Statistical modeling for simultaneous data clustering, features selection, and outliers rejection

Model-based approaches and in particular finite mixture models are widely used for data clustering, which is a crucial step in several applications of practical importance. Indeed, many pattern recognition, computer vision, and image processing applications can be approached as feature space clustering problems. However, the use of these approaches for complex high-dimensional data presents several challenges such as the presence of many irrelevant features, which may affect the speed, and compromise the accuracy of the used learning algorithm. Another problem is the presence of outliers which potentially influence the resulting model parameters. Generally; clustering, features selection, and outliers detection problems have been approached separately. In this thesis, we propose a unified statistical framework to address the three problems simultaneously. The proposed statistical model partitions a given data set without a priori information about the number of clusters, the saliency of the features, or the number of outliers. We illustrate the performance of our approach using different applications involving synthetic data, real data, and objects shape clustering

Joint-MAP Bayesian Tomographic Reconstruction with a Gamma-Mixture Prior

We address the problem of Bayesian image reconstruction with a prior that captures the notion of a clustered intensity histogram. The problem is formulated in the framework of a joint-MAP (maximum a posteriori) estimation with the prior pdf modeled as a mixture-of-gammas density. This prior pdf has appealing properties, including positivity enforcement. The joint MAP optimization is carried out as an iterative alternating descent wherein a regularized likelihood estimate is followed by a mixture decomposition of the histogram of the current tomographic image estimate. The mixture decomposition step estimates the hyperparameters of the prior pdf. The objective functions associated with the joint MAP estimation are complicated and difficult to optimize, but we show how they may be transformed to allow for much easier optimization while preserving the fixed point of the iterations. We demonstrate the method in the context of medical emission and transmission tomography