From Relational Data to Graphs: Inferring Significant Links using Generalized Hypergeometric Ensembles

The inference of network topologies from relational data is an important problem in data analysis. Exemplary applications include the reconstruction of social ties from data on human interactions, the inference of gene co-expression networks from DNA microarray data, or the learning of semantic relationships based on co-occurrences of words in documents. Solving these problems requires techniques to infer significant links in noisy relational data. In this short paper, we propose a new statistical modeling framework to address this challenge. It builds on generalized hypergeometric ensembles, a class of generative stochastic models that give rise to analytically tractable probability spaces of directed, multi-edge graphs. We show how this framework can be used to assess the significance of links in noisy relational data. We illustrate our method in two data sets capturing spatio-temporal proximity relations between actors in a social system. The results show that our analytical framework provides a new approach to infer significant links from relational data, with interesting perspectives for the mining of data on social systems.Comment: 10 pages, 8 figures, accepted at SocInfo201

Are you going to the party: depends, who else is coming? [Learning hidden group dynamics via conditional latent tree models]

Scalable probabilistic modeling and prediction in high dimensional multivariate time-series is a challenging problem, particularly for systems with hidden sources of dependence and/or homogeneity. Examples of such problems include dynamic social networks with co-evolving nodes and edges and dynamic student learning in online courses. Here, we address these problems through the discovery of hierarchical latent groups. We introduce a family of Conditional Latent Tree Models (CLTM), in which tree-structured latent variables incorporate the unknown groups. The latent tree itself is conditioned on observed covariates such as seasonality, historical activity, and node attributes. We propose a statistically efficient framework for learning both the hierarchical tree structure and the parameters of the CLTM. We demonstrate competitive performance in multiple real world datasets from different domains. These include a dataset on students' attempts at answering questions in a psychology MOOC, Twitter users participating in an emergency management discussion and interacting with one another, and windsurfers interacting on a beach in Southern California. In addition, our modeling framework provides valuable and interpretable information about the hidden group structures and their effect on the evolution of the time series

Modelling Players' Interactions in Football: A Multilevel Hypernetworks Approach.

Na presente tese procura-se avançar com fundamentação teórica e prática, assim como com demonstrações empíricas referentes à reconceptualização das equipas de futebol enquanto redes sociais complexas. Estas redes evidenciam comportamentos sinérgicos emergentes e auto-organizados cuja complexidade, enraizada nas redes de interações dos jogadores, pode ser discernida através da análise de redes sociais. Não obstante, as técnicas tradicionais de rede exibem algumas limitações que podem levar a dados imprecisos e falaciosos. Essas limitações estão relacionadas com a exagerada ênfase que é colocada nos comportamentos de ataque das equipas, negligenciando-se as ações defensivas. Tal leva a que: a troca de informações incida maioritariamente nos comportamentos de passe; a variabilidade do comportamento dos jogadores seja, na maioria dos casos, desconsiderada; e a maioria das métricas usadas para modelar as interações dos jogadores se baseiem em distâncias geodésicas. Assim, as hiperredes multiníveis são aqui propostas enquanto nova abordagem metodológica capaz de superar aquelas limitações. Esta abordagem multinível caracteriza-se por um conjunto de conceitos e ferramentas metodológicas coerentes com a análise da dinâmica relacional subjacente aos processos sinergísticos evidenciados durante a competição. Por um lado, estes processos foram capturados na dinâmica de alteração das configurações táticas exibidas pelas equipas durante a competição, pela quantificação do tipo de simplices (interações de grupos de jogadores, e.g., 2vs.1) atendendo à localização da bola, e na dinâmica de interação, transformação dos simplices em determinados eventos do jogo. Por outro lado, a aplicação das hiperredes multiníveis permitiu, de igual modo, capturar as tendências de sincronização local (nível meso) emergentes em contextos de prática. Esta tese destacou o valor da adoção de uma abordagem de hiperredes multiníveis para melhorar a compreensão sobre os processos sinérgicos dos jogadores e equipas de futebol emergentes durante a prática e a competição. Estas poderão vir a revelar-se ferramentas promissoras na análise da performance desportiva, tendo igualmente um papel relevante na monitorização e controlo do treino.PALAVRAS-CHAVE: FUTEBOL, CIÊNCIA DAS REDES, HIPERREDES MULTINÍVEL, DINÂMICA DA EQUIPA, ANÁLISE DA PERFORMANCEThis thesis aims to advance practical and theoretical understanding, as well as empirical evidence regarding the re-conceptualisation of Football teams as complex social networks. These networks display synergetic, emergent and self-organised behaviour and the complexity rooted in the networks of players' interactions can be discerned through analysis of social networks. Notwithstanding, traditional network techniques display some limitations that can lead to inaccurate and misleading data. Such limitations are related with an over-emphasis on network attacking behaviours thus neglecting the defensive actions of the opposing team. This leads to: information exchange mainly analysed through passing behaviours; the variability of players' performance is in most cases disregarded; most metrics used to model players' interactions are based on geodesic distances. Thus, multilevel hypernetworks are proposed as a novel methodological approach capable of overriding such limitations. This multilevel approach is characterised by a set of conceptual and methodological tools consistent with analysis of the relational dynamics underlying the synergistic processes evidenced during competition. On the one hand, these processes were captured in the changing dynamics of tactical configurations of teams during competition, by the quantification of the type of simplices (interactions between sub-groups of players, e.g., 2vs.1) in relation to ball location, and in the dynamics of simplices' interactions and transformations in certain game events. On the other hand, the application of multilevel hypernetworks allowed to capture local (meso level) synchronisation tendencies in practice contexts. This thesis highlighted the value of adopting a multilevel hypernetworks approach for enhancing understanding about the synergistic processes of players and football teams emerging during practice and competition. These tools may prove to be promising in the analysis of sports performance, also having an important role in the monitoring and control of training

