# Locating the Parameters of RBF Networks Using a Hybrid Particle Swarm Optimization Method
## 3 Experiments
### Experimental Results
As one can see from the experimental results, the proposed method significantly outperformed the other techniques in the majority of cases in terms of the average error in the test set. Moreover, the difference from the established method of training RBF networks was of the order of 40%, and in some cases, this percentage can be doubled. The statistical difference of the proposed technique against the rest is also shown in Figures 4 and 5. However, the proposed technique was significantly slower than the original training technique, as it is a two-stage technique. In the first stage, an optimal interval of values \begin{table}
\begin{tabular}{c c c c c c} \hline
**Dataset** & **NN-RPROP** & **NN-GENETIC** & **RBF-KMEANS** & **IRBF-100** & **IRBF-1000** \\ \hline Popfailures & **4.81\%** & 5.94\% & 7.04\% & 5.21\% & 5.10\% \\ \hline Regions2 & 27.53\% & 29.39\% & 38.29\% & 26.08\% & **25.77\%** \\ \hline Saheart & 34.90\% & 34.86\% & 32.19\% & **27.94\%** & 28.91\% \\ \hline Segment & 52.14\% & 57.72\% & 59.68\% & 47.19\% & **40.28\%** \\ \hline Spiral & 46.59\% & 44.50\% & 44.87\% & **19.43\%** & 19.56\% \\ \hline Wdbc & 21.57\% & 8.56\% & 7.27\% & **5.33\%** & 5.44\% \\ \hline Wine & 30.73\% & 19.20\% & 31.41\% & 9.20\% & **6.84\%** \\ \hline Z\_F\_S & 29.28\% & 10.73\% & 13.16\% & 4.19\% & **4.18\%** \\ \hline ZO\_NF\_S & 6.43\% & 8.41\% & 9.02\% & **4.31\%** & 4.35\% \\ \hline ZONF\_S & 27.27\% & 2.60\% & 4.03\% & 2.23\% & **2.08\%** \\ \hline ZOO & 15.47\% & 16.67\% & 21.93\% & **10.13\%** & 11.13\% \\ \hline
**AVERAGE** & **26.86\%(3)** & **24.87\%(1)** & **29.03\%(1)** & **19.43\%(8)** & **18.68\%(13)** \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline
**DATASET** & **NN-RPROP** & **NN-GENETIC** & **RBF-KMEANS** & **IRBF-100** & **IRBF-1000** \\ \hline ABALONE & **4.55** & 7.17 & 7.37 & 5.57 & 5.32 \\ \hline AIRFOIL & 0.002 & 0.003 & 0.27 & 0.004 & **0.003** \\ \hline BASEBALL & 92.05 & 103.60 & 93.02 & **78.89** & 85.58 \\ \hline BK & 1.60 & 0.03 & **0.02** & 0.04 & 0.03 \\ \hline BL & 4.38 & 5.74 & 0.013 & **0.0003** & 0.0003 \\ \hline CONCRETE & 0.009 & 0.009 & 0.011 & **0.007** & 0.007 \\ \hline DEE & 0.608 & 1.013 & 0.17 & **0.16** & 0.16 \\ \hline DIABETES & 1.11 & 19.86 & **0.49** & 0.78 & 0.89 \\ \hline HOUSING & 74.38 & 43.26 & 57.68 & **20.27** & 21.54 \\ \hline FA & 0.14 & 1.95 & **0.015** & 0.032 & 0.029 \\ \hline MB & 0.55 & 3.39 & 2.16 & 0.12 & **0.09** \\ \hline MORTGAGE & 9.19 & 2.41 & 1.45 & **0.39** & 0.78 \\ \hline NT & 0.04 & **0.006** & 8.14 & 0.007 & 0.007 \\ \hline PY & 0.039 & 1.41 & **0.012** & 0.024 & 0.014 \\ \hline QUAKE & 0.041 & 0.040 & 0.07 & 0.04 & **0.03** \\ \hline TREASURY & 10.88 & 2.93 & 2.02 & **0.33** & 0.51 \\ \hline WANKARA & 0.0003 & 0.012 & **0.001** & 0.002 & 0.002 \\ \hline
**AVERAGE** & **11.71(1)** & **11.34(1)** & **10.17(5)** & **6.27(7)** & **6.76(3)** \\ \hline \end{tabular}
\end{table} 
Table 3: Experimental results for the regression datasets. The first column is the name of the used regression dataset. for the network parameters is created with a modified PSO method, and in the second stage, the network is trained using a genetic algorithm. Of course, this extra time can be significantly reduced by incorporating parallel techniques, as was done experimentally using the OpenMP library. Furthermore, changing the normalization factor \(\lambda\) from 100 to 1000 did not have much effect on the mean error in the test set. This implies that the proposed method is quite robust, since it does not have much dependence on this parameter. Figure 4: Graphical comparison of all methods for the classification datasets. Figure 5: Graphical comparison of the methods for the regression datasets. An additional experiment was performed with different values for the parameter \(F\). The experimental results for this experiment are shown in Table 4 for the classification datasets and in Table 5 for the regression datasets. For this critical parameter, no large deviations appeared in the results of the proposed method.