarantee reaching convergence while avoiding the computational complexity of conventional Bayesian inference. In summary, our contributions are threefold. First, we propose a variational Bayesian learning framework for finite Scaled Dirichlet mixture models, in which the parameters and complexity of the models are naturally estimated through the process of minimizing the Kullback-Leibler (KL) divergence between the approximated posterior distribution and the true one. Secondly, we integrate component splitting into the first model, a local model selection scheme, which gradually splits the components based on their mixing weights to obtain the optimal number of components. Finally, an online variational inference framework for finite Scaled Dirichlet mixture models is developed by employing a stochastic approximation method in order to improve the scalability of finite mixture models for handling large scale data in real time. The effectiveness of our models is validated with real-life challenging problems including object, texture, and scene categorization, text-based and image-based spam email detection

Bayesian methods for non-gaussian data modeling and applications

Finite mixture models are among the most useful machine learning techniques and are receiving considerable attention in various applications. The use of finite mixture models in image and signal processing has proved to be of considerable interest in terms of both theoretical development and in their usefulness in several applications. In most of the applications, the Gaussian density is used in the mixture modeling of data. Although a Gaussian mixture may provide a reasonable approximation to many real-world distributions, it is certainly not always the best approximation especially in image and signal processing applications where we often deal with non-Gaussian data. In this thesis, we propose two novel approaches that may be used in modeling non-Gaussian data. These approaches use two highly flexible distributions, the generalized Gaussian distribution (GGD) and the general Beta distribution, in order to model the data. We are motivated by the fact that these distributions are able to fit many distributional shapes and then can be considered as a useful class of flexible models to address several problems and applications involving measurements and features having well-known marked deviation from the Gaussian shape. For the mixture estimation and selection problem, researchers have demonstrated that Bayesian approaches are fully optimal. The Bayesian learning allows the incorporation of prior knowledge in a formal coherent way that avoids overfitting problems. For this reason, we adopt different Bayesian approaches in order to learn our models parameters. First, we present a fully Bayesian approach to analyze finite generalized Gaussian mixture models which incorporate several standard mixtures, such as Laplace and Gaussian. This approach evaluates the posterior distribution and Bayes estimators using a Gibbs sampling algorithm, and selects the number of components in the mixture using the integrated likelihood. We also propose a fully Bayesian approach for finite Beta mixtures learning using a Reversible Jump Markov Chain Monte Carlo (RJMCMC) technique which simultaneously allows cluster assignments, parameters estimation, and the selection of the optimal number of clusters. We then validate the proposed methods by applying them to different image processing applications