Color Image Segmentation Using Generalized Inverted Finite Mixture Models By Integrating Spatial Information

In computer vision, image segmentation plays foundational role. Innumerable techniques, such as active contour, graph-cut-based, model-based, machine learning, and clustering-based methods have been proposed for tackling the image segmentation problem. But, none of them is universally applicable. Thus, the hunt for optimized and robust models for image segmentation is still under-process and also an open question. The challenges faced in image segmentation are the integration of spatial information, finding the exact number of clusters (M), and to segment the image smoothly without any inaccuracy specially in the presence of noise, a complex background, low contrast and, inhomogeneous intensity. The use of finite mixture model (FMMs) for image segmentation is very popular approach in the field of computer vision. The application of image segmentation using FMM ranges from automatic number plate recognition, content-based image retrieval, texture recognition, facial recognition, satellite imagery etc. Image segmentation using FMM undergoes some problems. FMM-based image segmentation considers neither spatial correlation among the peer pixels nor the prior knowledge that the adjacent pixels are most likely belong to the same cluster. Also, color images are sensitive to illumination and noise. To overcome these limitations, we have used three different methods for integrating spatial information with FMM. First method uses the prior knowledge of M. In second method, we have used Markov Random Field (MRF). Lastly, in third, we have used weighted geometric and arithmetic mean template. We have implemented these methods with inverted Dirichlet mixture model (IDMM), generalized inverted Dirichlet mixture model (GIDMM) and inverted Beta Liouville mixture model (IBLMM). For experimentation, the Berkeley 500 (BSD500) and MIT's Computational Visual Cognition Laboratory (CVCL) datasets are employed. Furthermore, to compare the image segmentation results, the outputs of IDMM, GIDMM, and IBLMM are compared with each other, using segmentation performance evaluation metrics

A Study on Online Variational learning : Medical Applications

Data mining is an extensive area of research which is applied in various critical domains. In clinical aspect, data mining has emerged to assist clinicians in early detection, diagnosis and prevention of diseases. On the other hand, advances in computational methods have led to the implementation of machine learning in multi-modal clinical image analysis such as in CT, X-ray, MRI, microscopy among others. A challenge to these applications is the high variability, inconsistent regions with missing edges, absence of texture contrast and high noise in the background of biomedical images. To overcome this limitation various segmentation approaches have been investigated to address these shortcomings and to transform medical images into meaningful information. It is of utmost importance to have the right match between the bio-medical data and the applied algorithm. During the past decade, finite mixture models have been revealed to be one of the most flexible and popular approaches in data clustering. Here, we propose a statistical framework for online variational learning of finite mixture models for clustering medical images. The online variational learning framework is used to estimate the parameters and the number of mixture components simultaneously in a unified framework, thus decreasing the computational complexity of the model and the over fitting problems experienced with maximum likelihood approaches guaranteeing convergence. In online learning, the data becomes available in a sequential order, thus sequentially updating the best predictor for the future data at each step, as opposed to batch learning techniques which generate the best predictor by learning the entire data set at once. The choice of distributions remains the core concern of mixture models in recent research. The efficiency of Dirichlet family of distributions for this purpose has been proved in latest studies especially for non-Gaussian data. This led us to analyze online variational learning approach for finite mixture models based on different distributions. iii To this end, our contribution is the application of online variational learning approach to design finite mixture models based on inverted Dirichlet, generalized inverted Dirichlet with feature selection and inverted Beta-Liouville distributions in medical domain. We evaluated our proposed models on different biomedical image data sets. Furthermore, in each case we compared the proposed algorithm with other popular algorithms. The models detect the disease patterns with high confidence. Computational and statistical approaches like the ones presented in our work hold a significant impact on medical image analysis and interpretation in both clinical applications and scientific research. We believe that the proposed models have the capacity to address multi modal biomedical image data sets and can be further applied by researchers to analyse correct disease patterns

Insights Into Multiple/Single Lower Bound Approximation for Extended Variational Inference in Non-Gaussian Structured Data Modeling

