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Multi-agent statistical discriminative sub-trajectory mining and an application to NBA basketball

Rory Bunker, Vo Nguyen Le Duy, Yasuo Tabei, Ichiro Takeuchi, Keisuke Fujii

TL;DR

A multi-agent statistically discriminative sub-trajectory mining (MA-Stat-DSM) method is proposed that takes a set of binary-labelled agent trajectory matrices as input and incorporates Hausdorff distance to identify sub-matrices that statistically significantly discriminate between the two groups of labelled trajectory matrices.

Abstract

Improvements in tracking technology through optical and computer vision systems have enabled a greater understanding of the movement-based behaviour of multiple agents, including in team sports. In this study, a Multi-Agent Statistically Discriminative Sub-Trajectory Mining (MA-Stat-DSM) method is proposed that takes a set of binary-labelled agent trajectory matrices as input and incorporates Hausdorff distance to identify sub-matrices that statistically significantly discriminate between the two groups of labelled trajectory matrices. Utilizing 2015/16 SportVU NBA tracking data, agent trajectory matrices representing attacks consisting of the trajectories of five agents (the ball, shooter, last passer, shooter defender, and last passer defender), were truncated to correspond to the time interval following the receipt of the ball by the last passer, and labelled as effective or ineffective based on a definition of attack effectiveness that we devise in the current study. After identifying appropriate parameters for MA-Stat-DSM by iteratively applying it to all matches involving the two top- and two bottom-placed teams from the 2015/16 NBA season, the method was then applied to selected matches and could identify and visualize the portions of plays, e.g., involving passing, on-, and/or off-the-ball movements, which were most relevant in rendering attacks effective or ineffective.

Multi-agent statistical discriminative sub-trajectory mining and an application to NBA basketball

TL;DR

A multi-agent statistically discriminative sub-trajectory mining (MA-Stat-DSM) method is proposed that takes a set of binary-labelled agent trajectory matrices as input and incorporates Hausdorff distance to identify sub-matrices that statistically significantly discriminate between the two groups of labelled trajectory matrices.

Abstract

Improvements in tracking technology through optical and computer vision systems have enabled a greater understanding of the movement-based behaviour of multiple agents, including in team sports. In this study, a Multi-Agent Statistically Discriminative Sub-Trajectory Mining (MA-Stat-DSM) method is proposed that takes a set of binary-labelled agent trajectory matrices as input and incorporates Hausdorff distance to identify sub-matrices that statistically significantly discriminate between the two groups of labelled trajectory matrices. Utilizing 2015/16 SportVU NBA tracking data, agent trajectory matrices representing attacks consisting of the trajectories of five agents (the ball, shooter, last passer, shooter defender, and last passer defender), were truncated to correspond to the time interval following the receipt of the ball by the last passer, and labelled as effective or ineffective based on a definition of attack effectiveness that we devise in the current study. After identifying appropriate parameters for MA-Stat-DSM by iteratively applying it to all matches involving the two top- and two bottom-placed teams from the 2015/16 NBA season, the method was then applied to selected matches and could identify and visualize the portions of plays, e.g., involving passing, on-, and/or off-the-ball movements, which were most relevant in rendering attacks effective or ineffective.
Paper Structure (14 sections, 6 equations, 11 figures, 3 tables, 1 algorithm)

This paper contains 14 sections, 6 equations, 11 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Data
  4. Trajectory data
  5. Effective and ineffective attack labeling
  6. Method
  7. Role Assignment
  8. Problem Setup
  9. Definitions
  10. MA-Stat-DSM Algorithm
  11. Results
  12. Experimental Setup
  13. Visualization and interpretation of SSD sub-matrix examples
  14. Discussion

Figures (11)

  • Figure 1: The attacks were cropped to consider the time interval from t2 to t0, i.e., the trajectories of the ball, 2 attackers (shooter and last passer), and 2 defenders (shooter defender, last passer defender) during the time from which the last passer receives the ball until a shot is made (t1 is the time at which the shooter receives the ball).
  • Figure 2: Los Angeles Lakers (effective - top, ineffective - bottom) attacks in our dataset from their 15 November 2015 match against the Detroit Pistons. The effective and ineffective attacks, based on our definition proposed, are shown in the top and bottom panels, respectively. The SSD sub-matrices are depicted by plus signs.
  • Figure 3: Main steps of the MA-Stat-DSM algorithm. *See Figures 3 and 4 in le2020stat for more details of the tree representation and pruning properties of Stat-DSM, which also apply to MA-Stat-DSM but by replacing trajectory and sub-trajectory with trajectory matrix and sub-matrix, respectively.
  • Figure 4: An effective Golden State attack with an SSD sub-matrix result from the 5 January 2016 match between the Golden State Warriors and Los Angeles Lakers. The agent sub-trajectories constituting the sub-matrix are denoted by plus signs.
  • Figure 5: An effective Lakers attack with an SSD sub-matrix from the 5 January 2016 match between the Golden State Warriors and Los Angeles Lakers.
  • ...and 6 more figures