# Local Coupled Extreme Learning Machine Based on Particle Swarm Optimization
## 4 Simulations and Performance Verification
### Performance Comparison of LC-ELM Based on Two Different Optimization Methods of DE and PSO  
Performance comparison results of the ELC-ELM [12] and the LC-PSO-ELM algorithms on regression or classification problems are listed in Table 9. Here, in the ELC-ELM algorithm, the differential evolution (DE) optimization algorithm is used for improving the generalization performance of the ELC-ELM (evolution local coupled extreme learning machine) algorithm, in which the parameters of the hidden neuron address and the radiuses of the fuzzy membership functions are optimized; otherwise, the input weights and hidden biases are still preset randomly in this algorithm.  
The function approximation problem of Autompg and the classification problem of the Iris data sets are used for comparing the generalization performance of the two algorithms. The number of hidden neurons in the LC-PSO-ELM algorithm is the same as or less than that in the ELC-ELM  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Algorithms**} & \multicolumn{6}{c}{**Diabetes**} & \multicolumn{6}{c}{**Satimage**} \\ \cline{2-10}  & **Training time (s)** & **Testing time (s)** & **Training accuracy** & **Testing time (s)** & **Training time (s)** & **Testing time (s)** & **Training accuracy** & **Testing Accuracy** \\  & **STD** & **STD** & **STD** & **STD** & **STD** & **STD** & **STD** \\ \hline \multirow{3}{*}{ELM} & 0.0234 & 0.0125 & 0.8004 & 0.7835 & 0.0187 & 0.0047 & 0.8299 & 0.8248 \\  & 0.0305 & 0.0263 & 0.0075 & 0.0153 & 0.0242 & 0.0148 & 0.0071 & 0.0064 \\ \hline \multirow{3}{*}{LC-ELM} & 0.0125 & 0.0062 & 0.7933 & 0.7779 & 0.0154 & 0.0234 & 0.8307 & 0.8238 \\  & 0.0230 & 0.0197 & 0.0079 & 0.0117 & \(\begin{array}{c}4.9453\times\\ 10^{-4}\end{array}\) & 0.0247 & 0.0082 & 0.0081 \\ \hline \multirow{3}{*}{PSO-ELM} & 114.5703 & 0.0109 & 0.7937 & 0.7912 & 384.5331 & 0.0094 & 0.8513 & 0.8522 \\  & 4.8491 & 0.0345 & 0.0118 & **0.0103** & 9.3345 & 0.0296 & 0.0035 & **0.0041** \\ \hline \multirow{3}{*}{LC-PSO-ELM} & 299.1179 & 0.0250 & 0.7966 & **0.7918** & \(\begin{array}{c}3.9371\times\\ 10^{3}\end{array}\) & 0.3401 & 0.8583 & **0.8685** \\  & 0.6804 & 0.0168 & 0.0171 & 0.0198 & 42.8024 & 0.0161 & 0.0032 & 0.0062 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Performance comparison of different algorithms on classification problems of Diabetes and Satimage.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Algorithms**} & \multicolumn{6}{c}{**Autompg**} & \multicolumn{3}{c}{**Iris**} \\ \cline{2-9}  & **Training Time (s)** & **Training Error** & **Testing Error** & **Number Hidden Neurons** & **Training Time (s)** & **Training Accuracy** & **Testing Accuracy** & **Number of Hidden Neurons** \\ \hline \multirow{3}{*}{ELC-ELM} & \multirow{3}{*}{37.1688} & 0.0805 & 0.0769 & \multirow{3}{*}{15} & \multirow{3}{*}{11.8374} & 97.40 & 97.20 & \multirow{3}{*}{15} \\  & & 0.0059 & 0.0048 & & & 0.52 & 2.70 & \\ \hline \multirow{3}{*}{LC-PSO-ELM} & \multirow{3}{*}{191.3243} & 0.0681 & **0.0696** & \multirow{3}{*}{15} & \multirow{3}{*}{126.8756} & **0.9882** & **0.9860** & \multirow{3}{*}{10} \\  & & 0.0035 & **0.0049** & & & **0.0060** & **0.0150** & \\ \hline \hline \end{tabular}
\end{table}
Table 9: Performance comparison of the ELC-ELM and LC-PSO-ELM algorithms.  
algorithm. As can be seen from Table 9 (the data of simulation results in the ELC-ELM algorithm came from reference [12]), compared with the ELC-ELM algorithm, although the learning speed of the LC-PSO-ELM is slower than the ELC-ELM, the generalization performance of the LC-PSO-ELM algorithm for optimizing four parameter values is better than the ELC-ELM algorithm for optimizing two parameter values.