## 3 Experiments
### Results  
Table 2 and Figure 4 show the results of the accuracy metrics of our proposed representation framework incorporating each pooling operation, as evaluated by STCN. The metric values in Table 2 were rounded to four places and minimum values were marked with a bold typeface according to their original values before they were rounded. It can be seen that in terms of MSE, MAV achieved minimum average daily errors with 0.0050 for 30 min, 0.0052 for 40 min, and 0.0052 for 60 min. As for MAE, MAV performed better than the other three with 0.0189 for 10 min, 0.0211 for 30 min, 0.0219 for 40 min, 0.0219 for 60 min. With regard to roMAPE, MAV produced three minimum average daily errors with 5.6986 for 20 min, 5.8901 for 40 min, and 5.8229 for 50 min. Considering MSE, MAE, and roMAPE, in more than half of these six prediction horizons, MAV produced minimum errors when predicting traffic congestion levels. Additionally, Figure 2 illustrates the trends of MAE and MSE according to the four pooling operations along the prediction horizon. It can be observed that the prediction errors generally go upward, which might be caused by more uncertainties as the prediction horizon moves further into the future. However, MAV produces optimal overall prediction errors with a more stable trend than the others. Hence, it can be inferred that when used as a pooling operation, MAV together with our proposed framework can properly and effectively represent traffic congestion data for short-term traffic congestion prediction. The reason for MAV's overall optimal performance might be twofold. Firstly, MAV always chooses the most serious congestion level in each grid, which is foremostly representative for real-world regions corresponding to these grids. Secondly, serious traffic congestion in one region is more likely to propagate to other ones. As for the other three pooling operations, NNV misses the most congested level in 75% cases, while the other two reduce the significance and representativeness of the most congested level through averaging. Figure 4: Prediction errors for prediction horizons of 10, 20, 30, 40, 50, and 60 min. (**a**) Mean absolute error (MAE). (**b**) Mean squared error (MSE). As an example of the prediction errors by day, details about the daily prediction performance in terms of MAE and MSE with a horizon of 40 min are shown in Figure 5. It can be seen that MAV has a smaller variation than ANZ, AMM, and NNV, which is confirmed by the standard deviation values shown in Table 3.  
To evaluate requirement of computational resources, Table 4 lists the usage of GPU time and memory both by the original matrices and compressed ones derived using our proposed framework with MAV as the pooling reduction operation. When original traffic congestion matrices are used as input, STCN and these input data could not fit onto the one graphics card of our experiment device. Therefore, it had to be evaluated on another workstation with the same configuration as our experimental device, the difference being that it had two graphics cards of the same type described in Section 3.3. In addition, it was run with the help of a distributed deep learning framework--Horovod [66]. Metric values are reported as recorded on each experimental device. It can been seen the compressed matrices derived using our proposed representation framework combined with MAV save more than 73% GPU time and use only a little more than 55% of GPU memory when compared to the original matrices. Using a grid size of \(2\times 2\), original matrices are reduced by 75% in size and thus our proposed representation framework is cost-efficient in terms of GPU time and memory.