Coordinate transformations for characterization and cluster analysis of spatial configurations in football

Current technologies allow movements of the players and the ball in football matches to be tracked and recorded with high accuracy and temporal frequency. We demonstrate an approach to analyzing football data with the aim to find typical patterns of spatial arrangement of the field players. It involves transformation of original coordinates to relative positions of the players and the ball with respect to the center and attack vector of each team. From these relative positions, we derive features for characterizing spatial configurations in different time steps during a football game. We apply clustering to these features, which groups the spatial configurations by similarity. By summarizing groups of similar configurations, we obtain representation of spatial arrangement patterns practiced by each team. The patterns are represented visually by density maps built in the teams’ relative coordinate systems. Using additional displays, we can investigate under what conditions each pattern was applied

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

Constructing Spaces and Times for Tactical Analysis in Football

A possible objective in analyzing trajectories of multiple simultaneously moving objects, such as football players during a game, is to extract and understand the general patterns of coordinated movement in different classes of situations as they develop. For achieving this objective, we propose an approach that includes a combination of query techniques for flexible selection of episodes of situation development, a method for dynamic aggregation of data from selected groups of episodes, and a data structure for representing the aggregates that enables their exploration and use in further analysis. The aggregation, which is meant to abstract general movement patterns, involves construction of new time-homomorphic reference systems owing to iterative application of aggregation operators to a sequence of data selections. As similar patterns may occur at different spatial locations, we also propose constructing new spatial reference systems for aligning and matching movements irrespective of their absolute locations. The approach was tested in application to tracking data from two Bundesliga games of the 2018/2019 season. It enabled detection of interesting and meaningful general patterns of team behaviors in three classes of situations defined by football experts. The experts found the approach and the underlying concepts worth implementing in tools for football analysts

Quasiperiodic Heisenberg antiferromagnets in two dimensions

This is a review of the properties of 2d quantum quasiperiodic antiferromagnets as reported in studies that have been carried out in the last decade. Many results have been obtained for perfectly ordered as well as for disordered two dimensional bipartite quasiperiodic tilings. The theoretical methods used include spin wave theory, and renormalization group along with Quantum Monte Carlo simulations. These methods all show that the ground state of these unfrustrated antiferromagnets have N\'eel type order but with a highly complex spatial distribution of local staggered magnetization. The ground state properties, excitation energies and spatial dependence, structure factor, and local susceptibilities are presented. The effects of introducing geometrical disorder on the magnetic properties are discussed.Comment: 21 pages, 29 figure

Residual acceleration data on IML-1: Development of a data reduction and dissemination plan

The research performed consisted of three stages: (1) identification of sensitive IML-1 experiments and sensitivity ranges by order of magnitude estimates, numerical modeling, and investigator input; (2) research and development towards reduction, supplementation, and dissemination of residual acceleration data; and (3) implementation of the plan on existing acceleration databases

Chatbot-Based Natural Language Interfaces for Data Visualisation: A Scoping Review

Rapid growth in the generation of data from various sources has made data visualisation a valuable tool for analysing data. However, visual analysis can be a challenging task, not only due to intricate dashboards but also when dealing with complex and multidimensional data. In this context, advances in Natural Language Processing technologies have led to the development of Visualisation-oriented Natural Language Interfaces (V-NLIs). In this paper, we carry out a scoping review that analyses synergies between the fields of Data Visualisation and Natural Language Interaction. Specifically, we focus on chatbot-based V-NLI approaches and explore and discuss three research questions. The first two research questions focus on studying how chatbot-based V-NLIs contribute to interactions with the Data and Visual Spaces of the visualisation pipeline, while the third seeks to know how chatbot-based V-NLIs enhance users' interaction with visualisations. Our findings show that the works in the literature put a strong focus on exploring tabular data with basic visualisations, with visual mapping primarily reliant on fixed layouts. Moreover, V-NLIs provide users with restricted guidance strategies, and few of them support high-level and follow-up queries. We identify challenges and possible research opportunities for the V-NLI community such as supporting high-level queries with complex data, integrating V-NLIs with more advanced systems such as Augmented Reality (AR) or Virtual Reality (VR), particularly for advanced visualisations, expanding guidance strategies beyond current limitations, adopting intelligent visual mapping techniques, and incorporating more sophisticated interaction methods

