## 2 Modeling of a Multi-Dimensional Evaluation Indicator System
### Methodology for Screening Key Evaluation Indicators  
A landslide is a very complex nonlinear process. Owing to the multitude of indicators influencing slope stability and the presence of certain correlations among these indicators, if they are directly substituted into the model for risk assessment, they may lead to issues, such as model complexity, a slowed model running rate, model overfitting, and other problems, which would negatively impact the assessment results [19]. Therefore, it is necessary to analyze the evaluation indicator system and eliminate evaluation indicators with high redundancy, small differentiation, and low influence on slope landslides. Instead, select indicators with strong generalization, high information content, and significant influence on slope stability are used as key landslide risk assessment evaluation indicators. Since S1-S19 are the \"causes\" of landslides and S20 is the \"result\" of landslides, which is the direct criterion for whether a landslide occurs, S20 is not involved in the analysis and screening process. Instead, it is directly used as one of the final key evaluation indicators. To enhance the universality and professionalism of subsequent slope landslide risk assessment work, we obtained 1200 sets of hydropower station reservoir area slope assessment indicator system data from the Melbourne Kaggle ([[https://www.kaggle.com/](https://www.kaggle.com/)]([https://www.kaggle.com/](https://www.kaggle.com/)), accessed on 28 April 2024) data-mining website, including 300 sets each for attention level, warning level, alert level, and alarm level slope data. Firstly, we employed the Pearson correlation coefficient method to measure the degree of correlation between two different indicators, \(S_{X}\) and \(S_{Y}\); the formula is as follows:  
\[\rho_{S_{X},S_{Y}}=\frac{cov(S_{X},S_{Y})}{\sigma_{S_{X}}\sigma_{S_{Y}}}=\frac {E(S_{X}S_{Y})-E(S_{X})E(S_{Y})}{\sqrt{E(S_{X}^{2})-E^{2}(S_{X})}\sqrt{E(S_{ Y}^{2})-E^{2}(S_{Y})}} \tag{1}\]  
According to the correlation judgment rule proposed in [19], when the absolute value of Pearson's correlation coefficient is less than 0.2, it indicates no obvious correlation between the two indicators. When the absolute value is more than 0.7, it indicates a strong correlation between the indicators. The final evaluation indicator correlation coefficient is calculated to obtain the results shown in Figure 2, where blue represents positive correlation and red represents negative correlation. The larger the color block, the higher the correlation coefficient. Figure 2: Heat map of the correlation coefficients. The graphical results show that the correlation coefficients between the terrain morphology indicators, reservoir water levels, and other indicators are generally low. The correlation coefficient between the slope, S2, and elevation, S4, is 0.46, indicating some relevance. The correlation coefficient between humidity (S5) and S7, S8, and S9 in the meteorological category of indicators is greater than 0.5, showing a moderate degree of correlation. Three-day cumulative precipitation S8 is strongly correlated with S9, S14, S16, S17, and S18, and five-day cumulative precipitation, S9, is strongly correlated with S8, S13, S16, S17, and S18. The correlation coefficient between the NDVI, S11, and the NDWI, S12, in the ecological environment category is 0.88, showing a strong correlation, while the correlation coefficients between S9, S12, S16, S17, and S18 are close to 0.5. The correlation coefficients of soil bulk density, S13, and soil moisture content, S16; the angle of internal soil friction, S14, and soil shear strength, S15; the Topographic Wetness Index, S18; and S16 and S17 in the soil condition category are close to 0.9, which is a very strong correlation. To determine the indicators that have a greater impact on landslide occurrences on slopes, the gray relational analysis (GRA) was used to determine the impact weight of each assessed indicator on landslides on slopes [20].