# A Gradient-Based Particle-Bat Algorithm for Stochastic Configuration Network
## 5 Discussion  
Tables 8-11 show that G-BAPSO-SCN converges faster than other models when the number of hidden nodes is the same, and the RVFL network and ELM have relatively poor performance.In regression experiment 1, the training RMSE of G-BAPSO-SCN increased by \(5.57\times 10^{-5}\) compared with that of SCN; in regression experiment 2, the training RMSE of G-BAPSO-SCN increased by 0.0032, indicating that the improvement degree of training RMSE not only depends on the algorithm itself, but is also closely related to the distribution \begin{table}
\begin{tabular}{c c c} \hline \hline
**Network** & **Training ACC** & **Test ACC** \\ \hline G-BAPSO-SCN & 99.93\% & 99.96\% \\ SCN & 99.79\% & 99.80\% \\ RVFL & 97.88\% & 97.90\% \\ ELM & 99.04\% & 98.50\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Performance comparison results (Dataset 3). Figure 10: The average convergence curve (Dataset 4). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Network** & **Training RMSE** & **Test RMSE** \\ \hline G-BAPSO-SCN & **0.0008** & **0.0021** \\ SCN & 0.0040 & 0.0050 \\ RVFL & 0.1491 & 0.1645 \\ ELM & 0.2056 & 0.2235 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance comparison results (Dataset 1). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Network** & **Training RMSE** & **Test RMSE** \\ \hline G-BAPSO-SCN & **6.4809 \(\times\) 10\({}^{-6}\)** & **4.0114 \(\times\) 10\({}^{-5}\)** \\ SCN & 6.2139 \(\times\) 10\({}^{-5}\) & 5.7800 \(\times\) 10\({}^{-4}\) \\ RVFL & 2.0778 \(\times\) 10\({}^{-2}\) & 1.0210 \(\times\) 10\({}^{-1}\) \\ ELM & 2.2864 \(\times\) 10\({}^{-1}\) & 2.7515 \(\times\) 10\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Performance comparison results (Dataset 3). characteristics of the data. In classification problems, G-BAPSO-SCN also has an advantage in recognition accuracy, with an average improvement of about 0.07% over SCN. At the same time, it could also be seen from the comparison of convergence curves in Figures 7-10 that G-BAPSO-SCN has faster convergence than SCN. Since RVFL and ELM are not incremental generation networks, and their hidden nodes are generated once, the convergence speed between them is not compared with the former two curves. G-BAPSO-SCN performs well because it introduces a more flexible mechanism in the search of input parameters, allowing it to explore the solution space more thoroughly. The algorithm combines the advantages of the intelligent optimization method and traditional optimization method, and the introduction of gradient makes it possible to approach the optimal solution quickly. By introducing the emission frequency mechanism of bats into the PSO framework, local search could be carried out according to individual fitness and emission frequency at the initial stage, and the poor individuals could be eliminated adaptively, thus accelerating the convergence rate. SCN uses the linear expansion searching method to select the input parameters, which cannot detect the optimal solution with a long distance in the initial stage. The initial configuration is not optimized, thus increasing the searching iterations and the number of nodes to a certain extent. RVFLN is a typical incremental network, so we also compare it with G-BAPSO-SCN. However, RVFLN could not guarantee the convergence, and the accuracy of the network is slightly inferior. ELM's performance is relatively poor under the same number of hidden nodes as G-BAPSO-SCN. In addition to the optimization of input weights and biases, CSSA-SCN [20] optimizes their search intervals and the regularization factor r of the model, which is the optimization of hyperparameters, and its objective function and optimized parameters are different from those in this paper. Most of the other methods used to optimize SCNS focus on the the output parameters or the generation of model structures.