A Novel Statistical Approach for Clustering Positive Data Based on Finite Inverted Beta-Liouville Mixture Models

Nowadays, a great number of positive data has been occurred naturally in many applications, however, it was not adequately analyzed. In this article, we propose a novel statistical approach for clustering multivariate positive data. Our approach is based on a finite mixture model of inverted Beta-Liouville (IBL) distributions, which is proper choice for modeling and analysis of positive vector data. We develop two different approaches to learn the proposed mixture model. Firstly, the maximum likelihood (ML) is utilized to estimate parameters of the finite inverted Beta-Liouville mixture model in which the right number of mixture components is determined according to the minimum message length (MML) criterion. Secondly, the variational Bayes (VB) is adopted to learn our model where the parameters and the number of mixture components can be determined simultaneously in a unified framework, without the requirement of using information criteria. We investigate the effectiveness of our model by conducting a series of experiments on both synthetic and real data sets

Variational Learning for the Inverted Beta-Liouville Mixture Model and Its Application to Text Categorization

he finite invert Beta-Liouville mixture model (IBLMM) has recently gained some attention due to its positive data modeling capability. Under the conventional variational inference (VI) framework, the analytically tractable solution to the optimization of the variational posterior distribution cannot be obtained, since the variational object function involves evaluation of intractable moments. With the recently proposed extended variational inference (EVI) framework, a new function is proposed to replace the original variational object function in order to avoid intractable moment computation, so that the analytically tractable solution of the IBLMM can be derived in an effective way. The good performance of the proposed approach is demonstrated by experiments with both synthesized data and a real-world application namely text categorization

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

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