Asset price dynamics with small world interactions under hetereogeneous beliefs

We propose a simple model of a financial market populated with heterogeneous agents. The market represents a network with nodes symbolizing the agents and edges standing for connections between them, thus, embodying local interactions in the market. By local interactions we mean any kind of interplay between the decisions of the agents unaffected by the market mechanism and unrelated to the physical distance between the agents. Using the rewiring procedure we restructure a network from regular lattice to random graph by varying the probability of the agents to switch from one trading strategy to another. We study how the network structure influences the asset price dynamics. The results show that for some intermediate values of the probability to switch, corresponding to a small world network, the price dynamics become reminiscent to the real. While for the boundary values of the probability the dynamics lacks some typical features of the real financial markets.local interactions, networks, small world, heterogeneous beliefs, price dynamics, bifurcations, chaos

Relational Network of People Constructed on the Basis of Similarity of Brain Activities.

The relational network of people (RNP) model has been attracting the interest of not only researchers but also industrial engineers. RNP can be constructed from friend lists in online social networking services (SNSs) and from inter-contact logs between individuals. One of the killer applications of RNP is the prediction of user demands, which is key to maximizing user satisfaction in content delivery services such as video streaming and video advertising. It is well known that an RNP representing social closeness between individuals (a so-called social network) can estimate user preferences simply, as we expect that people close to each other will have similar preferences. However, although there are many metrics that enable the social closeness between individuals to be measured, it is unclear which metric is best suited for individual services. Therefore, this paper introduces a new approach based on brain imaging. Brain imaging using functional Magnetic Resonance Imaging (fMRI) is powerful because it enables us to directly observe how a video content stimulates the brains of individual people. We propose a brain imaging-based RNP that represents the similarity of video-evoked brain activities between people as a network graph. We show an application scenario featuring predictive content delivery using the proposed RNP in which, when a user shows interest in a video content in some way, other users close to him or her can be expected to also be interested in it because their brain activities are correlated. Through numerical evaluation using multiple real datasets obtained by fMRI, we demonstrate that the proposed RNP is generalizable across brain imaging results for different sets of video content, thus suggesting that brain imaging data can be used to robustly generate RNP for utilization as a powerful tool for estimating user preferences

