## 4 Experimental Results
### Experimental Results  
The forecasted performance results of Model 1, Model 2, and Model 3 are presented in Table 2. The MAPE values of Model 2 and Model 3 in this table represent the best results obtained from the forecasting experiment according to the number of clusters. The overall results for this experiment are shown in Tables 3 and 4. In Table 3, the forecasted performance results of Model 2 using various prediction techniques are shown according to the number of clusters ranging from 2 to 6. Table 4 illustrates the forecasting performance results of Model 3. We measured the MAPE changing the number of clusters from 2 to 6 as we did with Model 2. In addition, we tested all possible combinations of prediction techniques used as components of the SELM and selected the best one. The best combination can be found in Table 4.  
Figure 5: (**a**) Model 1, (**b**) Model 2, and (**c**) Model 3. The “preprocess dataset” in the figure is the result of the original dataset having gone through the process of the front part of Figure 4.  
The forecasted performance results of Model 1 and Model 2 can be compared referring to the first and second columns of Table 2. The results indicate that, when SOM is used for clustering, performance is sometimes slightly more accurate, almost the same, or even less accurate than the results of Model 1. This contradicts the assumption that the forecasting performance improves when we take advantage of the reduced effect of overfitting that results from clustering the dataset into several clusters that contain data points with similar characteristics. The same number of forecasting models is trained on these clusters to produce predictions, which is the reason why SOM has been utilized in the literature. This occurs because clustering reduces the number of data samples in each model, thereby indicating that the chances of overfitting are very high, and the forecasting performance is rather poor for techniques that are sensitive to the number of data samples such as MLR. Figure 6 shows the forecasting performance of the ANN, the GBM, and ADB in Model 2 on every data point in the testing set. As shown in Figure 6, the forecasting performance of each technique varies depending on the data points. This demonstrates that a certain technique does not produce more accurate predictions than others at all times. That is, for every data point in the testing dataset, the best performing technique always differs point by point. Even if the overall forecasting performance of a technique is worse than other models, at some points it may outperform the other techniques. Hence, trying to combine several techniques to produce improved results is reasonable. In this context, the SELM combines the predictions produced by individual techniques with a weighting coefficient to improve the final prediction. To determine the weighting, various methods ranging from simple averaging to regularized linear regression and even an ensemble method [33] have been used. Our study uses a simple averaging method because other methods require a validation set or cross-validation process to train the aggregating model and because we assumed a small-size dataset context. \begin{table}
\begin{tabular}{c c c} \hline \hline
**\# of Clusters** & **Best Combination** & **Model 3** \\ \hline
2 & MLR/GBM/ANN & 6.4 \\
3 & MLR/SVR/GBM/ANN/XGB & 6.7 \\
4 & GBM/ANN & 6.81 \\
5 & GBM/ANN & 6.9 \\
6 & GBM/ANN & 7.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Forecasting performance of Model 3 in terms of MAPE according to the number of clusters.