## 2 Materials and Methods
### Landslide Susceptibility Algorithms  
In this study, LR, RF, and SVM methods were applied to the generation of the LSM, and their performances were compared with accuracy, F1 scores, recall, and ROC curves. The data-driven models used whether a landslide occurred as the dependent variable and the landslide imaging factor as the input feature (independent variables). In this way, the spatial probability of the occurrence of landslides in the area was obtained. Before calculating the LSM, this paper checked the multi-collinearity and the correlation among the influencing factors. In many studies, tolerance levels (TOL) and variance inflation factors (VIF) were utilized to examine variables [64]. According to Formula (2), the VIF and TOL were obtained by central normalization of the independent variables. The closer the VIF is to 1, the more it proves that the model-independent variables are generally free of multicollinearity, and conversely, with a VIF greater than 10, the data have severe multicollinearity. In Table 3, it can be seen that the VIF of all the factors is less than 10. In addition, we examined the correlation (Pearson index) between all factors using Formula (3). A correlation factor between factors greater than 0.75 was generally considered to indicate a linear relationship between factors [65]. These linear relationships affected the accuracy of the regression algorithm. As shown in Figure 6, the results indicate that none of the 12 factors exceeded the threshold value (>0.75). Therefore, all factors were used in the landslide susceptibility model. Combined with the factor correlation plots, it can be concluded that there is no multi-collinearity for all the landslide factors. \[VIF=\frac{1}{1-R^{2}(i)}\hskip 56.905512 ptTOL=1-R^{2}(i) \tag{2}\]  
Figure 5: A schematic diagram of the triangle of satellite and ground observations. \[r=\frac{\sum_{i=1}^{n}\left(X_{i}-\overline{X}\right)\left(Y_{i}-\overline{Y} \right)}{\sqrt{\sum_{i=1}^{n}\left(X_{i}-\overline{X}\right)^{2}}\sqrt{\sum_{i= 1}^{n}\left(Y_{i}-\overline{Y}\right)^{2}}} \tag{3}\]  
where \(X_{i}\) is the variable of landslides factors and \(R^{2}(i)\) is the complex correlation coefficient of the variable \(X_{i}\) with all other variables. Three major algorithms were selected for this paper. After the previous step of feature selection, 12 categories of landslide impact factors were applied as input variables, and landslide weights (1: landslides; 0: non-lanslides) were used as dependent variables. The algorithmic models chosen are described below. Multiple logistic regression is commonly used to assess the regression relationship between a dependent variable and several independent variables [66]. It is particularly suitable for categorical models, because it adds a suitable link function. Landslide influences were generally in a continuous or categorical form, and the maximum likelihood method was used to calculate the regression coefficients for each factor, followed by a gradient iteration to estimate the parameters, and finally we obtained a logistic multiple regression model. The probability values of landslide susceptibility were then calculated by the model \begin{table}
\begin{tabular}{c c c} \hline \hline
**Landslide Causative Factors** & **Tolerance (TOL)** & **VIF** \\ \hline rainfall & 0.1674 & 5.9713 \\ fault & 0.3113 & 3.2119 \\ river & 0.2588 & 3.8630 \\ Land use and land cover & 0.1262 & 7.9232 \\ TWI & 0.1496 & 6.6815 \\ aspect & 0.2623 & 3.8120 \\ slope & 0.1987 & 5.0327 \\ DEM & 0.15977 & 6.2618 \\ plan & 0.1748 & 5.7187 \\ NDVI & 0.14191 & 7.0452 \\ profile & 0.2388 & 4.1872 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Multi-collinearity analysis of landslide causative factors. Figure 6: Landslide factor categories and correlation for landslides. The horizontal and vertical axes indicate the landslide image factor, and the heat map indicates the magnitude of the correlation. (’Is’ indicates landslides and non-landslides). The color bar on the right indicates the correlation value (from \(-1\) to \(1\)).