SEGMENTATION, RECOGNITION, AND ALIGNMENT OF COLLABORATIVE GROUP MOTION

Modeling and recognition of human motion in videos has broad applications in behavioral biometrics, content-based visual data analysis, security and surveillance, as well as designing interactive environments. Significant progress has been made in the past two decades by way of new models, methods, and implementations. In this dissertation, we focus our attention on a relatively less investigated sub-area called collaborative group motion analysis. Collaborative group motions are those that typically involve multiple objects, wherein the motion patterns of individual objects may vary significantly in both space and time, but the collective motion pattern of the ensemble allows characterization in terms of geometry and statistics. Therefore, the motions or activities of an individual object constitute local information. A framework to synthesize all local information into a holistic view, and to explicitly characterize interactions among objects, involves large scale global reasoning, and is of significant complexity. In this dissertation, we first review relevant previous contributions on human motion/activity modeling and recognition, and then propose several approaches to answer a sequence of traditional vision questions including 1) which of the motion elements among all are the ones relevant to a group motion pattern of interest (Segmentation); 2) what is the underlying motion pattern (Recognition); and 3) how two motion ensembles are similar and how we can 'optimally' transform one to match the other (Alignment). Our primary practical scenario is American football play, where the corresponding problems are 1) who are offensive players; 2) what are the offensive strategy they are using; and 3) whether two plays are using the same strategy and how we can remove the spatio-temporal misalignment between them due to internal or external factors. The proposed approaches discard traditional modeling paradigm but explore either concise descriptors, hierarchies, stochastic mechanism, or compact generative model to achieve both effectiveness and efficiency. In particular, the intrinsic geometry of the spaces of the involved features/descriptors/quantities is exploited and statistical tools are established on these nonlinear manifolds. These initial attempts have identified new challenging problems in complex motion analysis, as well as in more general tasks in video dynamics. The insights gained from nonlinear geometric modeling and analysis in this dissertation may hopefully be useful toward a broader class of computer vision applications

Visual Analysis of Pressure in Football

Modern movement tracking technologies enable acquisition of high quality data about movements of the players and the ball in the course of a football match. However, there is a big difference between the raw data and the insights into team behaviors that analysts would like to gain. To enable such insights, it is necessary first to establish relationships between the concepts characterizing behaviors and what can be extracted from data. This task is challenging since the concepts are not strictly defined. We propose a computational approach to detecting and quantifying the relationships of pressure emerging during a game. Pressure is exerted by defending players upon the ball and the opponents. Pressing behavior of a team consists of multiple instances of pressure exerted by the team members. The extracted pressure relationships can be analyzed in detailed and summarized forms with the use of static and dynamic visualizations and interactive query tools. To support examination of team tactics in different situations, we have designed and implemented a novel interactive visual tool “time mask”. It enables selection of multiple disjoint time intervals in which given conditions are fulfilled. Thus, it is possible to select game situations according to ball possession, ball distance to the goal, time that has passed since the last ball possession change or remaining time before the next change, density of players’ positions, or various other conditions. In response to a query, the analyst receives visual and statistical summaries of the set of selected situations and can thus perform joint analysis of these situations. We give examples of applying the proposed combination of computational, visual, and interactive techniques to real data from games in the German Bundesliga, where the teams actively used pressing in their defense tactics

Evaluating the accuracy of knee kinematics measured in six degrees of freedom using surface markers

Injury to the anterior cruciate ligament (ACL) of the knee can result in joint instability even following reconstruction. This instability may be quantified by measuring in vivo knee kinematics in six degrees of freedom. Motion capture systems have been used for measuring kinematics but they are limited by system inaccuracies and error resulting from skin movement. Therefore, the overall objective of this thesis was to determine the level of accuracy that a motion capture system using surface markers provides for measuring knee kinematics. There are three specific aims in this thesis. The first specific aim was to mathematically investigate the effect of random errors in marker locations on the accuracy of knee kinematics calculated using the point cluster technique (PCT), triad and Helen Hayes marker sets. The results indicated that the PCT marker set had the greatest potential for accurately measuring knee kinematics. The second aim was to determine how inaccuracies of the motion capture system contribute to errors of joint kinematics measured with the PCT. Despite its high accuracy, the average errors of joint kinematics attributed to the system were up to 1° and 2 mm. The final specific aim was to investigate the efficacy of an algorithm called the interval deformation technique (IDT) for reducing errors of knee kinematics resulting from skin movement. The IDT reduced the errors of kinematics by 90% for an activity with skin movement simulating muscle contraction but was unable to reduce the errors resulting from skin movement at heel strike of gait. The overall errors of knee kinematics resulting from system inaccuracies and skin movement were estimated to be 2° and 4 mm. While this technique may be useful for measuring the changes in knee kinematics that result from ACL injury, this accuracy may not be sufficient to discern the small differences in knee kinematics between ACL intact and reconstructed subjects or for predicting ligament forces. Thus, further research is suggested in order to better quantify skin movement and provide data for improving the accuracy of kinematics measured with surface markers