# An Oversampling Method for Class Imbalance Problems on Large Datasets
## 4 Experimental Results
### Comparison against State of the Art Oversampling Methods  
In this experiment, we compare the proposed method Fast-SMOTE to the state-of-the-art oversampling methods in terms of oversampling quality and runtime. In this experiment, we used small-medium size datasets to allow applying SMOTE and other state of the art methods. We used all 66 imbalanced datasets from the KEEL repository [55] (shown in Table 2), and assessed the oversampling quality of the oversampling methods. This was done by oversampling a repository training dataset until reaching a full balance between classes and training a classifier with the oversampled dataset produced by an oversampling method. The testing set that is also available in the repository was used to evaluate the trained classifier. The quality of the classification result is interpreted as the oversampling quality of the employed oversampling method. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Features Mode**} \\ \cline{2-3}  & \(x\) & \(y\) \\ \hline \hline \multicolumn{1}{c}{mamography} & \(-0.55\) & \(0.06\) \\ \multicolumn{1}{c}{glass} & \(0.42\) & \(0.73\) \\ \multicolumn{1}{c}{ecoli} & \(0.32\) & \(0.79\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mode values of \(x\) and \(y\) axis for for Figures 1–3. Figure 3: Synthetic objects (blue diamonds) generated by SMOTE (**a**), NDO (**b**), and Fast-SMOTE (**c**) over a 2-D projection of the dataset Ecoli. Green circles represent objects of the majority class, and red crosses represent objects of the minority class. Since all oversampling methods generate random numbers when a synthetic object is built, the oversampling methods were applied 30 times for each one of the 66 imbalanced datasets using the 5-fold cross-validation partition available in the repository. We used the supervised classifiers CART (Classification and Regression Tree), KNN (K-Nearest Neighbor Classifier) (K = 5), and Naive Bayes. Additionally, as suggested in [56], we used AUC (Area Under Curve) to assess the classification results, the most used measure for evaluating classification quality on imbalance class problems. Table 3 shows the average AUC of the 150 results (30 repetitions for each one of the 5 folds) obtained with each classifier (CART, KNN, and Naive Bayes; see rows) over the 66 datasets for each oversampling method (see columns). As mentioned above, most of the compared oversampling methods are based on finding the \(k\)-nearest neighbors; it is observed from the results shown in Table 3 that these methods obtain the best AUC results. In particular, we can observe that SMOTE and S-RSB* obtained the best average oversampling quality. On the other hand, the methods that are not based on finding the nearest neighbors (NDO and Fast-SMOTE) do not obtain the lowest oversampling quality. The methods that obtain the worst AUC results were K-Means-S and G-SMOTE. The proposed method and NDO, obtain lower average AUC results than SMOTE and S-RSB* although unlike these methods, Fast-SMOTE and NDO can be applied on large datasets. Additionally, in this experiment we assessed the runtime employed by the oversampling methods. This experiment was run in MATLAB 2020b, using a computer with a Ryzen 5300X 3.60 GHz processor with 32 GB DDR4 RAM, running 64-bit Windows 10.