# Local Coupled Extreme Learning Machine Based on Particle Swarm Optimization
## 4 Simulations and Performance Verification
### Performance Comparison of Classification Problems  
Performance comparison among ELM, LC-ELM, PSO-ELM and LC-PSO-ELM algorithms is given in Tables 7 and 8. The generalization performance of the problems is justified by testing classification accuracy (testing accuracy). The simulation results in the tables show that the LC-PSO-ELM algorithm is obviously superior to the other algorithms in terms of generalization performance, except for the Iris dataset. From the Tables 7 and 8, we can also conclude that the PSO-ELM algorithm and the LC-PSO-ELM algorithm have the comparable generalization performance in the Iris dataset. From the subgraph of Figure 1, there are 16 times to 100% in the testing classification accuracy of the proposed algorithm in 20 trials with the increasing of the number of hidden neurons and the PSO-ELM learning algorithm has 15 times to 100%, which also shows the same conclusion. Therefore, the preferable performance of the proposed algorithm illustrates that the selection of optimized parameters in these specific problems is suitable for improving the generalization performance of the model. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Algorithms**} & \multicolumn{4}{c}{**Abalone**} & \multicolumn{4}{c}{**Calhousing**} \\ \cline{2-9}  & **Training time (s)** & **Testing Time (s)** & **Training Error** & **Testing Time (s)** & **Training Time (s)** & **Training Error** & **Testing Error** \\  & **STD** & **STD** & **STD** & **STD** & **STD** & **STD** & **STD** & **STD** \\ \hline ELM & 0.0078 & 0.0094 & 0.0756 & 0.0771 & 0.0172 & 0.0187 & 0.1441 & 0.1453 \\  & 0.0198 & 0.0197 & \(\begin{array}{c}9.3903\times\\ 10^{-4}\end{array}\) & 0.0019 & 0.0289 & 0.0301 & 0.0030 & 0.0033 \\ \hline LC\_ELM & 0.0593 & 0.0125 & 0.0758 & 0.0849 & 0.0577 & 0.0421 & 0.1449 & 0.1589 \\  & 0.0498 & 0.0218 & \(\begin{array}{c}7.2119\times\\ 10^{-4}\end{array}\) & 0.0067 & 0.0255 & 0.0221 & 0.0022 & 0.0140 \\ \hline PSO-ELM & 308.3157 & 0.0312 & 0.0747 & 0.0761 & 486.9368 & 0 & 0.1386 & 0.1395 \\  & 7.2990 & 0.0504 & \(\begin{array}{c}9.4281\times\\ 10^{-4}\end{array}\) & 0.0022 & 6.2410 & 0 & 0.0015 & 0.0023 \\ \hline LC-PSO-ELM & \(\begin{array}{c}1.8441\times\\ 10^{3}\end{array}\) & 0.1576 & 0.0743 & \(\begin{array}{c}\mathbf{0.0748}\\ 10^{3}\end{array}\) & \(\begin{array}{c}8.2110\times\\ 10^{3}\end{array}\) & 0.7653 & 0.1260 & \(\begin{array}{c}\mathbf{0.1317}\end{array}\) \\  & 55.4315 & 0.0307 & 0.0011 & \(\begin{array}{c}\mathbf{9.9337}\times\\ \mathbf{10^{-4}}\end{array}\) & 70.2587 & 0.0689 & 0.0052 & \(\begin{array}{c}\mathbf{0.0023}\end{array}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison of different algorithms on regression problems of Abalone and Calhousing. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Algorithms**} & \multicolumn{4}{c}{**Wine**} & \multicolumn{4}{c}{**Iris**} \\ \cline{2-9}  & **Training time (s)** & **Testing Time (s)** & **Training Accuracy** & **Testing Time (s)** & **Testing Time (s)** & **Training Time (s)** & **Training Accuracy** & **Testing Accuracy** \\  & **STD** & **STD** & **STD** & **STD** & **STD** & **STD** & **STD** & **STD** \\ \hline ELM & 0.0047 & 0.0125 & 0.9952 & 0.9741 & 0.0390 & 0 & 0.9642 & 0.9334 \\  & 0.0148 & 0.0263 & 0.0068 & 0.0096 & 0.0287 & 0 & 0.0173 & 0.0219 \\ \hline LC-ELM & 0.0156 & 0 & 0.9911 & 0.9537 & 0.0218 & 0.0062 & 0.977  
Moreover, the STD value of the PSO-ELM learning algorithm is the least in the four algorithms, which shows that it is more easily obtained from the global solution in terms of searching two parameters than four parameters for the PSO algorithm. In addition, the LC-ELM is also the most unstable learning algorithm in most cases. In summary, by analyzing all of the obtained results, the following conclusions can be drawn:  
1. The generalization performance of the ELM algorithm can be improved by means of the parameter optimization based on the PSO. 2.