## Example Analysis
### Model Analysis
#### 6.2.2 Operation of the Model  
To test the performance of the EN-GMDH short-term load prediction model, a small amount of data is input into the model and analyzed in detail. According to the network expansion rule of EN-GMDH, when a layer of \(w_{\text{min}}\) is no longer reduced, the network will not be expanded. By calculation, the \(w_{\text{min}}\) of the second layer of the model network is greater than that of the first layer of the network, indicating that the prediction error is no longer reduced and that the network stops expanding. A two-layer GMDH network model was obtained. The model-related parameters are shown below. Figure 4: Spearman correlation analysis coefficient \(\rho\). The parameter \(\alpha\) in elastic net traverses the values in the range of \((0,1]\). Each neuron in each layer of the network requires an optimal \(\alpha\) for the weight balance of lasso and ridge regression in Equation (10). The \(\alpha\) can be assigned in two ways. One is to assign \(\alpha\) directly to the empirical value. This method has a small amount of computation, however it is easy to expand the error and requires existing experience as a reference. Another method is to take a value for \(\alpha\) traversal and select according to the minimum MSE of the predicted results. This method has a large amount of computation but small error, which is employed in this paper. In the model, the first layer and the second layer of the network each produce 45 optimal \(\alpha\). The selected \(\alpha\) value of the first layer of network neurons is shown in Figure 5a, and the selected \(\alpha\) value of the second layer of network neurons is shown in Figure 5b. \(\alpha=1\) denotes that Equation (10) is lasso regression, and \(\alpha\)\(\rightarrow\)0 denotes that Equation (10) is a ridge regression. The value of \(\alpha\) is between 0 and 1 denotes that Equation (10) is elastic net. Through each \(\alpha\) in this picture, you can see the characteristics of the data. \(\alpha\) is close to 1, which indicates that there is a heavy overfitting of data. At this time, elastic net produces sparseness through the L1 norm penalty to avoid large error. \(\alpha\) is close to 0, indicating that there is a heavy multicollinearity phenomenon in the data. At this time, elastic net can guarantee the stability and accuracy of the model through the L2 norm penalty compression regression coefficient. It can be seen from Figure 5 that the point where \(\alpha\) is less than 0.5 accounts for the majority, indicating that the data has significant multicollinearity. The process of \(\alpha\) change is the presentation of multicollinearity and overfitting problem solved by EN-GMDH. After estimating the coefficients of the K-G polynomial by elastic net, the polynomial coefficients of the model output are as shown in Table 2.  
The 45 neurons in each layer of the network need to be taken into the external criterion of Equation (4) to calculate their \(w\) to judge the performance of each neuron. The \(w\) values of neurons in the first layer and second layer of the network are shown in Figure 6. \begin{table}
\begin{tabular}{c c|c c} \hline \hline
**Coefficient Name** & **Value** & **Coefficient Name** & **Value** \\ \hline \(a_{0}\) & 49.19759 & \(a_{3}\) & 0.00003 \\ \(a_{1}\) & 0.48066 & \(a_{4}\) & \(-\)0.01520 \\ \(a_{2}\) & 1.84231 & \(a_{5}\) & \(-\)0.00775 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Kolmogorov-Gabor (K–G) polynomial coefficients. Figure 5: Weighting factor \(\alpha\) of each neuron. (**a**) represents the selected \(\alpha\) value of the first layer of network neurons and (**b**) represents the selected \(\alpha\) value of the second layer of network neurons. As shown in Figure 6, the blue line represents the \(w\) calculated by Equation (4) of the neurons in the first layer of the network. The brown line represents the \(w\) of the second-layer neurons of the network. The input of the first layer of the network contains all the characteristic variables.