## 3 Results and Discussion
### Model Validation Using ROC Curve
#### 3.5.2 Model Performance Across Spatial Clusters  
To evaluate spatial generalizability, we applied a Leave-One-Cluster-Out (LOCO) cross-validation scheme by dividing the study area into three distinct clusters (1, 2, and 3), as shown in Figure 14a. Each cluster served as an independent test fold, while the remaining two were used for training. This spatially independent validation simulated realistic deployment scenarios, where predictions had to be made in previously unseen and geologically distinct regions. The performance of three classifiers, LR, RF, and XGBoost,  
Figure 13: ROC curves for 10-fold cross-validation using X and Y coordinate-based random partitioning. The colored lines represent the average ROC for each model, the shaded lines show individual fold performance, and the dashed inclined line indicates an AUC value of 0.5. The embedded boxplot displays the AUC score distribution across folds.  
was evaluated using two key metrics: the Area Under the Receiver Operating Characteristic Curve (ROC AUC) and the Area Under the Precision-Recall Curve (PR AUC). The results are summarized in Supplementary Table S3, while fold-wise and mean ROC curves are presented in Figure 14b.  
In Fold 1, LR exhibited the weakest performance (ROC AUC = 0.670, PR AUC = 0.735), highlighting its limitations in capturing non-linear spatial patterns. In contrast, RF and XGBoost performed substantially better, with RF achieving an ROC AUC of 0.833 and a PR AUC of 0.864 and XGBoost reaching an ROC AUC of 0.804 and a PR AUC of 0.851. For Fold 2, all models improved. LR achieved an RO AUC = 0.869, while RF and XGBoost reached ROC AUC values of 0.920 and 0.926, respectively. Their PRAUC scores (RF = 0.900, XGBoost = 0.905) also underscore their superiority in predicting landslide-prone zones. In Fold 3, all models maintained relatively high performance. LR recorded an ROC AUC = 0.892 and a PR AUC = 0.836, while RF and XGBoost showed consistent accuracy with ROC AUCs of 0.906 and 0.905 and PR AUCs of 0.863 and 0.857, respectively.  
These results (Figure 14) demonstrate that tree-based models consistently outperform LR, especially under spatially independent conditions. The LOCO framework effectively highlights model robustness and minimizes the risks of overfitting due to spatial auto-correlation, making RF and XGBoost reliable tools for operational landslide susceptibility mapping. Overall, the results indicate that tree-based ensemble models (RF and XGBoost) consistently outperform linear classifiers, such as LR, across spatially distinct regions. These findings highlight the advantage of non-linear, ensemble learning methods in capturing complex spatial interactions among landslide conditioning factors. Moreover, the Leave-One-Cluster-Out spatial cross-validation approach emphasizes the importance of accounting for geographic heterogeneity during model training and validation. It mitigates the risk of spatial leakage and overfitting, which are common in random cross-validation settings, and thus provides a more realistic and conservative estimate of model performance for spatial landslide susceptibility prediction.  
Figure 14: (**a**) Spatial clusters used for Leave-One-Cluster-Out (LOCO) cross-validation within the study area. (**b**) ROC curves illustrating fold-wise and mean AUC performance of models under the LOCO scheme. Bold lines represent mean ROC curves across folds while the dashed inclined line indicates an AUC value of 0.5.