# A Study of Cellular Traffic Data Prediction by Kernel ELM with Parameter Optimization
## 4 Experiment Results and Analysis
### Study of the Prediction Using Other Regression Algorithms  
As noted in the previous section, we investigated the performance of kELM's predicted cellular traffic data under different kernel functions. As a second step, we used \(v\)-support vector regression (\(\
u\)SVR), backpropagation neural networks, and basic ELM for predicting cellular traffic data in public settings and compared the results. To study the predictive traffic data of kELM, we optimized its parameters. To make the comparison accurate, we first searched for the optimal prediction of traffic data by \(v\)SVR, BP, and ELM.  
To optimize the parameters of \(v\)SVR, we chose MFO as the search algorithm. All the variable settings were kept the same for optimization of MFO by \(v\)SVR as those for optimization of kELM parameters except for the variable boundary settings. The upper and lower boundary settings of parameters c, g, and v to be optimized were [1500, 10,001] and [0.01, 0.01], respectively. To prevent overlearning, the MAPE for the MFO test set was used as the fitness function. The MAPE curve in the optimization process is shown in Figure 6.  
In pattern recognition or machine learning, the performance of BP neural network and ELM is closely related to the nodes in the hidden layer. A small number of nodes will lead to weak model learning, increase the model training time, and even lead to overlearning, which will degrade the model performance. Therefore, the BP neural network and ELM should select the appropriate number of hidden layer nodes. In our experiment, the implementation of BP was done in a MATLAB neural network toolbox. The learning rate was set to 0.2, the maximum fail was set to 30, the hidden layer and output layer activation function selection was {'logsig','tansig'}, and other parameters were set to default.  
As the initial part of ELM weights and all the weights of the BP neural network are random, these will affect its performance, especially the BP neural network. When the initial weights are not set  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Kernel**} & \multicolumn{3}{c}{**MFO**} & \multicolumn{3}{c}{**MVO**} & \multicolumn{3}{c}{**PSO**} \\ \cline{2-10}  & **Time (s)** & **Train** & **Test** & **Time (s)** & **Train** & **Test** & **Time (s)** & **Train** & **Test** \\ \hline Gaussian & 149.49 & 9.411\% & 11.150\% & 146.18 & 9.156\% & 11.236\% & 148.91 & 9.767\% & 11.193\% \\ Linear & 97.69 & 15.449\% & 15.234\% & 96.86 & 15.448\% & 15.236\% & 96.43 & 15.477\% & 15.293\% \\ Polynomial & 227.67 & 9.938\% & 11.611\% & 235.40 & 9.909\% & 11.495\% & 255.35 & 9.739\% & 11.496\% \\ Sigmoid & 223.80 & 11.928\% & 11.715\% & 224.17 & 11.379\% & 11.650\% & 195.61 & 11.692\% & 12.123\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of optimizing the kELM by different search algorithms.  
hidden layer nodes was greater than 100. Therefore, the hidden layer node value of ELM was 100. In Figure 7, the average error of the BP training set decreased with the increase in hidden layer nodes. When the number of nodes was greater than 30, the error of the test set increased with the increase in nodes, showing that the model had a learning phenomenon. In conclusion, when predicting cellular flow data, the hidden layer node of BP should be set to 30.  
From Figures 7 and 8, we can also see that the consumption time of ELM had an approximately linear relationship with the number of hidden nodes. In contrast, for BP, there was an exponential relationship, and the training time of BP was much longer than that of ELM.