For most of the non-Gaussian statistical models, the data being modeled represent strongly structured properties, such as scalar data with bounded support (e.g., beta distribution), vector data with unit length (e.g., Dirichlet distribution), and vector data with positive elements (e.g., generalized inverted Dirichlet distribution). In practical implementations of non-Gaussian statistical models, it is infeasible to find an analytically tractable solution to estimating the posterior distributions of the parameters. Variational inference (VI) is a widely used framework in Bayesian estimation. Recently, an improved framework, namely, the extended VI (EVI), has been introduced and applied successfully to a number of non-Gaussian statistical models. EVI derives analytically tractable solutions by introducing lower bound approximations to the variational objective function. In this paper, we compare two approximation strategies, namely, the multiple lower bounds (MLBs) approximation and the single lower bound (SLB) approximation, which can be applied to carry out the EVI. For implementation, two different conditions, the weak and the strong conditions, are discussed. Convergence of the EVI depends on the selection of the lower bound, regardless of the choice of weak or strong condition. We also discuss the convergence properties to clarify the differences between MLB and SLB. Extensive comparisons are made based on some EVI-based non-Gaussian statistical models. Theoretical analysis is conducted to demonstrate the differences between the weak and strong conditions. Experimental results based on real data show advantages of the SLB approximation over the MLB approximation

Positive Data Clustering based on Generalized Inverted Dirichlet Mixture Model

Recent advances in processing and networking capabilities of computers have caused an accumulation of immense amounts of multimodal multimedia data (image, text, video). These data are generally presented as high-dimensional vectors of features. The availability of these highdimensional data sets has provided the input to a large variety of statistical learning applications including clustering, classification, feature selection, outlier detection and density estimation. In this context, a finite mixture offers a formal approach to clustering and a powerful tool to tackle the problem of data modeling. A mixture model assumes that the data is generated by a set of parametric probability distributions. The main learning process of a mixture model consists of the following two parts: parameter estimation and model selection (estimation the number of components). In addition, other issues may be considered during the learning process of mixture models such as the: a) feature selection and b) outlier detection. The main objective of this thesis is to work with different kinds of estimation criteria and to incorporate those challenges into a single framework. The first contribution of this thesis is to propose a statistical framework which can tackle the problem of parameter estimation, model selection, feature selection, and outlier rejection in a unified model. We propose to use feature saliency and introduce an expectation-maximization (EM) algorithm for the estimation of the Generalized Inverted Dirichlet (GID) mixture model. By using the Minimum Message Length (MML), we can identify how much each feature contributes to our model as well as determine the number of components. The presence of outliers is an added challenge and is handled by incorporating an auxiliary outlier component, to which we associate a uniform density. Experimental results on synthetic data, as well as real world applications involving visual scenes and object classification, indicates that the proposed approach was promising, even though low-dimensional representation of the data was applied. In addition, it showed the importance of embedding an outlier component to the proposed model. EM learning suffers from significant drawbacks. In order to overcome those drawbacks, a learning approach using a Bayesian framework is proposed as our second contribution. This learning is based on the estimation of the parameters posteriors and by considering the prior knowledge about these parameters. Calculation of the posterior distribution of each parameter in the model is done by using Markov chain Monte Carlo (MCMC) simulation methods - namely, the Gibbs sampling and the Metropolis- Hastings methods. The Bayesian Information Criterion (BIC) was used for model selection. The proposed model was validated on object classification and forgery detection applications. For the first two contributions, we developed a finite GID mixture. However, in the third contribution, we propose an infinite GID mixture model. The proposed model simutaneously tackles the clustering and feature selection problems. The proposed learning model is based on Gibbs sampling. The effectiveness of the proposed method is shown using image categorization application. Our last contribution in this thesis is another fully Bayesian approach for a finite GID mixture learning model using the Reversible Jump Markov Chain Monte Carlo (RJMCMC) technique. The proposed algorithm allows for the simultaneously handling of the model selection and parameter estimation for high dimensional data. The merits of this approach are investigated using synthetic data, and data generated from a challenging namely object detection

