In many scientific areas, it is crucial to group (cluster) a set of objects, based on a set of observed features. Such operation is widely known as Clustering and it has been exploited in the most different scenarios ranging from Economics to Biology passing through Psychology. Making a step forward, there exist contexts where it is crucial to group objects and simultaneously identify the features that allow to recognize such objects from the others. In gene expression analysis, for instance, the identification of subsets of genes showing a coherent pattern of expression in subsets of objects/samples can provide crucial information about active biological processes. Such information, which cannot be retrieved by classical clustering approaches, can be extracted with the so called Biclustering, a class of approaches which aim at simultaneously clustering both rows and columns of a given data matrix (where each row corresponds to a different object/sample and each column to a different feature). The problem of biclustering, also known as co-clustering, has been recently exploited in a wide range of scenarios such as Bioinformatics, market segmentation, data mining, text analysis and recommender systems. Many approaches have been proposed to address the biclustering problem, each one characterized by different properties such as interpretability, effectiveness or computational complexity. A recent trend involves the exploitation of sophisticated computational models (Graphical Models) to face the intrinsic complexity of biclustering, and to retrieve very accurate solutions. Graphical Models represent the decomposition of a global objective function to analyse in a set of smaller/local functions defined over a subset of variables. The advantages in using Graphical Models relies in the fact that the graphical representation can highlight useful hidden properties of the considered objective function, plus, the analysis of smaller local problems can be dealt with less computational effort. Due to the difficulties in obtaining a representative and solvable model, and since biclustering is a complex and challenging problem, there exist few promising approaches in literature based on Graphical models facing biclustering. 3 This thesis is inserted in the above mentioned scenario and it investigates the exploitation of Graphical Models to face the biclustering problem. We explored different type of Graphical Models, in particular: Factor Graphs and Bayesian Networks. We present three novel algorithms (with extensions) and evaluate such techniques using available benchmark datasets. All the models have been compared with the state-of-the-art competitors and the results show that Factor Graph approaches lead to solid and efficient solutions for dataset of contained dimensions, whereas Bayesian Networks can manage huge datasets, with the overcome that setting the parameters can be not trivial. As another contribution of the thesis, we widen the range of biclustering applications by studying the suitability of these approaches in some Computer Vision problems where biclustering has been never adopted before. Summarizing, with this thesis we provide evidence that Graphical Model techniques can have a significant impact in the biclustering scenario. Moreover, we demonstrate that biclustering techniques are ductile and can produce effective solutions in the most different fields of applications
