## 4 Results  
### Hyperparameter Optimization  
Hyperparameter optimization is a crucial step in enhancing the performance of machine learning models. Default hyperparameter settings often fail to fully exploit the potential of algorithms. To ensure optimal predictive performance, the systematic tuning of hyperparameters is necessary prior to formal training [83]. Notably, while grid search was employed for its deterministic exhaustiveness, this study acknowledges the potential of the novel optimization methods proposed in [72], which adaptively explore hyperparameter spaces using probabilistic models or evolutionary strategies. These methods may offer more efficient global optimization in large datasets. However, we prioritized grid search here for its reproducibility and computational tractability. The hyperparameter search spaces were determined through a systematic integration of literature-based benchmarks, framework recommendations, pre-experimental validation, and computational feasibility. The defined ranges thus strike a balance between empirical effectiveness and practical implementation, ensuring both model performance and computational efficiency for the debris flow dataset.  
Model performance under different parameter combinations is assessed using ten-fold cross-validation, leading to the selection of optimized parameter configurations [84]. Table 3 presents the key hyperparameters and their optimal values for each classifier. Based on the selected optimal parameter combinations, all classifiers were retrained to ensure stability and a generalization capability.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Hyperparameter** & **Definition** & **Optimum** \\ \hline \multirow{4}{*}{SVM} & \multirow{4}{*}{C} & Regularization parameter that controls the trade-off & \multirow{4}{*}{10} \\  & & between achieving a low error and keeping the model & & \\  & & simple. Higher values reduce bias but may & \\  & & increase variance. & \\  & & Defines how far the influence of a single training & \multirow{4}{*}{scale} \\  & gamma & example reaches. A lower value means a larger & \\  & & influence region. & \\  & kernel & Specifies the kernel type to be used in the algorithm, & \\  & & affecting decision boundaries. & RBF \\ \hline \multirow{4}{*}{RF} & n\_estimators & The number of trees in the forest. More trees generally & \multirow{4}{*}{200} \\  & & improve performance but increase computation time. & \\  & max\_depth & The maximum depth of each decision tree. If none, & \\  & & nodes are expanded until all leaves are pure. & \\  & min\_samples\_split & The minimum number of samples required to split an & \\  & min\_samples\_leaf & internal node. Higher values prevent overfitting. & \\  & & The minimum number of samples required to be at a & \\  & & leaf node. Higher values make the model more robust. & \\ \hline XGBoost & n\_estimators & The number of boosting rounds. More rounds can & \multirow{4}{*}{100} \\  & max\_depth & improve performance but may lead to overfitting. & \\  & & Maximum depth of a tree. Larger values capture more & \\  & & patterns but increase complexity. & \\  & learning\_rate & Controls the step size in updating weights. Lower & \\  & & values lead to slower but more stable convergence. & \\  & subsample & Fraction of training samples used in each boosting & \\  & & iteration to prevent overfitting. & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Tuned hyperparameters in each classifier model.