## 3 Research Methods  
### Correlation of Evaluation Factors  
Based on the disaster-forming mechanisms of landslides and collapses, this study selects ten factors--slope, aspect, slope shape, terrain relief, cover layer thickness, engineering geological lithology, vegetation coverage, land use type, slope structure, and cut-slope height [19]. From four dimensions: topography and geomorphology, geological background, surface cover, and hazard characteristics (Figure 2). The high correlation between evaluation factors may affect the accuracy of the disaster-susceptibility assessment model for geological hazards, leading to factor data redundancy and subsequently reducing the model's evaluation precision. Therefore, it is necessary to conduct a correlation analysis of the factors before establishing the assessment model [20]. Factor correlation refers to using statistical methods to assess the strength of relationships between different factors to identify redundant information and improve model accuracy. Advanced correlation analysis methods, such as Pearson, Spearman, and Cramer's correlation coefficients, can more comprehensively reveal complex relationships between factors, thereby optimizing model performance and enhancing decision-making support. In this study, the Pearson correlation coefficient was employed for the correlation analysis of evaluation factors, based on a comprehensive consideration of data characteristics, methodological suitability, and research objectives. The evaluation factors involved in the study (such as slope, terrain relief, and cover thickness) are primarily continuous variables, and the Pearson correlation coefficient can directly quantify such linear associations. Although the Spearman coefficient can measure nonlinear monotonic relationships, the data were preprocessed to approximate a normal distribution (e.g., the Pearson coefficient between slope and terrain relief is 0.48, indicating a moderate linear relationship), and introducing Spearman analysis would increase redundant calculations (due to data ranking) without providing additional useful information [21]. Moreover, categorical variables (such as land use type and engineering geological lithology) were incorporated into the continuous analysis framework through numerical encoding (e.g., agricultural land = 1), and their linear independence was validated by the Pearson coefficient (e.g., the coefficient between \"land use type\" and vegetation coverage is \(-0.25\)). Since [PERSON]'s V coefficient is specifically designed for pure categorical variable analysis, it is not compatible with the research objective (verifying linear independence), and applying mixed methods would compromise the consistency of model inputs [22]. The Pearson correlation coefficient measures the strength and direction of the linear relationship between two continuous variables. It has strong data compatibility and is minimally affected by the random distribution of the original variables [23]. This approach avoids redundant analysis while ensuring methodological simplicity and efficiency, delivering reliable and comparable results that comprehensively balance data characteristics and model requirements. The correlation coefficient is usually denoted by \(r\). Given two random variables \(X\) and \(Y\), the calculation formula for \(r\) is shown in Equation (1):  
\[r=\frac{\sum_{i=1}^{n}(X_{i}-\bar{X})(Y_{i}-\bar{Y})}{\sqrt{(\sum_{i=1}^{n}(X_ {i}-\bar{X})^{2})(\sum_{i=1}^{n}(Y_{i}-\bar{Y}^{2}))}} \tag{1}\]  
In Equation (1), \(n\) represents the number of samples; \(X_{i}\) and \(Y_{i}\) are the observed values of variables \(X\) and \(Y\) at the \(i\) point, while \(\bar{X}\) and \(\bar{Y}\) represent the means of the \(X\) and \(Y\) samples, respectively. The value of the correlation coefficient \(r\) ranges from \(-1\) to \(1\), where a value of \(1\) indicates a perfect positive correlation, \(-1\) indicates a perfect negative correlation, and \(0\) indicates no correlation.