Unsupervised Selection and Estimation of Non-Gaussian Mixtures for High Dimensional Data Analysis

Lately, the enormous generation of databases in almost every aspect of life has created a great demand for new, powerful tools for turning data into useful information. Therefore, researchers were encouraged to explore and develop new machine learning ideas and methods. Mixture models are one of the machine learning techniques receiving considerable attention due to their ability to handle efficiently and effectively multidimensional data. Generally, four critical issues have to be addressed when adopting mixture models in high dimensional spaces: (1) choice of the probability density functions, (2) estimation of the mixture parameters, (3) automatic determination of the number of components M in the mixture, and (4) determination of what features best discriminate among the different components. The main goal of this thesis is to summarize all these challenging interrelated problems in one unified model. In most of the applications, the Gaussian density is used in 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 computer vision and image processing applications where we often deal with non-Gaussian data. Therefore, we propose to use three highly flexible distributions: the generalized Gaussian distribution (GGD), the asymmetric Gaussian distribution (AGD), and the asymmetric generalized Gaussian distribution (AGGD). 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. Recently, researches have shown that model selection and parameter learning are highly dependent and should be performed simultaneously. For this purpose, many approaches have been suggested. The vast majority of these approaches can be classified, from a computational point of view, into two classes: deterministic and stochastic methods. Deterministic methods estimate the model parameters for a set of candidate models using the Expectation-Maximization (EM) framework, then choose the model that maximizes a model selection criterion. Stochastic methods such as Markov chain Monte Carlo (MCMC) can be used in order to sample from the full a posteriori distribution with M considered unknown. Hence, in this thesis, we propose three learning techniques capable of automatically determining model complexity while learning its parameters. First, we incorporate a Minimum Message Length (MML) penalty in the model learning step performed using the EM algorithm. Our second approach employs the Rival Penalized EM (RPEM) algorithm which is able to select an appropriate number of densities by fading out the redundant densities from a density mixture. Last but not least, we incorporate the nonparametric aspect of mixture models by assuming a countably infinite number of components and using Markov Chain Monte Carlo (MCMC) simulations for the estimation of the posterior distributions. Hence, the difficulty of choosing the appropriate number of clusters is sidestepped by assuming that there are an infinite number of mixture components. Another essential issue in the case of statistical modeling in general and finite mixtures in particular is feature selection (i.e. identification of the relevant or discriminative features describing the data) especially in the case of high-dimensional data. Indeed, feature selection has been shown to be a crucial step in several image processing, computer vision and pattern recognition applications not only because it speeds up learning but also because it improves model accuracy and generalization. Moreover, the learning of the mixture parameters ( i.e. both model selection and parameters estimation) is greatly affected by the quality of the features used. Hence, in this thesis, we are trying to solve the feature selection problem in unsupervised learning by casting it as an estimation problem, thus avoiding any combinatorial search. Finally, the effectiveness of our approaches is evaluated by applying them to different computer vision and image processing applications

Bayesian Learning of Asymmetric Gaussian-Based Statistical Models using Markov Chain Monte Carlo Techniques

A novel unsupervised Bayesian learning framework based on asymmetric Gaussian mixture (AGM) statistical model is proposed since AGM is shown to be more effective compared to the classic Gaussian mixture. The Bayesian learning framework is developed by adopting sampling-based Markov chain Monte Carlo (MCMC) methodology. More precisely, the fundamental learning algorithm is a hybrid Metropolis-Hastings within Gibbs sampling solution which is integrated within a reversible jump MCMC (RJMCMC) learning framework, a self-adapted sampling-based MCMC implementation, that enables model transfer throughout the mixture parameters learning process, therefore, automatically converges to the optimal number of data groups. Furthermore, a feature selection technique is included to tackle the irrelevant and unneeded information from datasets. The performance comparison between AGM and other popular solutions is given and both synthetic and real data sets extracted from challenging applications such as intrusion detection, spam filtering and image categorization are evaluated to show the merits of the proposed approach