Complex networks analysis in team sports performance: multilevel hypernetworks approach to soccer matches

Humans need to interact socially with others and the environment. These interactions lead to complex systems that elude naïve and casuistic tools for understand these explanations. One way is to search for mechanisms and patterns of behavior in our activities. In this thesis, we focused on players’ interactions in team sports performance and how using complex systems tools, notably complex networks theory and tools, can contribute to Performance Analysis. We began by exploring Network Theory, specifically Social Network Analysis (SNA), first applied to Volleyball (experimental study) and then on soccer (2014 World Cup). The achievements with SNA proved limited in relevant scenarios (e.g., dynamics of networks on n-ary interactions) and we moved to other theories and tools from complex networks in order to tap into the dynamics on/off networks. In our state-of-the-art and review paper we took an important step to move from SNA to Complex Networks Analysis theories and tools, such as Hypernetworks Theory and their structural Multilevel analysis. The method paper explored the Multilevel Hypernetworks Approach to Performance Analysis in soccer matches (English Premier League 2010-11) considering n-ary cooperation and competition interactions between sets of players in different levels of analysis. We presented at an international conference the mathematical formalisms that can express the players’ relationships and the statistical distributions of the occurrence of the sets and their ranks, identifying power law statistical distributions regularities and design (found in some particular exceptions), influenced by coaches’ pre-match arrangement and soccer rules.Os humanos necessitam interagir socialmente com os outros e com o envolvimento. Essas interações estão na origem de sistemas complexos cujo entendimento não é captado através de ferramentas ingénuas e casuísticas. Uma forma será procurar mecanismos e padrões de comportamento nas atividades. Nesta tese, o foco centra-se na utilização de ferramentas dos sistemas complexos, particularmente no contributo da teoria e ferramentas de redes complexas, na Análise do Desempenho Desportivo baseado nas interações dos jogadores de equipas desportivas. Começámos por explorar a Teoria das Redes, especificamente a Análise de Redes Sociais (ARS) no Voleibol (estudo experimental) e depois no futebol (Campeonato do Mundo de 2014). As aplicações da ARS mostraram-se limitadas (por exemplo, na dinâmica das redes em interações n-árias) o que nos trouxe a outras teorias e ferramentas das redes complexas. No capítulo do estadoda- arte e artigo de revisão publicado, abordámos as vantagens de utilização de outras teorias e ferramentas, como a análise Multinível e Teoria das Híperredes. No artigo de métodos, apresentámos a Abordagem de Híperredes Multinível na Análise do Desempenho em jogos de futebol (Premier League Inglesa 2010-11) considerando as interações de cooperação e competição nos conjuntos de jogadores, em diferentes níveis de análise. Numa conferência internacional, apresentámos os formalismos matemáticos que podem expressar as relações dos jogadores e as distribuições estatísticas da ocorrência dos conjuntos e a sua ordem, identificando regularidades de distribuições estatísticas de power law e design (encontrado nalgumas exceções estatísticas específicas), promovidas pelos treinadores na preparação dos jogos e constrangidas pelas regras do futebol

Collective behaviour monitoring in football using spatial temporal and network analysis: application and evaluations.

