## 4 Results
### Validation Results  
With the aim of selecting the best hybrid configuration (the optimal clusters number), a test has been performed using the testing dataset. This data were created with the 5% of the data of each cluster. This data were used as new input data for the nine different hybrid models, and also for the global model. Inside the hybrid model, each new sample was assigned to its local model using the euclidean distance to each cluster centroid, and the output is predicted to calculate the model error. Table 8 shows different error values to compare the hybrid configurations.  
The best hybrid configuration is the one that divides the model internally into nine local models. In Table 7, it is possible to see the different algorithms and their configurations used in the final hybrid  
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Global**} & \multicolumn{8}{c}{**Hybrid Model (Local Models)**} \\ \cline{3-11}  & & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline Cl-1 & 16.8972 & 3.1161 & 1.0321 & 5.9668 & 6.2402 & 5.6794 & 6.3455 & 6.3268 & 6.1555 & 5.9393 \\ \hline Cl-2 & & 21.8021 & 9.8955 & 0.4348 & 6.9023 & 0.6041 & 9.0305 & 8.0789 & 9.4405 & 12.1097 \\ \hline Cl-3 & & & 26.6203 & 9.7590 & 0.3851 & 0.3093 & 0.5586 & 7.6646 & 7.6268 & 8.0194 \\ \hline Cl-4 & & & 26.2704 & 19.9626 & 7.4397 & 0.2725 & 0.5744 & 10.5137 & 10.7156 \\ \hline Cl-5 & & & & 26.4265 & 21.2670 & 7.0769 & 0.2332 & 0.5387 & 11.0445 \\ \hline Cl-6 & & & & & 26.1993 & 22.3688 & 14.7125 & 0.2308 & 0.4686 \\ \hline Cl-7 & & & & & & 25.9529 & 19.6236 & 15.8058 & 0.2294 \\ \hline Cl-8 & & & & & & & 31.8514 & 18.4699 & 10.7052 \\ \hline Cl-9 & & & & & & & & 32.7775 & 25.8231 \\ \hline Cl-10 & & & & & & & & & 33.1709 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Mean squared error (MSE) for each individual hybrid model; all values \(\times 10^{-4}\).  
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Global**} & \multicolumn{8}{c}{**Hybrid Model (Local Models)**} \\ \cline{3-11}  & & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline Cl-1 & ANN-14 & ANN-5 & ANN-14 & ANN-9 & ANN-4 & ANN-10 & ANN-12 & ANN-6 & ANN-9 & ANN-9 \\ \hline Cl-2 & & ANN-13 & ANN-14 & ANN-14 & ANN-5 & ANN-6 & LS-SVR & LS-SVR & LS-SVR \\ \hline Cl-3 & & & ANN-14 & ANN-10 & ANN-12 & Poly-1 & ANN-14 & ANN-4 & ANN-8 & ANN-4 \\ \hline Cl-4 & & & ANN-15 & ANN-14 & ANN-3 & Poly-1 & ANN-12 & ANN-6 & ANN-10 \\ \hline Cl-5 & & & & ANN-14 & ANN-8 & ANN-3 & ANN-6 & ANN-12 & LS-SVR \\ \hline Cl-6 & & & & & ANN-15 & ANN-9 & ANN-8 & ANN-6 & ANN-10 \\ \hline Cl-7 & & & & & & ANN-14 & ANN-10 & LS-SVR & ANN-6 \\ \hline Cl-8 & & & & & & & ANN-13 & ANN-11 & LS-SVR \\ \hline Cl-9 & & & & & & & ANN-14 & ANN-11 \\ \hline Cl-10 & & & & & & & & ANN-10 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Configuration for each individual hybrid model.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Global**} & \multicolumn{8}{c}{**Hybrid Model (Local Models)**} \\ \cline{3-11}  & & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \multirow{2}{*}{MSE} & 0.0016 & 0.0016 & 0.0015 & 0.0015 & 0.0015 & 0.0015 & 0.0015 & 0.0015 & 0.0014 & 0.0014 \\ \hline MAE & 0.0272 & 0.0270 & 0.0258 & 0.0257 & 0.0258 & 0.0259 & 0.0259 & 0.0255 & 0.0247 & 0.0250 \\ \hline NMSE & 0.1116 & 0.1095 & 0.1038 & 0.1023 & 0.1036 & 0.1030 & 0.1047 & 0.1005 & 0.0977 & 0.1001 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Error values for the different hybrid configurations.