## 3 Establishment of Geological Hazard Risk Assessment Model
### Factor Selection  
Considering that the selection of indicators for geological hazard risk assessment should be objective and ensure the independence of each factor, it is essential to assess the correlation between the indicators to improve the model's evaluation accuracy. In this study, the Pearson correlation coefficient method [31] was used to analyze the correlations between the evaluation factors. The correlation coefficients between the factors are shown in Figure 4. The explanation is as follows. All factors form two feature sets, \(\{x_{1},x_{2},\cdots,x_{i},\cdots,x_{n}\}\) and \(\{y_{1},y_{2},\cdots,y_{i},\cdots,y_{n}\}\), with a length of \(n\). The calculation formula of the correlation coefficient r is as follows:  
Figure 3: Geological disaster evaluation factors. (**a**) Slope (Sl.); (**b**) Surface undulation (S.U.); (**c**) Aspect (As.); (**d**) Humidity (Hu.); (**e**) Distance to road (D.Ro.); (**f**) Distance to river (D.Ri.); (**g**) Distance to fault zone (D.F.Z.); (**h**) Formation lithology (F.L.); (**i**) Vegetation coverage (V.C.); (**j**) Rainfall (Ra.); (**k**) Land use type (L.U.); (**l**) Soil type (So.); (**m**) Ascending deformation (A.D.); (**n**) Descending deformation (D.D.).  
\[r=\frac{\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)\left(y_{i}-\overline{y} \right)}{\sqrt{\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)^{2}}\sqrt{\sum_{i= 1}^{n}\left(x_{i}-\overline{x}\right)^{2}}} \tag{1}\]  
where \(n\) is the sample size, \(\overline{x}\) and \(\overline{y}\) are the means of the samples within the two feature sets, and \(x_{i},y_{i}\) represent the values of the \(i\)-th sample in \(x\) and \(y\), respectively. In this study, the correlation between factors is evaluated based on the absolute value of \(r\). When \(0.8<|r|\leq 1\), the correlation between factors is considered extremely high; when \(0.6<|r|\leq 0.8\), the correlation is high; when \(0.4<|r|\leq 0.6\), the correlation is moderate; when \(0.2<|r|\leq 0.4\), the correlation is weak; and when \(|r|\leq 0.2\), the correlation between factors is considered very weak or negligible.  
The Pearson correlation coefficient method was used to quantify the correlations between different evaluation factors. When the absolute value of the correlation coefficient \(|r|\) exceeds 0.6, there is a high or very high correlation between the factors. In this study, for evaluation factors with a correlation greater than 0.6, only one factor is retained for analysis. This is because including highly correlated factors in the model can lead to collinearity, which can distort the model's calculations and reduce its accuracy. By following the correlation threshold principle, optimization and selection of strongly correlated factors are key measures to ensure the efficient and accurate operation of the model.  
As shown in Figure 4, the correlation coefficient between slope and aspect is 0.94, between land use type and soil moisture is 0.66, and between distance to the river and distance to the road is 0.61. These factors exhibit strong correlations. Based on the Pearson correlation coefficient method and the difficulty level of each factor in triggering geological hazards, this study excluded the following three factors: aspect, soil moisture, and distance to the road. Ultimately, the following 11 evaluation factors were selected for the geological hazard risk assessment: surface undulation, slope, cumulative deformation from ascending  
Figure 4: Correlation coefficients among evaluation factors.  
orbit, cumulative deformation from descending orbit, soil type, land use type, precipitation, vegetation cover, lithology, distance to fault zones, and distance to rivers.