# The Debris Flow Risk Prediction Model Based on PCA-Elman
## 2 Materials and Methods
### PCA-Elman Model  
When constructing the PCA-Elman model, the process begins by selecting appropriate debris flow risk assessment indicators based on the actual conditions of the study area and the characteristics of the sample data. Next, Pearson's correlation coefficient is utilized to perform a correlation analysis on the sample data to clarify the interrelations among the assessment indicators. Subsequently, PCA is employed within IBM SPSS Statistics 29 software to dimensionally reduce the original sample data, extracting composite indicators and eliminating the correlations between the original indicators. Finally, within the Elman program code in MATLAB (R2023a) software, the composite indicators are set as input nodes, and the debris flow risk levels are set as output nodes. After several iterations of parameter optimization, the optimal number of iterations and the learning rate are determined, thereby establishing the PCA-Elman model.  
When operating the model, traditional debris flow datasets are simply divided into training and prediction sets according to a fixed ratio, which fails to fully utilize the available data and results in predictions with certain limitations. In contrast, cross-validation can assess the model's fit to the debris flow data by averaging multiple predictions of debris flow risk derived from the same dataset, thereby better reflecting the model's performance quality [18]. Therefore, this model employs cross-validation to partition the training and prediction sets. Taking this study as an example, the principal components F1, F2, F3, and F4 are used asinput variables for the model, while the debris flow risk levels 1, 2, and 3 (low, moderate, high) are used as output results: hence, the neural network has 4 input nodes and 1 output node. Considering the model's runtime and bias, a 5-fold cross-validation method is selected to extract training and testing samples, dividing 37 debris flow samples into 5 subsets, with 3 subsets containing 7 samples each and 2 subsets containing 8 samples each. Sequentially, one subset is chosen as the prediction sample, and the other four subsets serve as training samples for model training and prediction. This experiment is repeated 4 more times, and the model's accuracy is determined by averaging the accuracy of the 5 predictions.  
Once the model has been executed, the performance can be evaluated using the areas under the ROC curve (AUC value) and the PR curve (AP value). The ROC curve is a method for assessing the performance of predictive models based on true-positive rates and false-positive rates, known for its intuitiveness and robustness. The PR curve, on the other hand, evaluates the classification performance of a model using recall as the horizontal axis and precision as the vertical axis. Particularly in cases of unbalanced sample data, the PR curve more accurately reflects the model's ability to identify positive-class samples. The AUC and AP values largely indicate the quality of the model's performance, and the closer these values are to 1, the better the model performs [19; 20]. The specific process of the model is shown in (Figure 3), which illustrates the complete steps from data preprocessing to model establishment, validation, and evaluation. It demonstrates the systematic and scientific nature of the PCA-Elman model in predicting debris flow risks, providing a new methodological approach for efficient modeling of complex nonlinear relationships.  
Figure 3: PCA-Elman debris flow risk prediction model calculation process diagram.