# Modeling and Predicting Human Actions in Soccer Using Tensor-SOM
## 7 Experimental Results  
As experimental results, we compared the moving speed of the agent actually used during training with the speed output when the system inputs environmental information after training. As a representative example, the results for the blue team with \(j=1\)-\(4\) are shown in Figures 9-16. Orange is the Agent's movement speed during training, and blue is the result of the decision-making system using Tensor-SOM. These data are the same Frame clipped for each Agent from all data. Furthermore, the root mean square errors (RMSE) of \(V_{x}\) and \(V_{y}\) for each agent are presented in Table 2.  
Figure 8: Average Error per Unit (mode2 \((j)\)) to Visualize Learning Convergence. Figure 7: Average Error per Unit (model \((i)\)) to Visualize Learning Convergence. Figure 9: \(V_{x}\) according to the situation of \(j=1\). Figure 11: \(V_{x}\) according to the situation of \(j=3\). Figure 12: \(V_{x}\) according to the situation of \(j=4\). Figure 13: \(V_{y}\) according to the situation of \(j=1\). First, as a decision-making system utilizing Tensor-SOM, unique output results were obtained for all inputs. This is an inherent characteristic of Tensor-SOM; however, it does not pose a problem as the system is capable of interpolating data that was not included in the training process and uniquely determining decisions. The x-direction refers to the longitudinal direction of the field. The output results for velocity in the x-direction are characterized for each section, as shown in Figures 9-12. The transition from the Section 1 to the Section 4 occurs where the velocity changes positively and negatively during the training of Tensor-SOM. We believe that these characteristics reflect whether the team is on offense or defense, depending on the game situation. Furthermore, the Tensor-SOM decision-making system exhibits a similar pattern, following these characteristics consistently from the Section 1 to the Section 3. However, in the Section 4, the positive and negative velocities vary among different agents. This is because the system is capable of interpolating data that was not included in the training process and uniquely determining decisions. Figure 16: \(V_{y}\) according to the situation of \(j=4\). Figure 14: \(V_{y}\) according to the situation of \(j=2\). cause each agent has a distinct role. Nevertheless, Tensor-SOM functions effectively as a decision-making system, successfully capturing and reflecting the unique characteristics of each agent. On the other hand, the results for velocity in the y-direction are less effective in capturing the characteristics of the original data compared to those in the x-direction. We believe this is because the y-direction represents the shorter dimension of the field, and the direction in which an agent should move varies depending on their position and the specific game situation. As a result, the decision-making system deviates from the original training data in many aspects in the y-direction compared to the x-direction. This trend is quantitatively confirmed by the Root Mean Square Error (RMSE) values reported in Table 3. Although the difference is modest, the average RMSE for \(V_{y}\) is consistently greater than that for \(V_{x}\), suggesting that the estimation performance for the \(V_{x}\) component is comparatively superior. We believe this issue can be mitigated in the future by utilizing data that better captures these characteristics, such as representing velocity as a vector rather than decomposing it into x- and y-components. Additionally, the decision-making system, as a whole, does not reflect sudden changes in speed. This is likely due to the generalization property of Tensor-SOM, which could be improved by shortening the data acquisition period. Several potential reasons are considered for why the decision-making system failed to predict some cases accurately. These are as follows:  
1. Influence of Other Agents: Since Tensor-SOM learns all agents simultaneously, the state of other agents may influence the prediction results.