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

Revealing networks from dynamics: an introduction

What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct interactions) from accessing the dynamics of the units. Potential applications range from interaction networks in physics, to chemical and metabolic reactions, protein and gene regulatory networks as well as neural circuits in biology and electric power grids or wireless sensor networks in engineering. Moreover, we briefly mention some standard ways of inferring effective or functional connectivity.Comment: Topical review, 48 pages, 7 figure

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

Synchronization in networks with multiple interaction layers

The structure of many real-world systems is best captured by networks consisting of several interaction layers. Understanding how a multilayered structure of connections affects the synchronization properties of dynamical systems evolving on top of it is a highly relevant endeavor in mathematics and physics and has potential applications in several socially relevant topics, such as power grid engineering and neural dynamics. We propose a general framework to assess the stability of the synchronized state in networks with multiple interaction layers, deriving a necessary condition that generalizes the master stability function approach. We validate our method by applying it to a network of Rössler oscillators with a double layer of interactions and show that highly rich phenomenology emerges from this. This includes cases where the stability of synchronization can be induced even if both layers would have individually induced unstable synchrony, an effect genuinely arising from the true multilayer structure of the interactions among the units in the network

Unravelling the complexity of metabolic networks

Network science provides an invaluable set of tools and techniques for improving our understanding of many important biological processes at the systems level. A network description provides a simplied view of such a system, focusing upon the interactions between a usually large number of similar biological units. At the cellular level, these units are usually interacting genes, proteins or small molecules, resulting in various types of biological networks. Metabolic networks, in particular, play a fundamental role, since they provide the building blocks essential for cellular function, and thus, have recently received a lot of attention. In particular, recent studies have revealed a number of universal topological characteristics, such as a small average path-length, large clustering coecient and a hierarchical modular structure. Relations between structure, function and evolution, however, for even the simplest of organisms is far from understood. In this thesis, we employ network analysis in order to determine important links between an organism's metabolic network structure and the environment under which it evolved. We address this task from two dierent perspectives: (i) a network classication approach; and (ii) a more physiologically realistic modelling approach, namely hypernetwork models. One of the major contributions of this thesis is the development of a novel graph embedding approach, based on low-order network motifs, that compares the structural properties of large numbers of biological networks simultaneously. This method was prototyped on a cohort of 383 bacterial networks, and provides powerful evidence for the role that both environmental variability, and oxygen requirements, play in the forming of these important networked structures. In addition to this, we consider a hypernetwork formalism of metabolism, in an attempt to extend complex network reasoning to this more complicated, yet physiologically more realistic setting. In particular, we extend the concept of network reciprocity to hypernetworks, and again evidence a signicant relationship between bacterial hypernetwork structure and the environment in which these organisms evolved. Moreover, we extend the concept of network percolation to undirected hypernetworks, as a technique for quantifying robustness and fragility within metabolic hypernetworks, and in the process nd yet further evidence of increased topological complexity within organisms inhabiting more uncertain environments. Importantly, many of these relationships are not apparent when considering the standard approach, thus suggesting that a hypernetwork formalism has the potential to reveal biologically relevant information that is beyond the standard network approach

Model-free inference of direct network interactions from nonlinear collective dynamics

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.Comment: 10 pages, 7 figure

