Multiple graph matching and applications

En aplicaciones de reconocimiento de patrones, los grafos con atributos son en gran medida apropiados. Normalmente, los vértices de los grafos representan partes locales de los objetos i las aristas relaciones entre estas partes locales. No obstante, estas ventajas vienen juntas con un severo inconveniente, la distancia entre dos grafos no puede ser calculada en un tiempo polinómico. Considerando estas características especiales el uso de los prototipos de grafos es necesariamente omnipresente. Las aplicaciones de los prototipos de grafos son extensas, siendo las más habituales clustering, clasificación, reconocimiento de objetos, caracterización de objetos i bases de datos de grafos entre otras. A pesar de la diversidad de aplicaciones de los prototipos de grafos, el objetivo del mismo es equivalente en todas ellas, la representación de un conjunto de grafos. Para construir un prototipo de un grafo todos los elementos del conjunto de enteramiento tienen que ser etiquetados comúnmente. Este etiquetado común consiste en identificar que nodos de que grafos representan el mismo tipo de información en el conjunto de entrenamiento. Una vez este etiquetaje común esta hecho, los atributos locales pueden ser combinados i el prototipo construido. Hasta ahora los algoritmos del estado del arte para calcular este etiquetaje común mancan de efectividad o bases teóricas. En esta tesis, describimos formalmente el problema del etiquetaje global i mostramos una taxonomía de los tipos de algoritmos existentes. Además, proponemos seis nuevos algoritmos para calcular soluciones aproximadas al problema del etiquetaje común. La eficiencia de los algoritmos propuestos es evaluada en diversas bases de datos reales i sintéticas. En la mayoría de experimentos realizados los algoritmos propuestos dan mejores resultados que los existentes en el estado del arte.In pattern recognition, the use of graphs is, to a great extend, appropriate and advantageous. Usually, vertices of the graph represent local parts of an object while edges represent relations between these local parts. However, its advantages come together with a sever drawback, the distance between two graph cannot be optimally computed in polynomial time. Taking into account this special characteristic the use of graph prototypes becomes ubiquitous. The applicability of graphs prototypes is extensive, being the most common applications clustering, classification, object characterization and graph databases to name some. However, the objective of a graph prototype is equivalent to all applications, the representation of a set of graph. To synthesize a prototype all elements of the set must be mutually labeled. This mutual labeling consists in identifying which nodes of which graphs represent the same information in the training set. Once this mutual labeling is done the set can be characterized and combined to create a graph prototype. We call this initial labeling a common labeling. Up to now, all state of the art algorithms to compute a common labeling lack on either performance or theoretical basis. In this thesis, we formally describe the common labeling problem and we give a clear taxonomy of the types of algorithms. Six new algorithms that rely on different techniques are described to compute a suboptimal solution to the common labeling problem. The performance of the proposed algorithms is evaluated using an artificial and several real datasets. In addition, the algorithms have been evaluated on several real applications. These applications include graph databases and group-wise image registration. In most of the tests and applications evaluated the presented algorithms have showed a great improvement in comparison to state of the art applications

Information transfer in community structured multiplex networks

The study of complex networks that account for different types of interactions has become a subject of interest in the last few years, specially because its representational power in the description of users interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.). The mathematical description of these interacting networks has been coined under the name of multilayer networks, where each layer accounts for a type of interaction. It has been shown that diffusive processes on top of these networks present a phenomenology that cannot be explained by the naive superposition of single layer diffusive phenomena but require the whole structure of interconnected layers. Nevertheless, the description of diffusive phenomena on multilayer networks has obviated the fact that social networks have strong mesoscopic structure represented by different communities of individuals driven by common interests, or any other social aspect. In this work, we study the transfer of information in multilayer networks with community structure. The final goal is to understand and quantify, if the existence of well-defined community structure at the level of individual layers, together with the multilayer structure of the whole network, enhances or deteriorates the diffusion of packets of information.Comment: 13 pages, 6 figure

Antagonistic Structural Patterns in Complex Networks

Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other arrangements --e.g. nestedness or core-periphery-- have been studied in parallel, but to a much lesser extent. However, empirical evidence increasingly suggests that characterizing a network with a unique pattern typology may be too simplistic, since a system can integrate properties from distinct organizations at different scales. Here, we explore the relationship between some of those organizational patterns: two at the mesoscale (modularity and in-block nestedness); and one at the macroscale (nestedness). We analytically show that nestedness can be used to provide approximate bounds for modularity, with exact results in an idealized scenario. Specifically, we show that nestedness and modularity are antagonistic. Furthermore, we evince that in-block nestedness provides a parsimonious transition between nested and modular networks, taking properties of both. Far from a mere theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent modularity and nestedness are known to place heavy constraints on the stability of several dynamical processes, specially in ecology.Comment: 7 pages, 4 figures and 1 supplemental information fil

Measuring and mitigating behavioural segregation using Call Detail Records

The overwhelming amounts of data we generate in our daily routine and in social networks has been crucial for the understanding of various social and economic factors. The use of this data represents a low-cost alternative source of information in parallel to census data and surveys. Here, we advocate for such an approach to assess and alleviate the segregation of Syrian refugees in Turkey. Using a large dataset of mobile phone records provided by Turkey's largest mobile phone service operator, Türk Telekom, in the frame of the Data 4 Refugees project, we define, analyse and optimise inter-group integration as it relates to the communication patterns of two segregated populations: refugees living in Turkey and the local Turkish population. Our main hypothesis is that making these two communities more similar (in our case, in terms of behaviour) may increase the level of positive exposure between them, due to the well-known sociological principle of homophily. To achieve this, working from the records of call and SMS origins and destinations between and among both populations, we develop an extensible, statistically-solid, and reliable framework to measure the differences between the communication patterns of two groups. In order to show the applicability of our framework, we assess how house mixing strategies, in combination with public and private investment, may help to overcome segregation. We first identify the districts of the Istanbul province where refugees and local population communication patterns differ in order to then utilise our framework to improve the situation. Our results show potential in this regard, as we observe a significant reduction of segregation while limiting, in turn, the consequences in terms of rent increase