## 3 Influencing Factors and Data Preprocessing
### Correlations among Input Features and Output  
Pearson correlation coefficient (PCC) was used to analyze the correlation degree of coal seam mining conditions and parameters to the height of WFFZ. The Pearson correlation coefficient is defined as follows:  
\[\rho_{X,Y}=\frac{\text{cov}(X,Y)}{\sigma_{X}\sigma_{Y}} \tag{2}\]  
where \(\rho_{X,Y}\) is the Pearson correlation coefficient, \(\text{cov}(\text{X},\text{Y})\) is the covariance of variables X and Y, \(\sigma_{X}\) and \(\sigma_{Y}\) are the standard deviation of variables X and Y, respectively. The range of \(\rho_{X,Y}\) is between \(-1\) and \(1\), when the value is \(1\), it denotes that there is a wholly positive correlation between the two random variables; when the value is \(-1\), it indicates a fully negative correlation between the two random variables; when the value is \(0\), it implies linear independence between the two random variables. The greater the absolute value of the correlation coefficient between the two random variables, the stronger the linear correlation between the variables. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Panel**} & \multicolumn{8}{c}{**Measured Value**} & \multicolumn{8}{c}{**Normalized Value**} \\ \cline{2-13}  & **I\({}_{\text{m}}\)** & **I\({}_{\text{r}}\)** & **I\({}_{\text{h}}\) (m)** & **I\({}_{\text{d}}\) (m)** & **I\({}_{\text{l}}\) (m)** & **I\({}_{\text{m}}\)** & **I\({}_{\text{r}}\)** & **I\({}_{\text{h}}\)** & **I\({}_{\text{d}}\)** & **I\({}_{\text{l}}\)** & **I\({}_{\text{a}}\)** \\ \hline Hulusu 21102 & ZC 1 & 1.53 & 2.85 & 634.8 & 320 & 45.6 & 0 & 0.04 & 0.01 & 0.87 & 0.85 & 0.00 \\ Hongqinghe 31101 & ZC & 2.82 & 6.5 & 669 & 240 & 106.1 & 0 & 0.65 & 0.51 & 0.95 & 0.56 & 0.30 \\ Nalinhe mine \#2 & ZC & 2.93 & 5.5 & 580 & 247 & 103.23 & 0 & 0.70 & 0.37 & 0.75 & 0.58 & 0.29 \\ Hangliawan 30101 & ZC & 3.13 & 4.8 & 248 & 300 & 122.02 & 0 & 0.80 & 0.28 & 0.00 & 0.78 & 0.38 \\ Tingnan mine 107 & ZF 2 & 1.45 & 9.9 & 650 & 116 & 165.83 & 1 & 0.00 & 0.97 & 0.91 & 0.10 & 0.60 \\ Xiaqou mine 2801 & ZF & 1.45 & 9.9 & 332 & 90 & 149 & 1 & 0.00 & 0.97 & 0.19 & 0.00 & 0.52 \\ Caojitan 122106 & ZC & 3.13 & 6.0 & 280 & 360 & 136.10 & 0 & 0.80 & 0.44 & 0.07 & 1.00 & 0.45 \\ Hueshizui mine \#712 & ZF & 1.45 & 10 & 628.16 & 200 & 220 & 1 & 0.00 & 0.99 & 0.86 & 0.41 & 0.87 \\ Dafosi 40106 & ZF & 1.45 & 9.1 & 450 & 180 & 245.51 & 1 & 0.00 & 0.86 & 0.45 & 0.33 & 1.00 \\ Huijahe 401101 & ZF & 1.45 & 10.1 & 644.52 & 180 & 225.43 & 1 & 0.00 & 1.00 & 0.89 & 0.33 & 0.90 \\ Yushuwan 20104 & ZC & 3.13 & 5 & 280 & 255 & 138.40 & 0 & 0.80 & 0.31 & 0.07 & 0.61 & 0.46 \\ Jinjitan 12\(-\)2, upper 101 & ZC & 3.13 & 5.0 & 260 & 300 & 120.25 & 0 & 0.80 & 0.31 & 0.03 & 0.78 & 0.37 \\ Lingxin mine L331 & ZC & 3.56 & 2.75 & 250 & 280 & 57.35 & 0 & 1.00 & 0.00 & 0.00 & 0.70 & 0.06 \\ Hongliu mine 1121 & ZC & 3.56 & 5.3 & 330 & 302 & 62.5 & 0 & 1.00 & 0.35 & 0.18 & 0.79 & 0.08 \\ Menkeqing 11-3102 & ZC & 1.53 & 4.75 & 692 & 300 & 117 & 0 & 0.04 & 0.27 & 1.00 & 0.78 & 0.36 \\ Muduchaideng mine, coal seam 3-1 & ZC & 1.53 & 4.8 & 685 & 250 & 106 & 0 & 0.04 & 0.28 & 0.98 & 0.59 & 0.30 \\ Jinfeng mine 011802 & ZC & 3.56 & 4.6 & 500 & 280 & 63.12 & 0 & 1.00 & 0.25 & 0.57 & 0.70 & 0.09 \\ Shilawusu mine 221, upper 06A & ZF & 1.53 & 9.5 & 660 & 300 & 240 & 1 & 0.04 & 0.92 & 0.93 & 0.78 & 0.97 \\ \hline \hline \end{tabular}  
* 1 ZC denotes fully mechanized mining. 2 ZF denotes fully-mechanized top coal caving.  
\end{table} 
Table 1: Measured values and normalized values of the heights of the WFFZ. Figure 2 is a distribution diagram of the Pearson correlation coefficient analysis results of input features and output. As shown in Figure 2, mining method, mining height, and buried depth are positively correlated with the height of WFFZ, and the ratio of the thickness of hard rock layers and soft rock layers in the bedrock and working face length are negatively correlated with the height of WFFZ.