Bayesian Learning Frameworks for Multivariate Beta Mixture Models

Mixture models have been widely used as a statistical learning paradigm in various unsupervised machine learning applications, where labeling a vast amount of data is impractical and costly. They have shown a significant success and encouraging performance in many real-world problems from different fields such as computer vision, information retrieval and pattern recognition. One of the most widely used distributions in mixture models is Gaussian distribution, due to its characteristics, such as its simplicity and fitting capabilities. However, data obtained from some applications could have different properties like non-Gaussian and asymmetric nature. In this thesis, we propose multivariate Beta mixture models which offer flexibility, various shapes with promising attributes. These models can be considered as decent alternatives to Gaussian distributions. We explore multiple Bayesian inference approaches for multivariate Beta mixture models and propose a suitable solution for the problem of estimating parameters using Markov Chain Monte Carlo (MCMC) technique. We exploit Gibbs sampling within Metropolis-Hastings for learning parameters of our finite mixture model. Moreover, a fully Bayesian approach based on birth-death MCMC technique is proposed which simultaneously allows cluster assignments, parameters estimation and the selection of the optimal number of clusters. Finally, we develop a nonparametric Bayesian framework by extending our finite mixture model to infinity using Dirichlet process to tackle the model selection problem. Experimental results obtained from challenging applications (e.g., intrusion detection, medical, etc.) confirm that our proposed frameworks can provide effective solutions comparing to existing alternatives

VIDEO FOREGROUND LOCALIZATION FROM TRADITIONAL METHODS TO DEEP LEARNING

These days, detection of Visual Attention Regions (VAR), such as moving objects has become an integral part of many Computer Vision applications, viz. pattern recognition, object detection and classification, video surveillance, autonomous driving, human-machine interaction (HMI), and so forth. The moving object identification using bounding boxes has matured to the level of localizing the objects along their rigid borders and the process is called foreground localization (FGL). Over the decades, many image segmentation methodologies have been well studied, devised, and extended to suit the video FGL. Despite that, still, the problem of video foreground (FG) segmentation remains an intriguing task yet appealing due to its ill-posed nature and myriad of applications. Maintaining spatial and temporal coherence, particularly at object boundaries, persists challenging, and computationally burdensome. It even gets harder when the background possesses dynamic nature, like swaying tree branches or shimmering water body, and illumination variations, shadows cast by the moving objects, or when the video sequences have jittery frames caused by vibrating or unstable camera mounts on a surveillance post or moving robot. At the same time, in the analysis of traffic flow or human activity, the performance of an intelligent system substantially depends on its robustness of localizing the VAR, i.e., the FG. To this end, the natural question arises as what is the best way to deal with these challenges? Thus, the goal of this thesis is to investigate plausible real-time performant implementations from traditional approaches to modern-day deep learning (DL) models for FGL that can be applicable to many video content-aware applications (VCAA). It focuses mainly on improving existing methodologies through harnessing multimodal spatial and temporal cues for a delineated FGL. The first part of the dissertation is dedicated for enhancing conventional sample-based and Gaussian mixture model (GMM)-based video FGL using probability mass function (PMF), temporal median filtering, and fusing CIEDE2000 color similarity, color distortion, and illumination measures, and picking an appropriate adaptive threshold to extract the FG pixels. The subjective and objective evaluations are done to show the improvements over a number of similar conventional methods. The second part of the thesis focuses on exploiting and improving deep convolutional neural networks (DCNN) for the problem as mentioned earlier. Consequently, three models akin to encoder-decoder (EnDec) network are implemented with various innovative strategies to improve the quality of the FG segmentation. The strategies are not limited to double encoding - slow decoding feature learning, multi-view receptive field feature fusion, and incorporating spatiotemporal cues through long-shortterm memory (LSTM) units both in the subsampling and upsampling subnetworks. Experimental studies are carried out thoroughly on all conditions from baselines to challenging video sequences to prove the effectiveness of the proposed DCNNs. The analysis demonstrates that the architectural efficiency over other methods while quantitative and qualitative experiments show the competitive performance of the proposed models compared to the state-of-the-art

