# Short-Term Power Load Forecasting Using an Improved Model Integrating GCN and Transformer
## 4 Analysis of Experimental Results
### Data Preprocessing  
Before making predictions, it is necessary to preprocess the data first, which is helpful to improve the prediction performance. The commonly used data preprocessing steps mainly include missing value filling and data normalization processing. Since the MLLA in the method proposed in this paper can only accept the input of an even number of sequences, it is also necessary to perform feature selection and dimension reduction processing on the dataset containing an odd number of sequences. Since there are no missing data in the three datasets in this study, the data preprocessing in this paper includes two steps: dimension reduction and normalization for datasets containing an odd number of sequences. In order to reduce the dimension of the data, the random forest method is adopted in this paper. The essence of the random forest method is to integrate decision trees for dimensionality reduction, calculate the correlation of data by using the out-of-bag (OOB) error, and sort and filter the sequences [38]. Specifically, a decision tree is generated first to select the input sequence and the segmentation points on the sequence. Therefore, the space containing the input sequence can be divided into two regions by the selected sequence and the segmentation points on the sequence. When the features are discrete, the two regions can be obtained by the following formula:  
\[ \begin{cases}K_{1}(s,p)=\{x_{m}|x_{m}^{s}=p\}\\ K_{2}(s,p)=\{x_{m}|x_{m}^{s}\
eq p\}\end{cases}  \tag{8}\]  
When the features are continuous, the two regions can be obtained by the following formula:  
\[ \begin{cases}K_{1}(s,p)=\{x_{m}|x_{m}^{s}\leq p\}\\ K_{2}(s,p)=\{x_{m}|x_{m}^{s}\geq p\}\end{cases}  \tag{9}\]  
In the above formulas, \(K_{1}\) and \(K_{2}\) represent the two regions obtained through division, \(s\) is the selected feature sequence, and \(p\) is the segmentation point. The operation of dividing the area is achieved through the following formula:  
\[min_{(s,p)}[min_{d_{1}}\sum_{x_{i}\in K_{1}(s,p)}(y_{i}-d_{1})^{2}+min_{d_{2}} \sum_{x_{i}\in K_{2}(s,p)}(y_{i}-d_{2})^{2}] \tag{10}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dataset** & **Prediction Target** &
\begin{tabular}{c} **Dataset Division (Training** \\ **Set:Validation Set:Test Set)** \\ \end{tabular} \\ \hline ETH1 & OT & 12,194:1742:3484 \\ \hline ETTm1 & OT & 48,776:6968:13,936 \\ \hline Australian Electricity Load & Electricity Load & 61,354:8765:17,529 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dataset description. In the formula, \(d_{1}\) and \(d_{2}\) are the predicted values of the data in the two regions. Next, the above operation is repeated for the divided areas until the value of the formula no longer continues to decrease, and then, the decision tree can be obtained. Therefore, the operation steps of feature selection by the random forest algorithm integrated from decision trees are as follows:  
1. Calculate the importance of each sequence and sort them in descending order. 2. Determine the elimination ratio each time and perform elimination based on the sequence importance calculated in step 1 to obtain a new sequence dataset. 3. Repeat the above steps for the new set until only the number of feature sequences that have been pre-imagined remains. Since both the ETTh1 and ETTm1 datasets contain an odd number of sequences, we performed dimensionality reduction selection on the exogenous variable sequences, transforming the odd-number sequence dataset into an even-number sequence dataset. The sequences obtained from the ETTh1 and ETTm1 datasets after random forest dimensionality reduction are shown in Figure 3.  
As shown in Figure 3, among the six exogenous variables in the ETTh1 dataset, we screened out the five exogenous variables that are of the highest importance for the prediction of the target sequence. Their ranking based on importance, from high to low, is HULL, MULL, LUFL, MUFL, and HUFL.