## 3 Data and Methods
### Methodology
#### 3.2.2 Estimation of Change Detection Threshold, \(f_{t}\)  
Data Preparation and Splitting  
Three supervised machine learning algorithms, namely, SVM, RF, and KNN, were employed for the determination of the change detection threshold \(f_{t}\). The models classified flood extents based on radar backscatter characteristics and were trained using field data and simulated flood extent layers for the recent cyclone and rainfall events. The flood point and non-flood point dataset from the study area (Figure 3) was split evenly, allocating 50% for training and 50% for testing. Class Imbalance Analysis and Bias Mitigation  
Prior to model training, class imbalance was assessed and addressed to reduce potential bias due to the unequal distribution of flooded and non-flooded samples. To measure the class imbalance, the imbalance ratio (\(IR\)) [58] was calculated using Equation (1). \[IR=\frac{n_{majority}}{n_{minority}}=\frac{n_{funded}}{n_{non-funded}} \tag{1}\]  
where \(n_{majority}\) and \(n_{minority}\) denote the number of samples in the majority (flooded) and minority (non-flooded) classes, respectively. Stratified sampling [59] was then applied during the train-test split to ensure that class proportions remained consistent across subsets. The class proportion in the training  
Figure 3: Location of flood and non-flood points derived from the study area. Figure 2: Methodology for SAR image analysis. set \(P_{train}(c_{i})\) was aligned with the original dataset distribution \(P_{original}(c_{i})\), as defined in Equation (2):  
\[P_{train}(c_{i})=P_{original}(c_{i}) \tag{2}\]  
where \(c_{i}\) represents the class label. Additionally, class weights were computed and incorporated into the RF and SVM models using a balanced weighting scheme [60]. This gave more influence on the minority class during training, thereby helping to mitigate classification bias. Class weights \(w_{i}\) were computed using Equation (3):  
\[w_{i}=\frac{n_{total}}{n_{class}\times n_{i}} \tag{3}\]  
where \(w_{i}\) is the weight assigned to class \(i\), \(n_{total}\) is the total number of samples, \(n_{classes}\) is the number of classes (2 for binary classification in our case), and \(n_{i}\) is the number of samples in class \(i\). Model Configuration and Hyperparameter Tuning  
Model configurations were tailored for each algorithm. The RF model used 100 estimators with a maximum depth of 15, along with class weighting to address class imbalance, enabling it to capture moderately complex, non-linear interactions. The SVM model employed a polynomial kernel of degree 3 with balanced class weights to effectively model non-linear decision boundaries. Meanwhile, the KNN classifier was implemented using the Euclidean distance metric (Minkowski distance with \(p\) = 2) and a neighborhood size of \(k\) = 5. Each model underwent hyperparameter tuning via cross-validation to optimize classification accuracy. Feature Importance in Machine Learning Models  
Feature importance (\(Importance_{f}\)) analysis varied by model type. For the RF model [61], feature importance was calculated using the mean decrease in impurity (MDI) method, which measures the average Gini impurity reduction achieved when a feature is used to split nodes across all decision trees and was calculated using Equation (4). \[Importance_{f}=\frac{1}{N}\sum\limits_{t=1}^{N}\sum\limits_{s\in S_{f}}\frac{ \Delta Impurity_{s,t}}{\Delta Impurity_{root}} \tag{4}\]  
where:  
o \(\Delta Impurity_{s,t}\) is the reduction in impurity (e.g., Gini) at split \(s\) for tree \(t\)  
o \(S_{f}\) represents the set of splits in which the feature \(f\) was used  
o \(N\) is the number of trees in the random forest  
o \(\Delta Impurity_{root}\) is the total impurity at the root node  
In the case of the SVM (with a linear kernel for interpretability) [62; 63], the importance of each feature was proportional to the absolute value of its corresponding weight in the hyperplane equation. The SVM optimization formulation is presented in Equation (5).