Spatial and temporal background modelling of non-stationary visual scenes

PhDThe prevalence of electronic imaging systems in everyday life has become increasingly apparent in recent years. Applications are to be found in medical scanning, automated manufacture, and perhaps most significantly, surveillance. Metropolitan areas, shopping malls, and road traffic management all employ and benefit from an unprecedented quantity of video cameras for monitoring purposes. But the high cost and limited effectiveness of employing humans as the final link in the monitoring chain has driven scientists to seek solutions based on machine vision techniques. Whilst the field of machine vision has enjoyed consistent rapid development in the last 20 years, some of the most fundamental issues still remain to be solved in a satisfactory manner. Central to a great many vision applications is the concept of segmentation, and in particular, most practical systems perform background subtraction as one of the first stages of video processing. This involves separation of ‘interesting foreground’ from the less informative but persistent background. But the definition of what is ‘interesting’ is somewhat subjective, and liable to be application specific. Furthermore, the background may be interpreted as including the visual appearance of normal activity of any agents present in the scene, human or otherwise. Thus a background model might be called upon to absorb lighting changes, moving trees and foliage, or normal traffic flow and pedestrian activity, in order to effect what might be termed in ‘biologically-inspired’ vision as pre-attentive selection. This challenge is one of the Holy Grails of the computer vision field, and consequently the subject has received considerable attention. This thesis sets out to address some of the limitations of contemporary methods of background segmentation by investigating methods of inducing local mutual support amongst pixels in three starkly contrasting paradigms: (1) locality in the spatial domain, (2) locality in the shortterm time domain, and (3) locality in the domain of cyclic repetition frequency. Conventional per pixel models, such as those based on Gaussian Mixture Models, offer no spatial support between adjacent pixels at all. At the other extreme, eigenspace models impose a structure in which every image pixel bears the same relation to every other pixel. But Markov Random Fields permit definition of arbitrary local cliques by construction of a suitable graph, and 3 are used here to facilitate a novel structure capable of exploiting probabilistic local cooccurrence of adjacent Local Binary Patterns. The result is a method exhibiting strong sensitivity to multiple learned local pattern hypotheses, whilst relying solely on monochrome image data. Many background models enforce temporal consistency constraints on a pixel in attempt to confirm background membership before being accepted as part of the model, and typically some control over this process is exercised by a learning rate parameter. But in busy scenes, a true background pixel may be visible for a relatively small fraction of the time and in a temporally fragmented fashion, thus hindering such background acquisition. However, support in terms of temporal locality may still be achieved by using Combinatorial Optimization to derive shortterm background estimates which induce a similar consistency, but are considerably more robust to disturbance. A novel technique is presented here in which the short-term estimates act as ‘pre-filtered’ data from which a far more compact eigen-background may be constructed. Many scenes entail elements exhibiting repetitive periodic behaviour. Some road junctions employing traffic signals are among these, yet little is to be found amongst the literature regarding the explicit modelling of such periodic processes in a scene. Previous work focussing on gait recognition has demonstrated approaches based on recurrence of self-similarity by which local periodicity may be identified. The present work harnesses and extends this method in order to characterize scenes displaying multiple distinct periodicities by building a spatio-temporal model. The model may then be used to highlight abnormality in scene activity. Furthermore, a Phase Locked Loop technique with a novel phase detector is detailed, enabling such a model to maintain correct synchronization with scene activity in spite of noise and drift of periodicity. This thesis contends that these three approaches are all manifestations of the same broad underlying concept: local support in each of the space, time and frequency domains, and furthermore, that the support can be harnessed practically, as will be demonstrated experimentally

Generative Models Based on the Bounded Asymmetric Student’s t-Distribution

Gaussian mixture models (GMMs) are a very useful and widely popular approach for clustering, but they have several limitations, such as low outliers tolerance and assumption of data normality. Another problem in relation to finite mixture models in general is the inference of an optimal number of mixture components. An excellent approach to solve this problem is model selection, which is the process of choosing the optimal number of mixture components that ensures the best clustering performance. In this thesis, we attempt to tackle both aforementioned issues: we propose using minimum message length (MML) as a model selection criterion for multivariate bounded asymmetric Student’s t-mixture model (BASMM). In fact, BASMM is chosen as an alternative to improve the GMM’s limitations, as it provides a better fit for the real-world data irregularities. We formulate the definition of MML and the BASMM, and we test their performance through multiple experiments with different problem settings. Hidden Markov models (HMMs) are popular methods for continuous sequential data modeling and classification tasks. In such applications, the observation emission densities of the HMM hidden states are typically modeled by elliptically contoured distributions, namely Gaussians or Student’s t-distributions. In this context, this thesis proposes BAMMHMM: a novel HMM with Bounded Asymmetric Student’s t-Mixture Model (BASMM) emissions. This HMM is destined to sufficiently fit skewed and outlier-heavy observations, which are typical in many fields, such as financial or signal processing-related datasets. We demonstrate the improved robustness of our model by presenting the results of different real-world applications

