# The Debris Flow Risk Prediction Model Based on PCA-Elman
## 3 Data Analysis and Processing
### Data Analysis
Initially, the Box-Cox transformation method is used to approximate the normal distribution of the evaluation indicators, followed by the application of Pearson's correlation coefficient for correlation analysis, with the results depicted in Figure 5. Figure 5 presents the correlation matrix of the debris flow hazard assessment indicators in Yunnan Province, revealing the linear relationships between various indicators through scatter plots and a correlation coefficient matrix. In the figure, the diagonal represents the distribution histograms of the original evaluation indicators, the lower left corner displays scatter plots between two indicators, and the upper right corner shows the correlation coefficients between the two indicators. In the scatter plots, each point represents the distribution of data points between two evaluation indicators; a close alignment of points along a straight line indicates a strong linear relationship, while the dispersion of points reflects the strength of the correlation. Additionally, scatter plots effectively identify outliers, which are isolated points that significantly deviate from other data points. The correlation coefficient matrix quantifies these trends numerically, providing an accurate measure of the correlation between two evaluation indicators. According to the correlation level criteria in Table 1, the closer the absolute value of the correlation coefficient is to one, the stronger the correlation; the closer to zero, the weaker the correlation. Observations from the scatter plots in Figure 5 reveal that the majority of the indicators exhibit a positive correlation trend, where an increase in one indicator is often accompanied by an increase in another, manifesting in the scatter plots as a trend from the lower left to the upper right. Moreover, the distribution of the scatter plots is relatively uniform without any apparent outliers, indicating high data quality and no extreme values adversely affecting the analysis results. In the correlation coefficient matrix located at the upper right, the correlations between S3 and S4, S1 and S7, S3 and S5, and S6 and S7 are rated as extremely strong, with correlation coefficient absolute values as high as 0.9, 0.86, 0.84, and 0.81, respectively. These high values suggest significant linear relationships between these indicators. This strong correlation may indicate a common role or interdependence among these indicators in the mechanism of debris flow formation. Apart from these extremely correlated indicator pairs, the correlations between other pairs of indicators, while not as significant as the aforementioned, still show a moderate degree of correlation, with most correlation coefficients greater than 0.4. This indicates that, aside from a few pairs, there is a certain degree of positive correlation among other indicators, which may reflect the interaction of multiple factors in the process of debris flow formation. Overall, the correlation analysis results in Figure 5 demonstrate extensive correlations among the debris flow assessment indicators. Highly correlated indicators suggest that they may provide redundant information when describing certain aspects of debris flow occurrence. For instance, the high correlation coefficients between S3 and S4, S1 and S7, S3 and S5, and S6 and S7 indicate that these indicators might be measuring similar geological or environmental characteristics. Therefore, utilizing PCA to extract key features and reduce redundancy in the dataset before constructing a predictive model is essential to avoid multicollinearity issues stemming from overlapping information among indicators. By doing so, the performance of the model can be optimized, ensuring that each selected indicator contributes unique and valuable information for predicting debris flow occurrence, thereby enhancing the model's accuracy and generalization capabilities.