# A Two-Phase Evolutionary Method to Train RBF Networks
## 3 Experiments
### Experimental Results  
The results for the classification datasets are listed in Table 3 and for the regression datasets the results are reported in Table 4. For the first case, the average classification error is reported and for the case of regression datasets, the total test error is reported. The column KRBF denotes the classic RBF training method, GRBF denotes the method proposed in [80] and the column \"proposed\" denotes the proposed method. The KBF simply consists of two phases: in the first phase, the centers and variances are estimated through the k-means algorithm and in the second phase, a system of equations is solved to obtain the weights \(w_{i}\) of the RBF network. From the experimental results, it is clear that the proposed method is significantly superior to other methods in almost all datasets. In the proposed method, the appropriate initialization interval was found for the parameters of RBF using k-means. A parallel genetic algorithm was then applied to this previous value range, creating a variety of neural networks. This combination of techniques obviously has very good results as it combines a very efficient clustering method and an excellent optimization method that is ideally parallelized. Of course, the new method requires much more execution time, due to the presence of the genetic algorithm, but the parallel execution of the software drastically reduces this time. Furthermore, in order to study the effectiveness of the selection of parameter \(F\) an additional experiment was conducted, where the best fitness of the genetic algorithm is plotted for the Wine problem. The outcome of this experiment is graphically outlined in Figure 1. The graph shows that the behavior of the proposed method does not change significantly for different values of the parameter \(F\). Furthermore, the plot for the Wine dataset of best, worst and average fitness for \(F=3\) is shown in Figure 2. An additional experiment was performed to evaluate the effect of the parameter change \(k\) on the results. In Figure 3, the plot for different values of \(k\) for the Housing dataset is outlined and in Figure 4 the same experiment is shown for the Z_F_S classification dataset. Of course, from the value \(k=4\) onwards, the error falls but not at the same rate. The proposed value \(k=10\) was used in all datasets in order to have a balance between the speed and the efficiency of the method. Finally, the classification performance was evaluated based on two evaluation metrics: precision and recall for some datasets as shown in Table 5. In these results, the precision of the proposed method showed the best classification performance under different datasets. We found the same trends in recall metric in two of three datasets (spiral and EEG datasets). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **KRBF** & **GRBF** & **Proposed** \\ \hline Abalone & 2559.48 & 4161.66 & 1960.22 \\ \hline Airfoil & 5.49 & 18.15 & 0.58 \\ \hline Anacalt & 11.628 & 5.58 & 0.003 \\ \hline BK & 0.17 & 0.21 & 0.23 \\ \hline BL & 0.05 & 0.019 & 0.0009 \\ \hline Concrete & 1.15 & 1.50 & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression error for different datasets.