# The Debris Flow Risk Prediction Model Based on PCA-Elman
## 3 Data Analysis and Processing
### Data Processing  
The analysis indicates that there is a strong correlation among the debris flow assessment indicators. Consequently, the PCA function in IBM SPSS Statistics 29 software is utilized to perform dimensionality reduction on the data, thereby eliminating the inter-correlation among the indicators. Based on the eigenvalues of the correlation coefficient matrix, the contribution rate and cumulative contribution rate of each principal component are calculated to determine the number of principal components, as shown in (Table 2). The eigenvalue of the first principal component (F1) is 4.760, with a variance contribution rate of 47.599%; the second principal component (F2) has an eigenvalue of 1.703, contributing 17.034% to the variance; the third principal component (F3) has an eigenvalue of 1.115, accounting for 11.155% of the variance; and the fourth principal component (F4) has an eigenvalue of 1.0001, contributing 10.011% to the variance. The eigenvalues of the fifth to tenth principal components (F5, F6, F7, F8, F9, and F10) are all less than one, and their variance contribution rates are relatively low. In principal component analysis, it is generally accepted that principal components with a cumulative contribution rate greater than 85% can effectively represent the valid information contained in the original set of assessment indicators [24]. The eigenvalues of the first four principal components (F1, F2, F3, and F4) are not only greater than one, but their cumulative variance contribution rate also reaches 85.800%, which is greater than 85%. Therefore, this study ultimately employs the first four principal components (F1, F2, F3, and F4) to replace the original ten assessment indicators (S1-S10). The loading values of each assessment indicator on the principal components, as shown in (Table 3), reveal that the maximum single discharge of debris flow (S1) and the frequency of debris flow occurrence (S2) have significant loadings on the first principal component (F1), indicating that F1 reflects the impact of debris flow scale on debris flow hazard; the watershed area (S3), main channel length (S4), maximum relative height difference in the watershed (S5), watershed incision density (S6), and vegetation coverage density (S7) have significant loadings on the second principal component (F2), indicating that F2 reflects the impact of topography on debris flow hazard; the loose solid material reserves (S8) and maximum 24 h rainfall (S9) have significant loadings on the third principal component (F3), indicating that F3 reflects the impact of material source conditions and rainfall on debris flow hazard; the watershed population density (S10) has a significant loading on the fourth principal component (F4), indicating that F4 reflects the impact of human activities on debris flow hazard. This aligns with the qualitative analysis of the aforementioned selection of assessment \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Components**} & \multicolumn{3}{c}{**Initial Eigenvalues**} & \multicolumn{3}{c}{**Extracted Principal Components**} \\ \cline{2-7}  & **Eigenvalues** & \begin{tabular}{c} **Contribution** \\ **Rate (\%)** \\ \end{tabular} & \begin{tabular}{c} **Cumulative** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Eigenvalues** \\ **(\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Contribution** \\ **Rate (\%)** \\ \end{tabular} &
\begin{tabular}{c} **Cumulative** \\ **(\%)** \\ \end{tabular} \\ \hline F1 & 4.760 & 47.599 & 47.599 & 4.760 & 47.599 & 47.599 \\ F2 & 1.703 & 17.034 & 64.634 & 1.703 & 17.034 & 64.634 \\ F3 & 1.115 & 11.155 & 75.789 & 1.115 & 11.155 & 75.789 \\ F4 & 1.001 & 10.011 & 85.800 & 1.001 & 10.011 & 85.800 \\ F5 & 0.540 & 5.403 & 91.203 & 1 & & \\ F6 & 0.353 & 3.532 & 94.735 & 1 & & \\ F7 & 0.272 & 2.725 & 97.459 & 1 & & \\ F8 & 0.135 & 1.346 & 98.806 & 1 & & \\ F9 & 0.090 & 0.904 & 99.710 & 1 & & \\ F10 & 0.029 & 0.290 & 100.00 & 1 & & \\ \hline \hline \end{tabular}
\end{table}