동적 멀티모달 데이터 학습을 위한 심층 하이퍼네트워크

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 2. 장병탁.Recent advancements in information communication technology has led the explosive increase of data. Dissimilar to traditional data which are structured and unimodal, in particular, the characteristics of recent data generated from dynamic environments are summarized as high-dimensionality, multimodality, and structurelessness as well as huge-scale size. The learning from non-stationary multimodal data is essential for solving many difficult problems in artificial intelligence. However, despite many successful reports, existing machine learning methods have mainly focused on solving practical problems represented by large-scaled but static databases, such as image classification, tagging, and retrieval. Hypernetworks are a probabilistic graphical model representing empirical distribution, using a hypergraph structure that is a large collection of many hyperedges encoding the associations among variables. This representation allows the model to be suitable for characterizing the complex relationships between features with a population of building blocks. However, since a hypernetwork is represented by a huge combinatorial feature space, the model requires a large number of hyperedges for handling the multimodal large-scale data and thus faces the scalability problem. In this dissertation, we propose a deep architecture of hypernetworks for dealing with the scalability issue for learning from multimodal data with non-stationary properties such as videos, i.e., deep hypernetworks. Deep hypernetworks handle the issues through the abstraction at multiple levels using a hierarchy of multiple hypergraphs. We use a stochastic method based on Monte-Carlo simulation, a graph MC, for efficiently constructing hypergraphs representing the empirical distribution of the observed data. The structure of a deep hypernetwork continuously changes as the learning proceeds, and this flexibility is contrasted to other deep learning models. The proposed model incrementally learns from the data, thus handling the nonstationary properties such as concept drift. The abstract representations in the learned models play roles of multimodal knowledge on data, which are used for the content-aware crossmodal transformation including vision-language conversion. We view the vision-language conversion as a machine translation, and thus formulate the vision-language translation in terms of the statistical machine translation. Since the knowledge on the video stories are used for translation, we call this story-aware vision-language translation. We evaluate deep hypernetworks on large-scale vision-language multimodal data including benmarking datasets and cartoon video series. The experimental results show the deep hypernetworks effectively represent visual-linguistic information abstracted at multiple levels of the data contents as well as the associations between vision and language. We explain how the introduction of a hierarchy deals with the scalability and non-stationary properties. In addition, we present the story-aware vision-language translation on cartoon videos by generating scene images from sentences and descriptive subtitles from scene images. Furthermore, we discuss the meaning of our model for lifelong learning and the improvement direction for achieving human-level artificial intelligence.1 Introduction 1.1 Background and Motivation 1.2 Problems to be Addressed 1.3 The Proposed Approach and its Contribution 1.4 Organization of the Dissertation 2 RelatedWork 2.1 Multimodal Leanring 2.2 Models for Learning from Multimodal Data 2.2.1 Topic Model-Based Multimodal Leanring 2.2.2 Deep Network-based Multimodal Leanring 2.3 Higher-Order Graphical Models 2.3.1 Hypernetwork Models 2.3.2 Bayesian Evolutionary Learning of Hypernetworks 3 Multimodal Hypernetworks for Text-to-Image Retrievals 3.1 Overview 3.2 Hypernetworks for Multimodal Associations 3.2.1 Multimodal Hypernetworks 3.2.2 Incremental Learning of Multimodal Hypernetworks 3.3 Text-to-Image Crossmodal Inference 3.3.1 Representatation of Textual-Visual Data 3.3.2 Text-to-Image Query Expansion 3.4 Text-to-Image Retrieval via Multimodal Hypernetworks 3.4.1 Data and Experimental Settings 3.4.2 Text-to-Image Retrieval Performance 3.4.3 Incremental Learning for Text-to-Image Retrieval 3.5 Summary 4 Deep Hypernetworks for Multimodal Cocnept Learning from Cartoon Videos 4.1 Overview 4.2 Visual-Linguistic Concept Representation of Catoon Videos 4.3 Deep Hypernetworks for Modeling Visual-Linguistic Concepts 4.3.1 Sparse Population Coding 4.3.2 Deep Hypernetworks for Concept Hierarchies 4.3.3 Implication of Deep Hypernetworks on Cognitive Modeling 4.4 Learning of Deep Hypernetworks 4.4.1 Problem Space of Deep Hypernetworks 4.4.2 Graph Monte-Carlo Simulation 4.4.3 Learning of Concept Layers 4.4.4 Incremental Concept Construction 4.5 Incremental Concept Construction from Catoon Videos 4.5.1 Data Description and Parameter Setup 4.5.2 Concept Representation and Development 4.5.3 Character Classification via Concept Learning 4.5.4 Vision-Language Conversion via Concept Learning 4.6 Summary 5 Story-awareVision-LanguageTranslation usingDeepConcept Hiearachies 5.1 Overview 5.2 Vision-Language Conversion as a Machine Translation 5.2.1 Statistical Machine Translation 5.2.2 Vision-Language Translation 5.3 Story-aware Vision-Language Translation using Deep Concept Hierarchies 5.3.1 Story-aware Vision-Language Translation 5.3.2 Vision-to-Language Translation 5.3.3 Language-to-Vision Translation 5.4 Story-aware Vision-Language Translation on Catoon Videos 5.4.1 Data and Experimental Setting 5.4.2 Scene-to-Sentence Generation 5.4.3 Sentence-to-Scene Generation 5.4.4 Visual-Linguistic Story Summarization of Cartoon Videos 5.5 Summary 6 Concluding Remarks 6.1 Summary of the Dissertation 6.2 Directions for Further Research Bibliography 한글초록Docto

Hyperharmonic analysis for the study of high-order information-theoretic signals

Network representations often cannot fully account for the structural richness of complex systems spanning multiple levels of organisation. Recently proposed high-order information-theoretic signals are well-suited to capture synergistic phenomena that transcend pairwise interactions; however, the exponential-growth of their cardinality severely hinders their applicability. In this work, we combine methods from harmonic analysis and combinatorial topology to construct efficient representations of high-order information-theoretic signals. The core of our method is the diagonalisation of a discrete version of the Laplace–de Rham operator, that geometrically encodes structural properties of the system. We capitalise on these ideas by developing a complete workflow for the construction of hyperharmonic representations of high-order signals, which is applicable to a wide range of scenarios