## 4 MIC-Based Feature Reconstruction
### Feature Selection and Feature Reconstruction  
Due to the composition of multiple loads, the extent to which the net load is influenced by external factors varies at different times of the day in electrical engineering. For example, the load is significantly affected by temperature factors at certain moments, while at other times, it is more correlated with historical loads. Additionally, weather factors such as temperature and irradiance have cumulative and lag effects on the load [40], which can result in different optimal feature sets influencing the load during different time periods. In this paper, a feature reconstruction method based on the MIC is employed to quantify the impact of different features on the load. By calculating the maximum information coefficient, the method ranks the features based on their influence on the current load and selects a set of feature variables with the highest impact as the input feature matrix. After feature selection, the MIC value is used as the weight of each input variable, and the input variable is reconstructed according to the weight. The reconstructed input matrix contains each characteristic variable and its weight, so as to show the influence degree of different variables in the prediction model. The proposed steps of feature selection and feature reconstruction are as follows:  
Step 1: As shown in Figure 3. Construct load sequence \(\mathbf{L}_{i}\) and feature sequence \(\mathbf{F}_{i}^{(m)}\) classified by sampling points. Extract the load values of the \(i\)-th sampling point for each day in a five-year period, and sort them in chronological order to obtain the load sequence at the corresponding time point. \[\mathbf{L}_{i}=[l_{i},l_{1,i},\ldots,l_{n,i}] \tag{8}\]  
where \(l_{n,i}\) represents the normalized load value corresponding to the \(n\)-th day and the \(i\)-th sampling point, \(i=1,2,\ldots,96\). For each feature's data that affects the load, the same operation is performed for reconstruction. By extracting the values of all the sampling points \(i\) for each date, we can obtain the values of the \(m\)-th feature sequence. \[\mathbf{F}_{i}^{(m)}=\left[f_{i}^{(m)},f_{1,j}^{(m)},\ldots,f_{n,i}^{(m)}\right] \tag{9}\]  
where \(f_{n,i}^{m}\) represents the normalized data of the \(m\)-th feature at the \(i\)-th sampling point on the \(n\)-th day. Step 2: Perform feature selection to determine the initial feature dataset. Using \(L_{i}\) as the target sequence and \(F_{i}^{(m)}\) as the candidate feature sequence, calculate the MIC (Maximal Information Coefficient) values between \(L_{i}\) and \(F_{i}^{(m)}\) F. For each feature, calculate the MIC value based on 96 sampling points. After calculating the average MIC value for each feature, sort the different features based on their average MIC values. Select the top 12 ranked feature variables to form the initial input feature set for the predictive model. This results in the initial input feature set \(F\) corresponding to the daily 96-point load. \[F= \begin{bmatrix}f_{1}^{(1)}&\ldots&f_{i}^{(1)}&\ldots&f_{96}^{(1)}\\ f_{1}^{(2)}&\ldots&f_{i}^{(2)}&\ldots&f_{96}^{(2)}\\ \vdots&&\vdots&&\vdots\\ f_{1}^{(12)}&\ldots&f_{i}^{(12)}&\ldots&f_{96}^{(12)}\end{bmatrix}  \tag{10}\]  
where \(f_{1}^{(1)}\) represents the normalized value of the first feature at the first sampling point of the day. Step 3: Reconstruct the input features based on the MIC values. The MIC improves upon the limitation of the PCC in capturing nonlinear relationships [41]. Compared to mutual information (MI), the MIC is easier to compute and provides better fairness for different types of associations [42]. Therefore, the MIC values of each variable at each sampling point are used as weights to measure the influence of each feature, forming the input weight matrix M.  
The weight value of the \(m\)-th input feature at the \(i\)-th sampling point is determined by the MIC value between that feature and the load, and it forms the weight matrix \(M\) for the input features.