## 5 Experiment
### Efficiency of Attention Module  
We conducted a study to compare our methods based on the number of parameters and FLOPs. We evaluated the efficiencies of methods with performance, FLOPs (Floating Point Operations), and parameters of each method. Since the range of RMSE varies across datasets, we used the average performance improvement rate compared to the baseline as the evaluation metric. And we added one to set the performance of baseline as a reference point to one. The equation of normalized performance can be expressed as follows:  
\[1+\frac{1}{N}\sum_{i}^{N}\frac{V_{i}^{base}-V_{i}}{V_{i}^{base}}, \tag{13}\]  
where \(i\in\{Call,Internet,SMS\}\), \(N=3\), and \(V_{i}\) denote the average RMSE of target method in sub-datasets, Call, Internet, or SMS. \(V_{i}^{base}\) is the constant that denotes the average RMSE of STDenseNet in sub-datasets, Call, Internet, or SMS.  
Figure 4 shows that most attention types contribute to better overall performance. Also it shows the general tendency of improved performance with increasing FLOPs. However, method with significantly larger FLOPs tend to result lower performance. This suggests that lightweight attention modules can provide more efficient trade-off between accuracy and complexity, while overly complex attention do not necessarily lead to meaningful performance gain. In Table 7, the performance of the non-local attention using the softmax function is the best; however, this method is not efficient since it necessitates high costs for FLOPs and parameters. When we changed the softmax function to the Gaussian kernel [46], although the number of model parameters increased, we could reduce the FLOPs and achieve a high-ranking overall performance. When we used triplet attentions, FLOPs and the number of parameters did not increase significantly while achieving better performance than the baseline, making it an efficient approach. Also, when using an attention mechanism with a kernel size of 7, the performance tends to be higher compared to a kernel size of 3, but lower than that with a kernel size of 5. This points out that while capturing spatial features between more distant pixels contributes to performance improvement, increasing the kernel size also includes more irrelevant pixels, which may hinder effective feature extraction.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Attention** & **Call** & **Internet** & **SMS** \\ \hline STDenseNet (baseline) & 152.08 (10.66) & 129.01 (11.33) & 153.33 (12.36) \\ \hline MVSTGN & **54.72 (10.97)** & **12.13 (0.59)** & **39.90 (4.43)** \\ \hline ADNet w. 3 \(\times\) 3 CBAM & 147.17 (9.15) & 128.61 (11.90) & 143.21 (9.83) \\ \hline ADNet w. 5 \(\times\) 5 Triplet & 144.41 (9.68) & 123.55 (6.26) & 139.47 (7.66) \\ \hline \hline \end{tabular}
\end{table}
Table 6: SMAPE (%) comparison of STDenseNet with different attention in Trentino dataset. The number in brackets denotes standard deviation. The bold numbers indicate the best performances in the table.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Attention** & **Call** & **Internet** & **SMS** \\ \hline MVSTGN & **39.30 (7.05)** & **16.70 (4.90)** & **35.39 (2.71)** \\ \hline ADNet w. 5 \(\times\) 5 Triplet & 68.78 (8.83) & 37.19 (10.50) & 63.65 (9.70) \\ \hline ADNet w. Non-local Softmax & 76.24 (10.08) & 34.09 (7.44) & 73.41 (10.07) \\ \hline \hline \end{tabular}
\end{table}
Table 5: SMAPE (%) comparison of STDenseNet with different attention in 100 \(\times\) 100 grid. The number in brackets denotes standard deviation. The bold numbers indicate the best performances in the table.