Modeling Semi-Bounded Support Data using Non-Gaussian Hidden Markov Models with Applications

With the exponential growth of data in all formats, and data categorization rapidly becoming one of the most essential components of data analysis, it is crucial to research and identify hidden patterns in order to extract valuable information that promotes accurate and solid decision making. Because data modeling is the first stage in accomplishing any of these tasks, its accuracy and consistency are critical for later development of a complete data processing framework. Furthermore, an appropriate distribution selection that corresponds to the nature of the data is a particularly interesting subject of research. Hidden Markov Models (HMMs) are some of the most impressively powerful probabilistic models, which have recently made a big resurgence in the machine learning industry, despite having been recognized for decades. Their ever-increasing application in a variety of critical practical settings to model varied and heterogeneous data (image, video, audio, time series, etc.) is the subject of countless extensions. Equally prevalent, finite mixture models are a potent tool for modeling heterogeneous data of various natures. The over-use of Gaussian mixture models for data modeling in the literature is one of the main driving forces for this thesis. This work focuses on modeling positive vectors, which naturally occur in a variety of real-life applications, by proposing novel HMMs extensions using the Inverted Dirichlet, the Generalized Inverted Dirichlet and the BetaLiouville mixture models as emission probabilities. These extensions are motivated by the proven capacity of these mixtures to deal with positive vectors and overcome mixture models’ impotence to account for any ordering or temporal limitations relative to the information. We utilize the aforementioned distributions to derive several theoretical approaches for learning and deploying Hidden Markov Modelsinreal-world settings. Further, we study online learning of parameters and explore the integration of a feature selection methodology. Extensive experimentation on highly challenging applications ranging from image categorization, video categorization, indoor occupancy estimation and Natural Language Processing, reveals scenarios in which such models are appropriate to apply, and proves their effectiveness compared to the extensively used Gaussian-based models

Mixture Models for Multidimensional Positive Data Clustering with Applications to Image Categorization and Retrieval

Model-based approaches have become important tools to model data and infer knowledge. Such approaches are often used for clustering and object recognition which are crucial steps in many applications, including but not limited to, recommendation systems, search engines, cyber security, surveillance and object tracking. Many of these applications have the urgent need to reduce the semantic gap of data representation between the system level and the human being understandable level. Indeed, the low level features extracted to represent a given object can be confusing to machines which cannot differentiate between very similar objects trivially distinguishable by human beings (e.g. apple vs tomato). Such a semantic gap between the system and the user perception for data, makes the modeling process hard to be designed basing on the features space only. Moreover those models should be flexible and updatable when new data are introduced to the system. Thus, apart from estimating the model parameters, the system should be somehow informed how new data should be perceived according to some criteria in order to establish model updates. In this thesis we propose a methodology for data representation using a hierarchical mixture model basing on the inverted Dirichlet and the generalized inverted Dirichlet distributions. The proposed approach allows to model a given object class by a set of components deduced by the system and grouped according to labeled training data representing the human level semantic. We propose an update strategy to the system components that takes into account adjustable metrics representing users perception. We also consider the "page zero" problem in image retrieval systems when a given user does not possess adequate tools and semantics to express what he/she is looking for, while he/she can visually identify it. We propose a statistical framework that enables users to start a search process and interact with the system in order to find their target "mental image". Finally we propose to improve our models by using a variational Bayesian inference to learn generalized inverted Dirichlet mixtures with features selection. The merit of our approaches is evaluated using extensive simulations and real life applications

