Mean field models for large data-clustering problems

We consider mean-field models for data--clustering problems starting from a generalization of the bounded confidence model for opinion dynamics. The microscopic model includes information on the position as well as on additional features of the particles in order to develop specific clustering effects. The corresponding mean--field limit is derived and properties of the model are investigated analytically. In particular, the mean--field formulation allows the use of a random subsets algorithm for efficient computations of the clusters. Applications to shape detection and image segmentation on standard test images are presented and discussed

Complex Networked Systems: Convergence Analysis, Dynamic Behaviour, and Security.

Complex networked systems are a modern reference framework through which very dierent systems from far disciplines, such as biology, computer science, physics, social science, and engineering, can be described. They arise in the great majority of modern technological applications. Examples of real complex networked systems include embedded systems, biological networks, large-scale systems such as power generation grids, transportation networks, water distribution systems, and social network. In the recent years, scientists and engineers have developed a variety of techniques, approaches, and models to better understand and predict the behaviour of these systems, even though several research and industrial challenges are still open. This thesis addresses the study of dierent properties of complex networked systems and their applications. The main contribution of the work can be considered as threefold: the study of interaction among agents and the relative data clustering in small groups, the analysis of convergence conditions towards a common or multiple agreements, and the investigation of security aspects concerning the detection of perturbations that can propagate across network components and subnetworks. Firstly, a novel approach to solve data clustering problems within wireless sensor networks is proposed, including additional constraints on the distance among cluster centroids. A key feature of the presented algorithm is its ability to partition the original raw dataset into a suboptimal set of clusters, without the requirement of a priori specication of the desired cluster number. Secondly, after introducing a mathematical framework describing the dynamic model of a complex network, a set of centralised and distributed conditions are determined, allowing the detection of the connectedness of the network's underlying topological structure, its convergence to a steady state, and even to an agreement. To this purpose, the so-called Hegselmann-Krause opinion dynamics model is adopted, which describes the way agents of a community dynamically in uence with each other. Thirdly, the problem of optimal sensor location within a class of networked systems, which requires the detection of unknown input disturbance, is addressed. To this aim, a measure simultaneously based on the properties of controllability and observability of the network is used, which allows dierent sensor locations to be evaluated with respect to the location of the signal to be detected. These results inform the design of robust networks, and they suggest that sensor location methods based on the network topology alone may lead to poor detection performance

Distributed Data Clustering via Opinion Dynamics

We provide a distributed method to partition a large set of data in clusters, characterized by small in-group and large out-group distances. We assume a wireless sensors network in which each sensor is given a large set of data and the objective is to provide a way to group the sensors in homogeneous clusters by information type. In previous literature, the desired number of clusters must be specified a priori by the user. In our approach, the clusters are constrained to have centroids with a distance at least \u3b5 between them and the number of desired clusters is not specified. Although traditional algorithms fail to solve the problem with this constraint, it can help obtain a better clustering. In this paper, a solution based on the Hegselmann-Krause opinion dynamics model is proposed to find an admissible, although suboptimal, solution. The Hegselmann-Krause model is a centralized algorithm; here we provide a distributed implementation, based on a combination of distributed consensus algorithms. A comparison with k-means algorithm concludes the paper