## 3 Experiments
### Results
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **10 min** & \multicolumn{8}{c}{**20 min**} \\ \hline \multirow{3}{*}{Averaged daily metrics} & AMM & ANZ & MAV & NNV & AMM & ANZ & MAV & NNV \\ \hline MSE & 0.0043 & 0.0044 & 0.0043 & **0.0042** & 0.0047 & 0.0047 & 0.0047 & **0.0047** \\ MAE & 0.0190 & 0.0195 & **0.0189** & 0.0193 & **0.0204** & 0.0206 & 0.0208 & 0.0205 \\ roMAPE & 5.0817 & **4.9862** & 5.0566 & 5.0022 & **5.3700** & 5.5199 & 5.5353 & 5.6462 \\ \hline \multicolumn{8}{c}{30 min} & \multicolumn{8}{c}{40 min} \\ \hline \multirow{3}{*}{Averaged daily metrics} & AMM & ANZ & MAV & NNV & AMM & ANZ & MAV & NNV \\ \hline MSE & 0.0052 & 0.0051 & **0.0050** & 0.0051 & 0.0054 & 0.0054 & **0.0052** & 0.0054 \\ MAE & 0.0217 & 0.0215 & **0.0211** & 0.0216 & 0.0222 & 0.0222 & **0.0219** & 0.0222 \\ roMAPE & 5.7817 & 5.8474 & **5.6986** & 5.8093 & 6.0554 & 5.9054 & **5.8901** & 5.9548 \\ \hline \multicolumn{8}{c}{50 min} & \multicolumn{8}{c}{60 min} \\ \hline \multirow{3}{*}{Averaged daily metrics} & AMM & ANZ & MAV & NNV & AMM & ANZ & MAV & NNV \\ \hline MSE & **0.0054** & 0.0055 & 0.0054 & 0.0055 & 0.0053 & 0.0052 & **0.0052** & 0.0053 \\ MAE & **0.0222** & 0.0225 & 0.0224 & 0.0227 & 0.0224 & 0.0221 & **0.0219** & 0.0223 \\ roMAEP & 5.8380 & 5.9921 & **5.8229** & 5.8546 & 5.8230 & **5.7164** & 5.7862 & 5.9178 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of overall prediction metrics by different methods during 20 days with a prediction horizon of 10, 20, 30, 40, 50, and 60 min. Minimum metric values are marked with a bold typeface. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **AMM** & **ANZ** & **MAV** & **NNV** \\ \hline Standard variation of MAE & 5.43353 \(\times\)\(10^{-6}\) & 5.87416 \(\times\)\(10^{-6}\) & 4.21447 \(\times\)\(10^{-6}\) & 5.75157 \(\times\)\(10^{-6}\) \\ Standard variation of MSE & 8.73426 \(\times\)\(10^{-7}\) & 7.32658 \(\times\)\(10^{-7}\) & 6.45158 \(\times\)\(10^{-7}\) & 8.28743 \(\times\)\(10^{-7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Standard variations corresponding to Figure 5.  
To compare the effectiveness of the original traffic congestion matrices (ORIGINAL) and the compressed ones derived using our proposed approach, Table 5 lists the average metric values of MAE and MSE across six prediction horizons. The metric values in Table 5 were rounded to four places and minimum values were marked with a bold typeface according to their original values before they were rounded. In terms of MSE, MAV commits smaller errors of 0.0047, 0.0050, 0.0052, respectively, for the \begin{table}
\begin{tabular}{l l} \hline \hline  & **Original Matrices (Using Horovod)** & **Down-Sampled Using MAV** \\ \hline Average training time per epoch (seconds) & \(32+32\) & \(17\) \\ GPU memory usage (megabytes) & \(9627+9627\) & \(10\),\(613\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the required computing resources on original traffic congestion matrices and down-sampled ones using maximum of all values (MAV). Figure 5: Comparison of the daily prediction metrics with a prediction horizon of 40 min during 20 days, evaluated with back-testing. **(a)** Daily MAE. **(b)** Daily MSE. prediction horizons of 20, 30, and 60 min. As for MAE, MAV performs better with error values of 0.0208, 0.0211, 0.0224, and 0.0219, respectively, for 20, 30, 50, 60 min into the future. It can be inferred that the compressed traffic congestion matrices derived using our proposed approach are at least as effective as the original ones, while at the same time are more efficient. This might be because the maximum value of a grid is characteristic of that gird. Particularly, when only a grid size of \(2\times 2\) is used in our experiment, it is possible for the maximum value to well represent its grid with no loss of information.