# Hybrid Oversampling and Undersampling Method (HOUM) via Safe-Level SMOTE and Support Vector Machine
## 7 Limitations and Future Directions  
In this study, the G-mean metric, which considers all elements of the confusion matrix, was prioritized. Additionally, the F-Score values for all datasets were calculated using the unprocessed original versions of the datasets, SMOTE-based methods, and the proposed algorithm. Although the original dataset achieved the highest F-Score in four out of the eight datasets, its G-mean values were significantly lower, indicating poor overall performance. As a result, improving the G-mean became the primary focus for comparison and further enhancement.  
Based on previous studies [45], SMOTETomek was shown to have a complexity of \(O(T.k.d)\) + \(O(n^{2}.d)\), and SMOTEENN was shown to have a complexity of \(O(T.k.d)\) + \(O(n.k.d)\) where \(T\) is the number of synthetic samples, k is the number of neighbors, n is the number of data points, and d is the dimensionality. HOUM-R, which incorporates SVM-based undersampling and SLS for oversampling, has a higher complexity of \(O(l(n^{2}+n.k.d))\)  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **HOUM** & **W-SIMO** & **RusAda** \\ \hline Diabetes & 72.70\% & **76.26\%** & 76.15\% \\ Liver & **73.60\%** & 69.08\% & * \\ Haberman & **70.50\%** & * & 64.79\% \\ Transfusion & **73.20\%** & * & 69.21\% \\ Ionosphere & **95.90\%** & 94.11\% & 90.14\% \\ \hline \hline \end{tabular} Bold numbers: highest performance per dataset across methods. *: result not available for the relevant dataset.  
\end{table}
Table 5: Comparing the performance of various methods with common datasets.  
where \(I\) is the number of iterations required to achieve balance. Despite the HOUM's increased computational cost, it offers a significant advantage by focusing on the decision boundary through the SVM, thus generating more informative samples and reducing the risk of overfitting, which can enhance classification performance in imbalanced datasets. This trade-off between computational cost and improved performance makes the HOUM a valuable approach in scenarios where the metric of G-mean is a critical concern.  
While the Hybrid Oversampling and Undersampling Method (HOUM) shows promising results in balancing binary class datasets, several limitations need to be addressed. The method's performance on multiclass imbalanced datasets remains unexplored, posing challenges in adapting it to more complex problems. Additionally, the HOUM's reliance on computationally expensive techniques like SVMs for undersampling can hinder its scalability when applied to large datasets. The method's efficiency may also vary depending on the classifiers used, with its adaptability across a broader range of algorithms yet to be thoroughly tested. Furthermore, the use of fixed parameters, which were not optimized across different datasets, could limit the method's generalization, requiring manual fine-tuning to achieve optimal performance in new domains. Lastly, the sequential nature of the oversampling and undersampling steps may risk overfitting or data loss, particularly in highly imbalanced datasets.  
To address these challenges, future research should focus on extending the HOUM to multiclass problems, optimizing parameters through automated techniques, and improving computational efficiency to make the method more scalable. Exploring hybrid models that integrate resampling with classification in a unified framework could also mitigate potential risks of overfitting or data loss. By addressing these limitations, the HOUM can be adapted for a wider range of real-world applications and larger, more complex datasets.