A Study on Variational Component Splitting approach for Mixture Models

Increase in use of mobile devices and the introduction of cloud-based services have resulted in the generation of enormous amount of data every day. This calls for the need to group these data appropriately into proper categories. Various clustering techniques have been introduced over the years to learn the patterns in data that might better facilitate the classification process. Finite mixture model is one of the crucial methods used for this task. The basic idea of mixture models is to fit the data at hand to an appropriate distribution. The design of mixture models hence involves finding the appropriate parameters of the distribution and estimating the number of clusters in the data. We use a variational component splitting framework to do this which could simultaneously learn the parameters of the model and estimate the number of components in the model. The variational algorithm helps to overcome the computational complexity of purely Bayesian approaches and the over fitting problems experienced with Maximum Likelihood approaches guaranteeing convergence. The choice of distribution 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 study the impact of variational component splitting approach on mixture models based on several distributions. Hence, our contribution is the application of variational component splitting approach to design finite mixture models based on inverted Dirichlet, generalized inverted Dirichlet and inverted Beta-Liouville distributions. In addition, we also incorporate a simultaneous feature selection approach for generalized inverted Dirichlet mixture model along with component splitting as another experimental contribution. We evaluate the performance of our models with various real-life applications such as object, scene, texture, speech and video categorization

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

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

Plantwide simulation and monitoring of offshore oil and gas production facility

Monitoring is one of the major concerns in offshore oil and gas production platform since the access to the offshore facilities is difficult. Also, it is quite challenging to extract oil and gas safely in such a harsh environment, and any abnormalities may lead to a catastrophic event. The process data, including all possible faulty scenarios, is required to build an appropriate monitoring system. Since the plant wide process data is not available in the literature, a dynamic model and simulation of an offshore oil and gas production platform is developed by using Aspen HYSYS. Modeling and simulations are handy tools for designing and predicting the accurate behavior of a production plant. The model was built based on the gas processing plant at the North Sea platform reported in Voldsund et al. (2013). Several common faults from different fault categories were simulated in the dynamic system, and their impacts on the overall hydrocarbon production were analyzed. The simulated data are then used to build a monitoring system for each of the faulty states. A new monitoring method has been proposed by combining Principal Component Analysis (PCA) and Dynamic PCA (DPCA) with Artificial Neural Network (ANN). The application of ANN to process systems is quite difficult as it involves a very large number of input neurons to model the system. Training of such large scale network is time-consuming and provides poor accuracy with a high error rate. In PCA-ANN and DPCA-ANN monitoring system, PCA and DPCA are used to reduce the dimension of the training data set and extract the main features of measured variables. Subsequently ANN uses this lower-dimensional score vectors to build a training model and classify the abnormalities. It is found that the proposed approach reduces the time to train ANN and successfully diagnose, detects and classifies the faults with a high accuracy rate

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

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