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.