Automatically recognizing strategic cooperative behaviors in various situations of a team sport

Analysis of contextualized intensity in Men's elite handball using graph-based deep learning

Manual annotation of data in invasion games is a costly task which poses a natural limit on sample sizes and the level of granularity used in match and performance analyses. To overcome this challenge, this work introduces FAUPA-ML, a Framework for Automatic Upscaled Performance Analysis with Machine Learning, which leverages graph neural networks to scale domain-specific expert knowledge to large data sets. Networks were trained using position data of match phases (counter/position attacks), annotated manually by domain experts in 10 matches. The best network was applied to contextualize N = 539 matches of elite handball (2019/20-2021/22 German Men's Handball Bundesliga) with 86% balanced accuracy. Distance covered, speed, metabolic power, and metabolic work were calculated for attackers and defenders and differences between counters and position attacks across seasons analyzed with an ANOVA. Results showed that counter attacks are shorter, less frequent and more intense than position attacks and that attacking is more intense than defending. Findings show that FAUPA-ML generates accurate replications of expert knowledge that can be used to gain insights in performance analysis previously deemed infeasible. Future studies can use FAUPA-ML for large-scale, contextualized analyses that investigate influences of team strength, score-line, or team tactics on performance.

Data-Driven Analysis for Understanding Team Sports Behaviors

Understanding the principles of real-world biological multi-agent behaviors is a current challenge in various scientific and engineering fields. The rules regarding the real-world biological multi-agent behaviors such as those in team sports are often largely unknown due to their inherently higher-order interactions, cognition, and body dynamics. Estimation of the rules from data, i.e., via data-driven approaches such as machine learning, provides an effective way to analyze such behaviors. Although most data-driven models have non-linear structures and high predictive performances, it is sometimes hard to interpret them. This survey focuses on data-driven analysis for quantitative understanding of behaviors in invasion team sports such as basketball and football, and introduces two main approaches for understanding such multi-agent behaviors: (1) extracting easily interpretable features or rules from data and (2) generating and controlling behaviors in visually-understandable ways. The first approach involves the visualization of learned representations and the extraction of mathematical structures behind the behaviors. The second approach can be used to test hypotheses by simulating and controlling future and counterfactual behaviors. Lastly, the potential practical applications of extracted rules, features, and generated behaviors are discussed. These approaches can contribute to a better understanding of multi-agent behaviors in the real world.

Physically-interpretable classification of biological network dynamics for complex collective motions

Understanding biological network dynamics is a fundamental issue in various scientific and engineering fields. Network theory is capable of revealing the relationship between elements and their propagation; however, for complex collective motions, the network properties often transiently and complexly change. A fundamental question addressed here pertains to the classification of collective motion network based on physically-interpretable dynamical properties. Here we apply a data-driven spectral analysis called graph dynamic mode decomposition, which obtains the dynamical properties for collective motion classification. Using a ballgame as an example, we classified the strategic collective motions in different global behaviours and discovered that, in addition to the physical properties, the contextual node information was critical for classification. Furthermore, we discovered the label-specific stronger spectra in the relationship among the nearest agents, providing physical and semantic interpretations. Our approach contributes to the understanding of principles of biological complex network dynamics from the perspective of nonlinear dynamical systems.

Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.