# Locating the Parameters of RBF Networks Using a Hybrid Particle Swarm Optimization Method
## 3 Experiments
### Experimental Results  
The RBF network for the tests was coded in ANSI C++ with the help of the freely available Armadillo library [101]. In addition, in order to have greater reliability of the experimental results, a 10-fold validation technique was used. All the experiments were executed 30 times with different seeds for the random generator each time, and the average was measured. For the classification datasets, the average classification error is reported and, for the regression datasets, the mean test error. The machine used for the experiments was an AMD Ryzen 5950X with 128 GB of RAM. The used operating system was Debian Linux. In order to accelerate the training process, the OpenMP library was incorporated [102]. The experimental settings are listed in Table 1. The experimental results for the classification datasets are listed in Table 2 and, for the regression datasets, in Table 3. For the experimental tables, the following were applied:  
1. The column NN-PROP indicates the application of the Rprop method [103] in an artificial neural network [104; 105] with 10 hidden nodes. The RPROP method is coded in the FCNN software package [106]. 2. The column NN-GENETIC denotes the application of a genetic algorithm in the artificial neural network with 10 hidden nodes. The parameters of the used genetic algorithm are the same as in the second phase of the proposed method. 3. The column RBF-KMEANS denotes the classic training method for RBF networks by estimating centers and variances through K-means and the output weights by solving a linear system of equations. 4. The column IRBF-100 denotes the application of the current method with \(\lambda=100\). 5. The column IRBF-1000 denotes the application of the current method with \(\lambda=1000\). 6. In both tables, an extra line is added, in which the mean error for each method is shown. This row is denoted by the name AVERAGE. This line also shows the number of times the corresponding method achieved the best result. This number is shown in parentheses. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(N_{c}\) & 200 \\ \hline \(N_{g}\) & 100 \\ \hline \(N_{s}\) & 50 \\ \hline \(c_{1}\) & 1.0 \\ \hline \(c_{2}\) & 1.0 \\ \hline \(F\) & 5.0 \\ \hline \(B\) & 100.0 \\ \hline \(k\) & 10 \\ \hline \(p_{s}\) & 0.90 \\ \hline \(p_{m}\) & 0.05 \\ \hline \end{tabular}
\end{table} 
Table 1: The used values for the experimental parameters. The first column denotes the name of the parameter and the second the used value. \begin{table}
\begin{tabular}{c c c c c} \hline
**Dataset** & **NN-RPROP** & **NN-GENETIC** & **RBF-KMEANS** & **IRBF-100** & **IRBF-1000** \\ \hline Appendicitis & 16.30\% & 18.10\% & **12.23\%** & 16.47\% & 14.03\% \\ \hline Australian & 36.12\% & 32.21\% & 34.89\% & 23.61\% & **22.39\%** \\ \hline Balance & **8.81\%** & 8.97\% & 33.42\% & 12.65\% & 13.15\% \\ \hline Bands & 36.32\% & **35.75\%** & 37.22\% & 37.38\% & 36.29\% \\ \hline Cleveland & 61.41\% & 51.60\% & 67.10\% & 49.77\% & **49.64\%** \\ \hline Dermatology & **15.12\%** & 30.58\% & 62.34\% & 38.24\% & 35.64\% \\ \hline Hayes Roth & 37.46\% & 56.18\% & 64.36\% & **33.62\%** & 34.13\% \\ \hline Heart & 30.51\% & 28.34\% & 31.20\% & 15.91\% & **15.60\%** \\ \hline HouseVotes & 6.04\% & 6.62\% & 6.13\% & 4.77\% & **3.90\%** \\ \hline Ionosphere & 13.65\% & 15.14\% & 16.22\% & 8.64\% & **7.52\%** \\ \hline Liverdisorder & 40.26\% & 31.11\% & 30.84\% & 27.36\% & **25.63\%** \\ \hline Lymphography & 24.67\% & 23.26\% & 25.31\% & **19.12\%** & 20.02\% \\ \hline Mammographic & 18.46\% & 19.88\% & 21.38\% & **17.17\%** & 17.30\% \\ \hline Parkinsons & 22.28\% & 18.05\% & 17.41\% & 15.51\% & **13.59\%** \\ \hline Pima & 34.27\% & 32.19\% & 25.78\% & 23.61\% & **23.23\%** \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental results for the classification datasets. The first column is the name of the used dataset.