Graphical Model approaches for Biclustering

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

Optimizing Information Gathering for Environmental Monitoring Applications

The goal of environmental monitoring is to collect information from the environment and to generate an accurate model for a specific phenomena of interest. We can distinguish environmental monitoring applications into two macro areas that have different strategies for acquiring data from the environment. On one hand the use of fixed sensors deployed in the environment allows a constant monitoring and a steady flow of information coming from a predetermined set of locations in space. On the other hand the use of mobile platforms allows to adaptively and rapidly choose the sensing locations based on needs. For some applications (e.g. water monitoring) this can significantly reduce costs associated with monitoring compared with classical analysis made by human operators. However, both cases share a common problem to be solved. The data collection process must consider limited resources and the key problem is to choose where to perform observations (measurements) in order to most effectively acquire information from the environment and decrease the uncertainty about the analyzed phenomena. We can generalize this concept under the name of information gathering. In general, maximizing the information that we can obtain from the environment is an NP-hard problem. Hence, optimizing the selection of the sampling locations is crucial in this context. For example, in case of mobile sensors the problem of reducing uncertainty about a physical process requires to compute sensing trajectories constrained by the limited resources available, such as, the battery lifetime of the platform or the computation power available on board. This problem is usually referred to as Informative Path Planning (IPP). In the other case, observation with a network of fixed sensors requires to decide beforehand the specific locations where the sensors has to be deployed. Usually the process of selecting a limited set of informative locations is performed by solving a combinatorial optimization problem that model the information gathering process. This thesis focuses on the above mentioned scenario. Specifically, we investigate diverse problems and propose innovative algorithms and heuristics related to the optimization of information gathering techniques for environmental monitoring applications, both in case of deployment of mobile and fixed sensors. Moreover, we also investigate the possibility of using a quantum computation approach in the context of information gathering optimization

A binary Factor Graph model for biclustering

Biclustering, which can be defined as the simultaneous clustering of rows and columns in a data matrix, has received increasing attention in recent years, particularly in the field of Bioinformatics (e.g. for the analysis of microarray data). This paper proposes a novel biclustering approach, which extends the Affinity Propagation [Frey 07] clustering algorithm to the biclustering case. In particular, we propose a new exemplar based model, encoded as a binary factor graph, which allows to cluster rows and columns simultaneously. Moreover, we propose a linear formulation of such model to solve the optimization problem using Linear Programming techniques. The proposed approach has been tested by using a well known synthetic microarray benchmark, with encouraging results