Quantitative Analysis of Point Clouds for the Description of Complex Dynamical Systems: New Formulation of Differential Entropy and Analytical Strategies in Football Matches
摘要
The study of complex systems involves understanding collective behaviors and global properties emerging from local interactions among multiple entities. This study presents a novel formulation of differential entropy specifically designed to analyze complex systems composed of a limited number of points. The method is applied to high-frequency spatial tracking data from football matches, enabling a detailed examination of player and ball configurations on the field. Various analytical configurations are explored, ranging from global team analysis to localized assessments centered on individual players or the ball, highlighting different aspects of spatial organization and interaction dynamics. The results demonstrate how differential entropy can effectively quantify spatial complexity and team compactness during a match. This framework offers significant potential for extension to other team sports, providing a robust and interpretable metric of spatial behavior. The proposed methodology establishes a solid basis for future research into the spatial-temporal dynamics of team sports.