# Ad-RuLer: A Novel Rule-Driven Data Synthesis Technique for Imbalanced Classification
## 4 Experiment
### Evaluation Metrics  
Handling imbalanced datasets poses unique challenges, especially when distinguishing between the majority (often labeled as the negative class) and minority classes (labeled as the positive class). While accuracy is a frequently used metric, it is not always appropriate for imbalanced classification scenarios. Instead, four specific metrics, namely G-mean, F1 score, AUC, and Precision, offer a more comprehensive assessment for such cases.  
The AUC calculates the area under the ROC curve, using the True Positive Rate (TPR) and the False Positive Rate (FPR)--making it a widely accepted metric for classification performance assessment. Precision, shown in Equation (1), defines the proportion of actual positive instances among all the predicted positive cases. A high Precision underscores the model's reliability in its positive predictions. G-mean, elucidated in Equation (2), computes the geometric mean of Sensitivity and Specificity. This measurement provides a balanced perspective on the performance across both classes. The F1 score, given in Equation (5), stands as the harmonic mean of Precision and Sensitivity, encapsulating the model's overall classification prowess.  
To ensure rigorous comparisons, we employ the Wilcoxon Signed-rank Test and the Friedman Test. The former tests for performance similarities between two algorithms, while the latter discerns significant performance variations across multiple algorithms. If the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Num** & **Dataset** & **S** & **Smin** & **Smaj** & **F** & **IR** \\ \hline
1 & Heart & 676 & 265 & 411 & 15 & 1.55 \\
2 & Breast & 569 & 212 & 357 & 31 & 1.68 \\
3 & Pima & 768 & 268 & 500 & 8 & 1.87 \\
4 & Vehicle0 & 846 & 199 & 647 & 18 & 3.25 \\
5 & Ecoli1 & 336 & 77 & 259 & 7 & 3.36 \\
6 & Yeast3 & 1484 & 163 & 1321 & 8 & 8.10 \\
7 & Yeast-0-2 & 1004 & 99 & 905 & 8 & 9.14 \\
8 & Abalone9 & 731 & 42 & 689 & 8 & 16.40 \\
9 & Car-good & 1728 & 69 & 1659 & 6 & 24.04 \\
10 & Winequality & 1599 & 53 & 1546 & 11 & 29.17 \\ \hline \hline \end{tabular}  
* Title Abbreviations: S, Total samples; Smin, Minority class samples; Smid, Majority class samples; F, Number of features; IR, Imbalance Ratio. Abbreviations for datasets: Heart, Heart Disease; Breast, Breast Cancer; Yeast-0-2, Yeast-0-2-5-7-9 vvs3-6-8; Abalone9, Abalone9-18; Winequality, winequality-red-4.  
\end{table}
Table 1: Details of the dataset used in the study.  
Friedman Test detect significant differences, the Nemenyi post hoc analysis is used to locate these disparities precisely.  
\[\text{Precision}=\frac{TP}{TP+FP} \tag{1}\]  
where \(TP\) and \(FP\) represent true positives and false positives, respectively.  
\[\text{$G$-mean}=\sqrt{\text{Specificity}*\text{Sensitivity}} \tag{2}\]  
where Sensitivity and Specificity are computed according to Equations (3) and (4), respectively.  
\[\text{Sensitivity}=\frac{TP}{TP+FN} \tag{3}\]  
\[\text{Specificity}=\frac{TN}{TN+FP} \tag{4}\]  
\[\text{F1}=2\times\frac{\text{Precision}\times\text{Sensitivity}}{\text{ Precision}+\text{Sensitivity}} \tag{5}\]