## 5 Experimental Results
### Imbalance Learning Performance Comparative Analysis
#### 5.4.1 Average Accuracy  
Table 3 shows the average accuracy achieved by the proposed margin based extended bagging algorithm, bagging, UnderBagging as well as SMOTEBagging on the 18 imbalanced data sets of Table 2. The experimental results in this table show that all the imbalance learning algorithms lead to an improved classification with respect to traditional bagging. Moreover, undersampling based \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Data** & **bagging** & **Under-bagging** & **SMOTE-Bagging** & **Max-Margin** & **Unsupervised Max-Margin** & **Sum-Margin** & **Unsupervised Max-Margin** \\ \hline Car & 81.6 (3) & **87.1** (1) & 79.9 (7) & 82.4 (2) & 81.5 (5) & 81.6 (4) & 81.4 (6) \\ Cleveland & 2.6 (7) & 28.6 (6) & 27.6 (6) & 29.3 (2) & 28.2 (9) & **24.0** (1) & 28.5 (4) \\ Cortygrade data & 36.4 (7) & **83.7** (1) & 52.0 (2) & 51.2 (6) & 51.5 (4) & 51.5 (4) & 51.8 (4) \\ Class & 91.1 (5) & 91.1 (5) & 96.6 (7) & **91.8** (1) & **91.8** (1) & 91.6 (25) & 91.6 (25) \\ Hayes-with & 77.9 (5) & 77.1 (7) & 77.3 (7) & 79.2 (8) & 80.0 (2) & **82.0** (1) & 79.9 (3) \\ Newslyth & 87.5 (7) & **94.8** (1) & 90.5 (9) & 94.0 (5) & 94.0 (5) & 94.1 (5) & 94.3 (2) \\ Osptight & 68.8 (7) & 85.2 (9) & 78.3 (6) & 87.3 (6) & 87.9 (1) & 87.1 (6) & 87.6 (2) \\ Papabacks & 88.1 (7) & 72.9 (6) & 70.0 (5) & 72.3 (6) & 72.4 (1) & 74.4 (7) & 73.9 (4) \\ Penabab & 90.7 (5) & 88.5 (7) & 88.8 (9) & 92.3 (9) & 92.4 (2) & 92.5 (1) & 92.1 (4) \\ Pendiggt & 69.0 (7) & 84.9 (5) & 70.0 (6) & 86.3 (6) & 86.7 (1) & 86.5 (2) & 86.2 (4) \\ Segment & 90.7 (5) & 90.0 (6) & 94.6 (5) & 94.2 (2) & 94.3 (1) & 94.2 (2) & 94.2 (3) \\ Statlog & 80.6 (7) & 81.9 (8) & 81.7 (6) & 88.6 (2) & 86.2 (5) & **82.0** (1) & 82.4 (4) \\ Urban-Lowover & 75.2 (5) & 87.5 (7) & 81.1 (7) & 71.1 (7) & 72.0 (7) & 70.0 (6) & 71.2 (4) \\ Vehicle & 73.1 (5) & 72.4 (7) & 73.0 (7) & 74.7 (7) & 75.0 (2) & 74.9 (3) & 78.1 (1) \\ Will & 94.1 (1) & 83.3 (5) & 85.1 (7) & 88.6 (2) & 85.3 (5) & 85.4 (3) & 85.3 (5) \\ Wine & 98.4 (3) & 96.7 (7) & 98.1 (6) & 98.2 (5) & 98.4 (3) & 98.7 (2) & **99.2** (1) \\ Winewingly-pad & 28.7 (5) & 30.6 (2) & 38.4 (1) & 29.4 (2) & 27.9 (6) & 26.6 (7) & 29.4 (4) \\ Winepability-while & 27.7 (2) & 27.6 (4) & 25.2 (6) & 28.3 (2) & 27.8 (3) & 27.3 (5) & **28.4** (1) \\ \hline Mean & 70.9 & 73.2 & 72.5 & 73.9 & **74.0** & **74.0** & **74.0** \\ Average rank & 5.1 & 4.7 & 5.3 & 3.4 & 3.0 & 3.2 & 3.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: F-measure of standard bagging, UnderBagging, SMOTEBagging and margin-based bagging with four margins. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Data** & **bagging** & **Under-bagging** & **SMOTE-Bagging** & **Max-Margin** & **Unsupervised Max-Margin** & **Sum-Margin** & **Unsupervised Max-Margin** \\ \hline Car & 79.7 (7) & 91.9 (5) & 84.0 (6) & **93.4** (1) & 92.4 (6) & 92.7 (2) & 92.3 (4) \\ Cleveland & 28.1 (6) & 29.2 (2.5) & 28.9 (4) & 29.2 (2.5) & 28.0 (7) & **28.0** (1) & 28.4 (5) \\ Cortygrade data & 32.0 (7) & 67.9 (3) & 65.7 (6) & 67.4 (5) & 67.6 (7) (9) & 68.1 (1) \\ Glass & 91.6 (6) & 92.9 (5) & 91.2 (7) & **93.4** (1) & 93.1 (3) & 93.1 (3) \\ Hayes-with & 77.3 (5)ensemble classifiers such as margin based bagging and UnderBagging outperform oversampling based ensemble classifiers (SMOTEBagging). This result is consistent with the state-of-the-art work presented in the previous section, where we have explained that oversampling based methods have a risk of injecting additional noise into the training set. The ensemble model based on margin achieves the best performance, especially in addressing the imbalance problem of many-majority and less-minority classes, that often occurs in the real world. These results put a clear emphasis on the importance of preprocessing the training set prior to building a base classifier by focusing on the examples with low margin values and not treating them uniformly.