## 4 Results  
### Optimization of Change Detection Threshold, \(f_{t}\)  
In this study, three machine learning algorithms--RF, SVM, and KNN--were applied to classify flood statuses and validated against observed data across a range of flood status thresholds. Among these, the threshold value of 1.025 emerged as the most significant. The RF model, which estimates feature importance through Gini impurity reduction, assigned the highest \(Importance_{f}\) score of 0.43 to this threshold. Similarly, the KNN model, evaluated based on classification accuracy using individual features, achieved its peak _Accuracy_ of 0.69 at the same threshold, while the SVM model reported a strong hyperplane coefficient of 0.70, confirming the high relevance of the 1.025 threshold. The field dataset exhibited a moderate class imbalance, with a 2.09:1 ratio between flooded (67.6%) and non-flooded (32.4%) samples, likely reflecting either actual flood prevalence or sampling constraints. To address potential bias arising from this imbalance, class weighting techniques and stratified cross-validation were applied during training, ensuring balanced model evaluation across both classes.  
Figure 4 illustrates a comparative analysis of normalized \(Importance_{f}\) scores, highlighting that RF and SVM effectively handled class imbalance by prioritizing critical features like the 1.025 threshold. In contrast, KNN's performance was limited by its lack of intrinsic class-balancing mechanisms, showing consistent _Accuracy_ (68.2%) across thresholds from 1.0 to 1.225 and dropping to random guessing (50%) for low-variance thresholds (\(\geq\)1.25). As a result, KNN's normalized \(Importance_{f}\) appeared binary (0 or 1), reflecting its  
inability to differentiate informative patterns under imbalance. This contrast emphasizes the superior adaptability of RF and SVM in imbalanced scenarios, as they generated nuanced importance gradients, while KNN struggled to deliver meaningful rankings under similar conditions.  
Figure 5 provides a comparative assessment of three machine learning models using four performance metrics. SVM outperformed both KNN and RF, achieving the highest _Accuracy_ (0.750), _F1_-score (0.756), _Precision_ (0.771), and _Recall_ (0.750), indicating consistent and balanced performance. KNN ranked second, while RF showed the lowest scores across all metrics. These results highlight SVM as the most effective model for this classification task.  
Figure 4: Comparative analysis of feature importance across machine learning models under class imbalance: RF, SVM, and KNN performance with normalized importance scores.  
Figure 5: Performance comparison of RF, SVM, and KNN models on threshold 1.025.  
The cross-validation results reveal different performance patterns among the three machine learning algorithms. SVM achieved the highest cross-validation accuracy (0.686 \(\pm\) 0.0555), demonstrating both superior performance and excellent stability with the lowest standard deviation. KNN showed moderate performance with cross-validation accuracy of 0.662 \(\pm\) 0.1061, while RF exhibited the lowest cross-validation accuracy (0.646 \(\pm\) 0.1670) and the highest variability in performance.  
Figure 6 shows that the SVM model achieved the highest _AUC_ (0.752), indicating that the dataset favors boundary-based separation, where support vectors effectively maximize class margins. The RF model followed closely with an _AUC_ of 0.743, suggesting limited benefit from its ability to capture complex feature interactions. KNN performed the lowest (_AUC_ 0.719), likely due to sensitivity to high-dimensional data and weak local clustering. The narrow _AUC_ range (0.719-0.752) implies moderate classification complexity, with SVM best aligning with the dataset's structure.  
The paired _t_-test and [PERSON]'s test results confirm statistically significant performance for all three machine learning models, as shown in Table 2.