Mixture-Based Clustering and Hidden Markov Models for Energy Management and Human Activity Recognition: Novel Approaches and Explainable Applications

In recent times, the rapid growth of data in various fields of life has created an immense need for powerful tools to extract useful information from data. This has motivated researchers to explore and devise new ideas and methods in the field of machine learning. Mixture models have gained substantial attention due to their ability to handle high-dimensional data efficiently and effectively. However, when adopting mixture models in such spaces, four crucial issues must be addressed, including the selection of probability density functions, estimation of mixture parameters, automatic determination of the number of components, identification of features that best discriminate the different components, and taking into account the temporal information. The primary objective of this thesis is to propose a unified model that addresses these interrelated problems. Moreover, this thesis proposes a novel approach that incorporates explainability. This thesis presents innovative mixture-based modelling approaches tailored for diverse applications, such as household energy consumption characterization, energy demand management, fault detection and diagnosis and human activity recognition. The primary contributions of this thesis encompass the following aspects: Initially, we propose an unsupervised feature selection approach embedded within a finite bounded asymmetric generalized Gaussian mixture model. This model is adept at handling synthetic and real-life smart meter data, utilizing three distinct feature extraction methods. By employing the expectation-maximization algorithm in conjunction with the minimum message length criterion, we are able to concurrently estimate the model parameters, perform model selection, and execute feature selection. This unified optimization process facilitates the identification of household electricity consumption profiles along with the optimal subset of attributes defining each profile. Furthermore, we investigate the impact of household characteristics on electricity usage patterns to pinpoint households that are ideal candidates for demand reduction initiatives. Subsequently, we introduce a semi-supervised learning approach for the mixture of mixtures of bounded asymmetric generalized Gaussian and uniform distributions. The integration of the uniform distribution within the inner mixture bolsters the model's resilience to outliers. In the unsupervised learning approach, the minimum message length criterion is utilized to ascertain the optimal number of mixture components. The proposed models are validated through a range of applications, including chiller fault detection and diagnosis, occupancy estimation, and energy consumption characterization. Additionally, we incorporate explainability into our models and establish a moderate trade-off between prediction accuracy and interpretability. Finally, we devise four novel models for human activity recognition (HAR): bounded asymmetric generalized Gaussian mixture-based hidden Markov model with feature selection~(BAGGM-FSHMM), bounded asymmetric generalized Gaussian mixture-based hidden Markov model~(BAGGM-HMM), asymmetric generalized Gaussian mixture-based hidden Markov model with feature selection~(AGGM-FSHMM), and asymmetric generalized Gaussian mixture-based hidden Markov model~(AGGM-HMM). We develop an innovative method for simultaneous estimation of feature saliencies and model parameters in BAGGM-FSHMM and AGGM-FSHMM while integrating the bounded support asymmetric generalized Gaussian distribution~(BAGGD), the asymmetric generalized Gaussian distribution~(AGGD) in the BAGGM-HMM and AGGM-HMM respectively. The aforementioned proposed models are validated using video-based and sensor-based HAR applications, showcasing their superiority over several mixture-based hidden Markov models~(HMMs) across various performance metrics. We demonstrate that the independent incorporation of feature selection and bounded support distribution in a HAR system yields benefits; Simultaneously, combining both concepts results in the most effective model among the proposed models

Real-Time, Multiple Pan/Tilt/Zoom Computer Vision Tracking and 3D Positioning System for Unmanned Aerial System Metrology

The study of structural characteristics of Unmanned Aerial Systems (UASs) continues to be an important field of research for developing state of the art nano/micro systems. Development of a metrology system using computer vision (CV) tracking and 3D point extraction would provide an avenue for making these theoretical developments. This work provides a portable, scalable system capable of real-time tracking, zooming, and 3D position estimation of a UAS using multiple cameras. Current state-of-the-art photogrammetry systems use retro-reflective markers or single point lasers to obtain object poses and/or positions over time. Using a CV pan/tilt/zoom (PTZ) system has the potential to circumvent their limitations. The system developed in this paper exploits parallel-processing and the GPU for CV-tracking, using optical flow and known camera motion, in order to capture a moving object using two PTU cameras. The parallel-processing technique developed in this work is versatile, allowing the ability to test other CV methods with a PTZ system using known camera motion. Utilizing known camera poses, the object\u27s 3D position is estimated and focal lengths are estimated for filling the image to a desired amount. This system is tested against truth data obtained using an industrial system

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