Connections between Classical and Parametric Network Entropies

This paper explores relationships between classical and parametric measures of graph (or network) complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity

Information Indices with High Discriminative Power for Graphs

In this paper, we evaluate the uniqueness of several information-theoretic measures for graphs based on so-called information functionals and compare the results with other information indices and non-information-theoretic measures such as the well-known Balaban index. We show that, by employing an information functional based on degree-degree associations, the resulting information index outperforms the Balaban index tremendously. These results have been obtained by using nearly 12 million exhaustively generated, non-isomorphic and unweighted graphs. Also, we obtain deeper insights on these and other topological descriptors when exploring their uniqueness by using exhaustively generated sets of alkane trees representing connected and acyclic graphs in which the degree of a vertex is at most four

A Large Scale Analysis of Information-Theoretic Network Complexity Measures Using Chemical Structures

This paper aims to investigate information-theoretic network complexity measures which have already been intensely used in mathematical- and medicinal chemistry including drug design. Numerous such measures have been developed so far but many of them lack a meaningful interpretation, e.g., we want to examine which kind of structural information they detect. Therefore, our main contribution is to shed light on the relatedness between some selected information measures for graphs by performing a large scale analysis using chemical networks. Starting from several sets containing real and synthetic chemical structures represented by graphs, we study the relatedness between a classical (partition-based) complexity measure called the topological information content of a graph and some others inferred by a different paradigm leading to partition-independent measures. Moreover, we evaluate the uniqueness of network complexity measures numerically. Generally, a high uniqueness is an important and desirable property when designing novel topological descriptors having the potential to be applied to large chemical databases

Recent Developments in Quantitative Graph Theory: Information Inequalities for Networks

In this article, we tackle a challenging problem in quantitative graph theory. We establish relations between graph entropy measures representing the structural information content of networks. In particular, we prove formal relations between quantitative network measures based on Shannon's entropy to study the relatedness of those measures. In order to establish such information inequalities for graphs, we focus on graph entropy measures based on information functionals. To prove such relations, we use known graph classes whose instances have been proven useful in various scientific areas. Our results extend the foregoing work on information inequalities for graphs

ANN multiscale model of anti-HIV Drugs activity vs AIDS prevalence in the US at county level based on information indices of molecular graphs and social networks

[Abstract] This work is aimed at describing the workflow for a methodology that combines chemoinformatics and pharmacoepidemiology methods and at reporting the first predictive model developed with this methodology. The new model is able to predict complex networks of AIDS prevalence in the US counties, taking into consideration the social determinants and activity/structure of anti-HIV drugs in preclinical assays. We trained different Artificial Neural Networks (ANNs) using as input information indices of social networks and molecular graphs. We used a Shannon information index based on the Gini coefficient to quantify the effect of income inequality in the social network. We obtained the data on AIDS prevalence and the Gini coefficient from the AIDSVu database of Emory University. We also used the Balaban information indices to quantify changes in the chemical structure of anti-HIV drugs. We obtained the data on anti-HIV drug activity and structure (SMILE codes) from the ChEMBL database. Last, we used Box-Jenkins moving average operators to quantify information about the deviations of drugs with respect to data subsets of reference (targets, organisms, experimental parameters, protocols). The best model found was a Linear Neural Network (LNN) with values of Accuracy, Specificity, and Sensitivity above 0.76 and AUROC > 0.80 in training and external validation series. This model generates a complex network of AIDS prevalence in the US at county level with respect to the preclinical activity of anti-HIV drugs in preclinical assays. To train/validate the model and predict the complex network we needed to analyze 43,249 data points including values of AIDS prevalence in 2,310 counties in the US vs ChEMBL results for 21,582 unique drugs, 9 viral or human protein targets, 4,856 protocols, and 10 possible experimental measures.Ministerio de Educación, Cultura y Deportes; AGL2011-30563-C03-0

Content-Based Visual Landmark Search via Multimodal Hypergraph Learning

Formerly IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics</p

Business Groups as Hierarchies of Firms: Determinants of Vertical Integration and Performance

