Optimal Graph Filters for Clustering Attributed Graphs

Many real-world systems can be represented as graphs where the different entities are presented by nodes and their interactions by edges. An important task in studying large datasets is graph clustering. While there has been a lot of work on graph clustering using the connectivity between the nodes, many real-world networks also have node attributes. Clustering attributed graphs requires joint modeling of graph structure and node attributes. Recent work has focused on graph convolutional networks and graph convolutional filters to combine structural and content information. However, these methods are mostly limited to lowpass filtering and do not explicitly optimize the filters for the clustering task. In this paper, we introduce a graph signal processing based approach, where we design polynomial graph filters optimized for clustering. The proposed approach is formulated as a two-step iterative optimization problem where graph filters that are interpretable and optimal for the given data are learned while maximizing the separation between different clusters. The proposed approach is evaluated on attributed networks and compared to the state-of-the-art graph convolutional network approaches.Comment: 5 pages, 3 figure

Modeling cooperative communications using game theory: applications for cognitive radios

In this paper, cooperative communications are presented to improve efficiency toward the use of telecommunication systems resources. In the special case of cognitive radio networks, main benefits and costs regarding cooperation are analyzed, as well as security issues that might rise in such a scenario. From a game theory model, the implementation of a coalitional game is described, where cognitive users pursue individual benefits as well as benefits for the coalition they belong. Simulation results confirm the gains achievable by means of cooperative communications, and reveal weakening performance in presence of security threats. This paper may help readers to have a more comprehensive understanding of cooperative communications based on game theory, as well as the main research trends and challenges in this area.En el presente trabajo se introducen las comunicaciones cooperativas con el objetivo de mejorar la eficiencia hacia el uso de los recursos en los sistemas de telecomunicaciones. En el caso especial de las redes de radio cognitivas, se analizan los principales beneficios y costos así como las cuestiones de seguridad que podrían surgir en tal escenario. Desde un modelo de teoría de juegos, se describe la implementación de coaliciones, donde los usuarios cognitivos persiguen beneficios individuales y para la coalición a la que pertenecen. Los resultados de la simulación confirman las ganancias alcanzables por medio de comunicaciones cooperativas y revelan las debilidades de desempeño ante la presencia de amenazas de seguridad. Este documento puede ayudar a los lectores a tener una comprensión mayor de las comunicaciones cooperativas basadas en la teoría de juegos, así como las principales tendencias y desafíos de investigación en esta área