## 4 Algorithm Analysis
### Feature Selection  
The correlation between input features is visualized using the Pearson correlation coefficient [46]. The correlation is expressed as a coefficient in the range of \([-1,1]\), where a coefficient closer to 1 indicates a stronger positive correlation. The calculation formula is as follows:  
\[r\ =\ \frac{\sum_{j=1}^{n}\left(x_{j}-\overline{x}\right)\left(y_{j}-\overline{y }\right)}{\sqrt{\sum_{j=1}^{n}\left(x_{j}-\overline{x}\right)^{2}}\sqrt{\sum_{j =1}^{n}\left(y_{j}-\overline{y}\right)^{2}}} \tag{13}\]  
In the formula, \(r\) represents the Pearson correlation coefficient, \(x\) and \(y\) represent the sample features, and \(n\) represents the sample size. The heatmap is shown as in Figure 3.  
From the figure, it is evident that main roof types are strongly positively correlated with the initial step distance of main roof pressure; immediate roof types are strongly positively correlated with the rock thickness coefficient and exhibit a strong negative correlation with the shearer slope cutting entry length; coal seam thickness is strongly positively correlated with the average mining height and the hydraulic support center distance. Due to the highly nonlinear relationships between coal burial depth and immediate roof thickness with factors such as sediment sources, water flow and weathering, and stratum uplift and subsidence, this paper does not focus on these complex geological features. Consequently, their linear correlations with other input features are weak. A linear correlation analysis was conducted among the input features to explore the relationship between geologic parameters and fully mechanized mining face conditions. By retaining geologic parameters and removing mining face condition parameters that exhibited strong correlations with them, the number of input features was optimized. As a result, the following features were removed: Initial step distance of main roof pressure, Rock thickness coefficient, Shearer slope cutting entry length, Average mining height, and Hydraulic support center distance, leaving a total of 21 features. Figure 2: Some of the feature box line plots. The features were transformed using Min-Max normalization, ensuring that the dataset operates on the same scale, which accelerates model training. \(x_{j}^{\prime}\) represents the normalized data, \(x_{j}\) is the original feature value, \(MIN(X)\) is the minimum value of the feature dataset, and \(MAX(X)\) is the maximum value. The formula is as follows:  
\[x_{j}^{\prime}\ =\ \frac{x_{j}-MIN(X)}{MAX(X)-MIN(X)} \tag{14}\]  
Since the Pearson coefficient heatmap reflects the linear relationships between feature data, the RF algorithm is employed to further identify nonlinear relationships within the data [47; 48]. The importance of each input feature is evaluated by calculating its contribution to the prediction of the out-of-bag (OOB) [49] data, which refers to the data not included in the decision tree's sampling process in RF. Based on the importance scores, feature selection is conducted by ranking the features accordingly. The training set is randomly selected from the sample data, and for each decision tree, the corresponding OOB data are used to make predictions. The error between the predicted and actual values is then calculated, representing the initial OOB prediction value [50]. The formula is as follows:  
\[F_{0}\ =\ \frac{1}{n}\sum_{j}^{n}(y_{j}-\hat{y}_{j})^{2} \tag{15}\]  
In the formula, \(F_{0}\) represents the initial OOB error. \(n\) is the number of data samples, \(y_{j}\) is the true value for each data point, and \(\hat{y}_{j}\) is the OOB predicted value. Figure 3: Pearson correlation coefficient among features. The process involves randomly selecting a feature from the non-OOB data and replacing it with the OOB value, followed by recalculating the OOB prediction.