Non-Gaussian data modeling with hidden Markov models

In 2015, 2.5 quintillion bytes of data were daily generated worldwide of which 90% were unstructured data that do not follow any pre-defined model. These data can be found in a great variety of formats among them are texts, images, audio tracks, or videos. With appropriate techniques, this massive amount of data is a goldmine from which one can extract a variety of meaningful embedded information. Among those techniques, machine learning algorithms allow multiple processing possibilities from compact data representation, to data clustering, classification, analysis, and synthesis, to the detection of outliers. Data modeling is the first step for performing any of these tasks and the accuracy and reliability of this initial step is thus crucial for subsequently building up a complete data processing framework. The principal motivation behind my work is the over-use of the Gaussian assumption for data modeling in the literature. Though this assumption is probably the best to make when no information about the data to be modeled is available, in most cases studying a few data properties would make other distributions a better assumption. In this thesis, I focus on proportional data that are most commonly known in the form of histograms and that naturally arise in a number of situations such as in bag-of-words methods. These data are non-Gaussian and their modeling with distributions belonging the Dirichlet family, that have common properties, is expected to be more accurate. The models I focus on are the hidden Markov models, well-known for their capabilities to easily handle dynamic ordered multivariate data. They have been shown to be very effective in numerous fields for various applications for the last 30 years and especially became a corner stone in speech processing. Despite their extensive use in almost all computer vision areas, they are still mainly suited for Gaussian data modeling. I propose here to theoretically derive different approaches for learning and applying to real-world situations hidden Markov models based on mixtures of Dirichlet, generalized Dirichlet, Beta-Liouville distributions, and mixed data. Expectation-Maximization and variational learning approaches are studied and compared over several data sets, specifically for the task of detecting and localizing unusual events. Hybrid HMMs are proposed to model mixed data with the goal of detecting changes in satellite images corrupted by different noises. Finally, several parametric distances for comparing Dirichlet and generalized Dirichlet-based HMMs are proposed and extensively tested for assessing their robustness. My experimental results show situations in which such models are worthy to be used, but also unravel their strength and limitations

Generative modeling of dynamic visual scenes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 301-312).Modeling visual scenes is one of the fundamental tasks of computer vision. Whereas tremendous efforts have been devoted to video analysis in past decades, most prior work focuses on specific tasks, leading to dedicated methods to solve them. This PhD thesis instead aims to derive a probabilistic generative model that coherently integrates different aspects, notably appearance, motion, and the interaction between them. Specifically, this model considers each video as a composite of dynamic layers, each associated with a covering domain, an appearance template, and a flow describing its motion. These layers change dynamically following the associated flows, and are combined into video frames according to a Z-order that specifies their relative depth-order. To describe these layers and their dynamic changes, three major components are incorporated: (1) An appearance model describes the generative process of the pixel values of a video layer. This model, via the combination of a probabilistic patch manifold and a conditional Markov random field, is able to express rich local details while maintaining global coherence. (2) A motion model captures the motion pattern of a layer through a new concept called geometric flow that originates from differential geometric analysis. A geometric flow unifies the trajectory-based representation and the notion of geometric transformation to represent the collective dynamic behaviors persisting over time. (3) A partial Z-order specifies the relative depth order between layers. Here, through the unique correspondence between equivalent classes of partial orders and consistent choice functions, a distribution over the spaces of partial orders is established, and inference can thus be performed thereon. The development of these models leads to significant challenges in probabilistic modeling and inference that need new techniques to address. We studied two important problems: (1) Both the appearance model and the motion model rely on mixture modeling to capture complex distributions. In a dynamic setting, the components parameters and the number of components in a mixture model can change over time. While the use of Dirichlet processes (DPs) as priors allows indefinite number of components, incorporating temporal dependencies between DPs remains a nontrivial issue, theoretically and practically. Our research on this problem leads to a new construction of dependent DPs, enabling various forms of dynamic variations for nonparametric mixture models by harnessing the connections between Poisson and Dirichlet processes. (2) The inference of partial Z-order from a video needs a method to sample from the posterior distribution of partial orders. A key challenge here is that the underlying space of partial orders is disconnected, meaning that one may not be able to make local updates without violating the combinatorial constraints for partial orders. We developed a novel sampling method to tackle this problem, which dynamically introduces virtual states as bridges to connect between different parts of the space, implicitly resulting in an ergodic Markov chain over an augmented space. With this generative model of visual scenes, many vision problems can be readily solved through inference performed on the model. Empirical experiments demonstrate that this framework yields promising results on a series of practical tasks, including video denoising and inpainting, collective motion analysis, and semantic scene understanding.by Dahua Lin.Ph.D

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