Analysis is an important part of understanding and exploiting performance of football teams. Traditional approaches of analysis have centred around events that may not fully incorporate the highly dynamic nature of matches. To circumvent this weakness, applications of collective behaviour metrics applying spatial temporal and social network analyses to data in football have been trending over the last 10 years. The aims of this PhD were to: 1) establish the strengths and limitations of current research investigating collective behaviour in football applying novel analytical procedures; 2) investigate the credibility of present methods informing coaching practice; and 3) provide guidance for practitioners in implementing complex analytical procedures with current data collection methods. These aims were achieved through the completion of five interlinked studies. The first two studies comprised systematic reviews evaluating the quality of previous research investigating collective behaviours. The first systematic review focussed on spatial temporal metrics and the second systematic review focussed on social network analysis metrics. In addition to standard review procedures, both systematic reviews included analyses of author quotes regarding the metrics used within each study. These included description and conceptualisation of each metric, along with practical applications and measurements of reliability. The first systematic review identified several limitations in the current literature base of spatial temporal metrics investigating collective behaviour in football. These included a lack of conceptualisation of the metrics used, assumptions of metric reliability, frequent use of broad and non-actionable practical recommendations, failure to justify sample sizes and a bias towards including males. Similar findings were found in the social network analysis systematic review where authors also seldom conceptualised metrics, provided vague practical applications and often failed to justify sample size. Literature including social network analysis were also inconsistent with the metric calculations and nearly all studies investigated elite male matches. The third study in this PhD attempted to quantify the reliability of spatial temporal metrics by simulating expected error values on top of real-world data. Through fitting linear mixed effects models on signal to noise ratios, metrics were established to be reliable where positioning systems are accurate to 0.5 m or less. In situations where positioning systems errors were approached 2 m, only some were considered to produce reliable values, (e.g. team centroid), whereas metrics using distances and numerical relations were considered to produce unreliable values. After assessing the literature and reliability, the PhD focussed on implementation of common and reliable metrics, leading into the final study of the PhD which employed an iterative design comprising multiple interviews to investigate coach perceptions of collective behaviour metrics. A thematic analysis identified themes that closely resembled the 10 traditional principles of play in football, further establishing their validity. Moreover, coaches reacted positively to presented measurements, most notable network intensity, distance between defenders, triads, team length, and team depth. Coaches stated they trained players with the concepts these measurements represent as a central focus. The PhD work was concluded with a final chapter set as pedagogical support for practitioners wishing to implement these techniques providing a guide to measuring the tactical concepts discussed within this thesis. Collectively, this PhD highlights that novel collective behaviour metrics have a place in current performance analysis systems in football. Additionally, a methodology is presented for practitioners to apply to their own teams and generate specific metrics relevant to the teams own tactical principles

Similar Neural Responses Predict Friendship

Human social networks are overwhelmingly homophilous: individuals tend to befriend others who are similar to them in terms of a range of physical attributes (e.g., age, gender). Do similarities among friends reflect deeper similarities in how we perceive, interpret, and respond to the world? To test whether friendship, and more generally, social network proximity, is associated with increased similarity of real-time mental responding, we used functional magnetic resonance imaging to scan subjects’ brains during free viewing of naturalistic movies. Here we show evidence for neural homophily: neural responses when viewing audiovisual movies are exceptionally similar among friends, and that similarity decreases with increasing distance in a real-world social network. These results suggest that we are exceptionally similar to our friends in how we perceive and respond to the world around us, which has implications for interpersonal influence and attraction

The spatial structure of mobile communication networks

There has been a recent surge of interest in the relationship between the spatial and topological structure of communication networks with the availability of large scale anonymous datasets on the communication and mobility patterns of individuals. These datasets, captured as a by-product of modern communications technology, provide a detailed view of the daily interpersonal interactions of millions of people. Mobile phone call logs in particular offer an unparalleled source of information given their personal portable nature and ubiquity in modern society. The use of mobile phones has become so common that these datasets are no longer merely communication logs but close approximations of the network of interpersonal relationships that forms society. The analysis of these proxy networks has the potential to uncover knowledge about society at a scale never previously possible. Networks, and social networks in particular, have been the subject of investigation for more than a century with a rich corpus of theory and methods now available to researchers. Computational approaches to the study of networks are more recent but there are now a wide variety of structural analysis methods that have been developed and applied across many different disciplines and subject areas. The study of interactions across space has developed in parallel with theory, methods, models and a variety of applications. Recent studies of these proxy networks have tended to use computational approaches for analysing community structure and modelling spatial interacitions without much regard for the theory upon which they were built. The underlying assumption has been that all phenomena that can be represented as networks can be analysed with the same methods. In this thesis we demonstrate that this is not the case and identify a number of problems and misinterpretations that can arise when inappropriate methods or network representations are employed. Through a detailed theoretical and empirical analysis we identify appropriate combinations of network representation, spatial scale, and analysis methods for studying the spatial structure of communication networks. Using these findings we demonstrate the potential of such analysis when the appropriate methodology is employed