This work presents a nonparametric Bayesian approach that utilizes a mixture of multivariate Libby-Novick Beta distributions to address clustering challenges. When using mixtures, model selection is a significant obstacle. As a solution to this problem, we extend the finite Libby-Novick Beta mixture model (FLNBMM)to the infinite case. This enables us to accurately represent the data distribution by accommodating an unspecified number of mixture components. We develop a Bayesian inference strategy based on Markov Chain Monte Carlo to estimate the posterior distribution, which provides strong power and flexibility for modeling and analyzing complicated data. Our suggested method’s effectiveness is assessed on three applications and contrasted with that of FLNBMM, the infinite Gaussian mixture model (IGMM), and the finite Gaussian mixture model (FGMM) to show the efficacy of our methodology. It is evident from the results that our proposed model is a good alternative.

Mixture models are widely used in unsupervised machine learning applications where annotating a large amount of data is not feasible. They have succeeded in various real-world problems, including medical applications, human activity recognition, and anomaly detection. This paper proposes a fully Bayesian analysis of the multivariate McDonald's Beta mixture model (McDBMM) using Gibbs sampling method and Metropolis-Hastings to estimate parameters. In addition, we integrated a feature selection technique which simultaneously determines the most relevant features for our mixture model. This allows for the simultaneous selection of the most relevant features, improving the accuracy and efficiency of the unsupervised learning process. Our approach is evaluated on challenging applications, including lung cancer image analysis and human activity recognition. Experimental results indicate that our proposed method is an effective solution compared to the Gaussian mixture model (GMM).

Abstract In this article, first, we propose a novel unsupervised learning method based on a hierarchical Dirichlet process mixture of shifted‐scaled Dirichlet (SSD) distributions. Second, we extend it to a hierarchical Pitman–Yor process mixture of SSD distributions. The goal is to find a model that properly fits complex real‐world data. Our models are based on SSD distributions that are more flexible than Dirichlet distribution in fitting proportional data. Simultaneous data fitting (parameter estimate) and model selection (model complexity determination) are possible with the suggested methods. We applied batch and online variational inference for learning the models. The online setting allows us to feed our models with large‐scale streaming data. The effectiveness of our proposed models is evaluated by four realistic and challenging applications, namely, spam email detection, texture clustering, traffic sign detection, and vehicle detection. Experimental results demonstrate the potential of our models to fit proportional data.

In this paper, we propose hierarchical Pitman-Yor process mixtures of multivariate Beta distributions and learn this novel clustering method by online variational inference. The flexibility of this mixture model and its non-parametric hierarchical structure help in fitting our data. Also, the model complexity and model parameters are estimated simultaneously. We apply our proposed model to real medical applications. Our motivation is that labelling healthcare data is sensitive and expensive. Also, interpretability and evidence-based decision-making are some basic needs of medicine. These conditions led us to focus on clustering as it doesn’t need labelling. Another driving reason is that the amount of publicly available data in medicine is less compared to other fields due to the confidential regulations. To evaluate our proposed model, we compare its performance with other similar alternatives. The experimental results indicate the potential of our proposed model.

Nowadays, there is considerable and growing interest in applying accurate analysis tools to obtain meaningful information and extract knowledge from a huge amount of data. In this sense, unsupervised algorithms and clustering techniques have gained an increasing interest. These methods are helpful specifically when data annotation is time-consuming and costly. In this paper, we propose a new clustering method based on a Dirichlet process mixture of multivariate Beta distributions. To learn this novel Bayesian nonparametric model, we applied stochastic expectation propagation inference framework. This framework is able to define the model complexity and estimate the model’s parameters simultaneously. To demonstrate the efficiency of our model, we perform an experimental analysis using three real applications, breast, lung and colon histopathological tissue analysis. Our goal is to show that our algorithm could be considered as a machine learning framework in computer-assisted diagnosis and play the role of a complementary opinion to help the pathologists in making decisions with more accuracy.

Variational inference approaches are gaining more and more success and are applied in various data mining applications. In this work, we present a variational learning framework for the Shifted Scaled Dirichlet finite mixture model. Furthermore, we introduce component splitting based on Entropy approximation to estimate the number of components in our model along with the parameters of the distribution. We test the performance of this model on two real-life datasets, both related to human activity recognition.

Abstract Technological advances led to the generation of large scale complex data. Thus, extraction and retrieval of information to automatically discover latent pattern have been largely studied in the various domains of science and technology. Consequently, machine learning experienced tremendous development and various statistical approaches have been suggested. In particular, data clustering has received a lot of attention. Finite mixture models have been revealed to be one of the flexible and popular approaches in data clustering. Considering mixture models, three crucial aspects should be addressed. The first issue is choosing a distribution which is flexible enough to fit the data. In this paper, a model based on multivariate Beta distributions is proposed. The two other challenges in mixture models are estimation of model's parameters and model complexity. To tackle these challenges, variational inference techniques demonstrated considerable robustness. In this paper, two methods are studied, namely, batch and online variational inferences and the models are evaluated on four medical applications including image segmentation of colorectal cancer, multi‐class colon tissue analysis, digital imaging in skin lesion diagnosis and computer aid detection of Malaria.

Data mining techniques have been successfully utilized in different applications of significant fields, including medical research. With the wealth of data available within health-care systems, there is a lack of practical analysis tools to discover hidden relationships and trends in data. Among all statistical frameworks, regression has been proven to be one of the most potent tools in prediction. The complexity of medical data that is unfavorable for most models is a considerable challenge in prediction. The ability of a model to perform accurately and efficiently in disease diagnosis is essential. Thus, a model must be selected to fit the data well, such that the learning from previous data is most efficient, and the diagnosis of the disease is highly accurate. In this work, a bivariate Beta regression model has been proposed, which is based on a flexible bivariate Beta distribution with three shape parameters. Then, the performance of this algorithm is evaluated in terms of the accuracy of the prediction and compared to a similar regression model. The accuracy of model performance depends on the nature and complexity of the dataset. The results in this paper show the merits of our work.