## 5 Discussion  
Principal Component Analysis (PCA) is an effective multivariate statistical method used to analyze and process the structure of data and variables [25]. It transforms multiple correlated indicators into a few independent composite indicators (principal components) without losing or with minimal loss of the original information. In this study, elevation, slope angle, slope orientation, geological unit, distance to rivers, and rainfall were selected as variables for PCA by SPSS software. The results are presented in Table 1 (Variance Contribution Table) and Table 2 (Loading Coefficient Matrix). \begin{table}
\begin{tabular}{c c c c} \hline
**Principal Components** & **Eigenvalue** & **Variance Contribution Rate \%** & **Cumulative Contribution Rate \%** \\ \hline
1 & 2.139 & 35.648 & 35.648 \\
2 & 1.196 & 19.941 & 55.589 \\
3 & 0.947 & 15.782 & 771.371 \\
4 & 0.769 & 12.814 & 84.185 \\
5 & 0.656 & 10.941 & 95.126 \\
6 & 0.292 & 4.874 & 100.000 \\ \hline \end{tabular}
\end{table} 
Table 1: Variance Contribution Table of different influencing factors. Figure 10: The relationship between landslide distribution and rainfall map. Table 1 shows the number of principal components to be extracted. The eigenvalue represents the direction stretching coefficient of each principal component, the variance contribution rate indicates the percentage of original data information reflected after the stretching of the eigenvalue, and the cumulative contribution rate is the sum of these percentages, which is generally greater than 80% in practical applications. According to Table 1, the contribution rate of the first eigenvalue is 35.648%, the second is 19.941%, the third is 15.782%, and the fourth is 12.814%. The cumulative contribution rate of these four eigenvalues is 84.185%, indicating that four principal components should be extracted. Further analysis of these four principal components reveals their information extraction from the influencing factors, as shown in Table 2, with a loading coefficient standard of 0.4. From Table 2, it can be observed that elevation, rainfall, and geological unit contribute the most to Principal Component 1. Distance to rivers has the highest contribution to Principal Component 2. Slope angle contributes significantly to Principal Component 3, while slope orientation has the largest contribution to Principal Component 4. Thus, it can be concluded that all six influencing factors affect landslides in the Zhaotong area, with elevation, rainfall, and geological unit having the greatest impact. The remaining influencing factors, in order of their contribution, are distance to rivers, slope angle, and slope orientation. Based on the distance to rivers and elevation, the relationship between landslides and these two influencing factors was further analyzed. As depicted in Figure 10(a), a total of 95 landslides were recorded within a distance of 2400 m from the rivers. Within the elevation range of 0 to 1860 m, where the distance to rivers was within 400 m, the highest concentration of landslides was documented, comprising 48 occurrences, representing 50.53% of all landslides within this elevation interval. As the distance from rivers increased, there was a gradual reduction in the number of landslides, accompanied by a corresponding decrease in their proportion. This result shows a possible association between lower elevations and closer proximity to rivers with heightened landslide susceptibility. Further analysis of the relationship between slope angle and the distance to rivers was conducted. As shown in Figure 10(b), for slopes with angles <10\({}^{\circ}\) and >40\({}^{\circ}\), there were only