We explore the nature of Business Groups, that is network-like forms of hierarchical organization between legally autonomous firms spanning both within and across national borders. Exploiting a unique dataset of 270,474 headquarters controlling more than 1,500,000 (domestic and foreign) affiliates in all countries worldwide, we find that business groups account for a significant part of value-added generation in both developed and developing countries, with a prevalence in the latter. In order to characterize their boundaries, we distinguish between an affiliate vs. a group-level index of vertical integration, as well as an entropy-like metric able to summarize the hierarchical complexity of a group and its trade-off between exploitation of knowledge as an input across the hierarchy and the associated communication costs. We relate these metrics to host country institutional characteristics, as well as to the performance of affiliates across business groups. Conditional on institutional quality, a negative correlation exists between vertical integration and organizational complexity in defining the boundaries of business groups. We also find a robust (albeit non-linear) positive relationship between a group's organizational complexity and productivity which dominates the already known correlation between vertical integration and productivity. Results are in line with the theoretical framework of knowledge-based hierarchies developed by the literature, in which intangible assets are a complementary input in the production processes

Knowledge discovery in multi-relational graphs

Ante el reducido abanico de metodologías para llevar a cabo tareas de aprendizaje automático relacional, el objetivo principal de esta tesis es realizar un análisis de los métodos existentes, modificando u optimizando en la medida de lo posible algunos de ellos, y aportar nuevos métodos que proporcionen nuevas vías para abordar esta difícil tarea. Para ello, y sin nombrar objetivos relacionados con revisiones bibliográficas ni comparativas entre modelos e implementaciones, se plantean una serie de objetivos concretos a ser cubiertos: 1. Definir estructuras flexibles y potentes que permitan modelar fenómenos en base a los elementos que los componen y a las relaciones establecidas entre éstos. Dichas estructuras deben poder expresar de manera natural propiedades complejas (valores continuos o categóricos, vectores, matrices, diccionarios, grafos,...) de los elementos, así como relaciones heterogéneas entre éstos que a su vez puedan poseer el mismo nivel de propiedades complejas. Además, dichas estructuras deben permitir modelar fenómenos en los que las relaciones entre los elementos no siempre se dan de forma binaria (intervienen únicamente dos elementos), sino que puedan intervenir un número cualquiera de ellos. 2. Definir herramientas para construir, manipular y medir dichas estructuras. Por muy potente y flexible que sea una estructura, será de poca utilidad si no se poseen las herramientas adecuadas para manipularla y estudiarla. Estas herramientas deben ser eficientes en su implementación y cubrir labores de construcción y consulta. 3. Desarrollar nuevos algoritmos de aprendizaje automático relacional de caja negra. En aquellas tareas en las que nuestro objetivo no es obtener modelos explicativos, podremos permitirnos utilizar modelos de caja negra, sacrificando la interpretabilidad a favor de una mayor eficiencia computacional. 4. Desarrollar nuevos algoritmos de aprendizaje automático relacional de caja blanca. Cuando estamos interesados en una explicación acerca del funcionamiento de los sistemas que se analizan, buscaremos modelos de aprendizaje automático de caja blanca. 5. Mejorar las herramientas de consulta, análisis y reparación para bases de datos. Algunas de las consultas a larga distancia en bases de datos presentan un coste computacional demasiado alto, lo que impide realizar análisis adecuados en algunos sistemas de información. Además, las bases de datos en grafo carecen de métodos que permitan normalizar o reparar los datos de manera automática o bajo la supervisión de un humano. Es interesante aproximarse al desarrollo de herramientas que lleven a cabo este tipo de tareas aumentando la eficiencia y ofreciendo una nueva capa de consulta y normalización que permita curar los datos para un almacenamiento y una recuperación más óptimos. Todos los objetivos marcados son desarrollados sobre una base formal sólida, basada en Teoría de la Información, Teoría del Aprendizaje, Teoría de Redes Neuronales Artificiales y Teoría de Grafos. Esta base permite que los resultados obtenidos sean suficientemente formales como para que los aportes que se realicen puedan ser fácilmente evaluados. Además, los modelos abstractos desarrollados son fácilmente implementables sobre máquinas reales para poder verificar experimentalmente su funcionamiento y poder ofrecer a la comunidad científica soluciones útiles en un corto espacio de tiempo