Fig 1.
Given a set of soccer videos, the proposed method consists of detecting and tracking the players in the field toward obtaining their (x,y)-coordinates. Then, we divided the tracking data into training and testing subsets, using the k-fold cross-validation protocol. Next, we model the interaction between players using complex networks, in which the nodes represent players, while edges the chances of passing the ball to teammates. Thus, we extract representations for the built complex network and use the visual rhythms technique to summarize such features for a time window. Finally, we use the visual rhythms maps to build a classifier for predicting the changes of an attack move reaching the attack zone, and also an explainable method to estimate the contribution of input features.
Fig 2.
Division of BPI possession windows.
Fig 3.
The figure depicts a graph built from the (x, y)-coordinates of each player.
Each vertex has a circle surrounding it, and the circle sizes aid to compare the betweenness entropy of a vertex with the others, where the larger the circle, the greater the betweenness entropy.
Fig 4.
The image shows a situation with a high value of eccentricity of t1 (team with the ball possession).
Here, it is possible to observe the players are separated in the highlighted green zone, but with many options to make passes.
Fig 5.
The image shows a situation with high local efficiency of player 11 at the moment that he received the ball, having five options to make the pass (green edges).
This situation demonstrates that if he was undermarked (unable to receive the ball) this play would not be possible.
Fig 6.
The image illustrates a high entropy situation for team t1 (with ball possession), where it is possible to observe that players 5 and 4 (the region highlighted in green in the figure) are free of marking and with several options of passes (edges incident on the vertex), thus having a greater chance of receiving passes.
Fig 7.
The image illustrates a high entropy situation for team t2 (without ball possession), where it is possible to observe that players 7, 4, and 5 (the region highlighted in green in the figure) are far from players of the team with possession, thus not marking any opponent, thus facilitating the performance of passes between opposing players.
Fig 8.
The figure demonstrate how the entropy values for two players vary over time, where the X axis represents the seconds of ball possession and the Y axis is the entropy measure at the moment.
(b) shows the same values of item (a), but in the visual rhythm format, where light tones represent higher values of entropy and dark shades the lower values.
Fig 9.
The X axis represents the pass of time and the Y axis the players (value of graph metric), the pixels with light colors represent higher values for the player at that moment, while dark tones mean lower values.
Fig 10.
Visual rhythm built by measuring the entropy of complex networks that represent the attacking (a) and defending (b) teams considering an interval of five seconds.
The x-axis represents the time elapsed, while the y-axis shows the entropy for each node (player) of complex networks. (a) Attacking team (with the control of the ball), (b) Defending team (without the control of the ball).
Fig 11.
Visual rhythm arrangement used as input for classification models.
This representation gathers eight different complex network metrics obtained from the attacking and defending teams: (1) Centrality; (2) Clustering coefficient; (3) Eccentricity; (4) Entropy; (5) Global efficiency; (6) Local efficiency; (7) PageRank; and (8) Vulnerability. Where each metric was represented by a channel in the image, in this way each image has sixteen dimensions (one for each of the eight metrics of both teams). So the image is represented with 11 pixels height (one for each player), 167 pixels width (representing time), and 16 dimensions (one for metric).
Table 1.
Balanced accuracy of the classifier for each test round.
Table 2.
Confusion matrices for each test round, where the first row shows the true positive and false negatives values respectively.
And the second row shows the false negative and true negative respectively.
Table 3.
Balanced accuracy of the classifier for each test round with random classifier.
Fig 12.
The figure shows the SHAP values of metrics of the attacking team.
Fig 13.
The figure shows the SHAP values of metrics of the defending team.