## 5 Experimental Results
### Imbalance Learning Performance Comparative Analysis
#### 5.4.3 Minimum Accuracy Per Class  
Table 5 organized as the previous table, presents the results on minimum accuracy per class obtained on the 18 imbalanced data sets of Table 2 by margin based bagging, traditional bagging, UnderBagging as well as SMOTEBagging. This table shows that our extended bagging algorithm outperforms traditional bagging on the recognition of the most difficult class. With respect to UnderBagging, the win frequency of our method is **13/18** and its improvement in per class classification accuracy is up to **15%** (data set _Hayes-roth_). When compared with SMOTEBagging, the margin based method also obtains a win frequency of **13/18** and improves the minimum accuracy per class of up to **39%** (data set _Pendigit_). Unlike in the previous average accuracy margin analysis, unsupervised max margin performs better than other margins in our margin based method for the classification of the smallest difficult class.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Data** & **Biggsing** & **Under-Bagging** & **SMOTEBagging** & **Max-Margin** & **Unsupervised Max-Margin** & **Sum-Margin** & **Unsupervised Max-Margin** \\ \hline Car & 59.3 (7) & 87.0 (4) & 68.5 (6) & **88.8 (8)** & 88.4 (2) & 87.9 (5) & 86.8 (5) \\ Cleveland & 0.0 (7) & 0.0 (7) & 0.0 (7) & 74.1 (1) & 4.4 (0) & 5.7(1) & 3.4 (4) \\ Covype\_data & 0.0 (7) & 41.2 (2) & **46.1** (1) & 31.4 (0) & 30.8 (6) & 31.8 (0) & 31.05 (5) \\ Glass & 80.0 (5) & 79.8 (7) & 80.0 (5) & 80.0 (5) & 80.0 (5) & 79.8 (7) & 79.8 (7) \\ Hayes-roth & 47.6 (6) & 53.5 (5) & 41.1 (7) & 68.1 (7) & **69.2** (1) & 67.8 (9) & 64.4 (4) \\ Neurhybrid & 61.8 (7) & 78.1 (1) & 72.4 (6) & 85.0 (2.5) & 85.0 (2.5) & 84.2 (4.5) & 84.2 (4.5) \\ Ondigit & 0.0 (7) & 71.4 (5) & 61.3 (6) & 78.1 (9) & **79.8** (1) & 76.2 (4) & 79.3 (2) \\ Page-blocks & 54.2 (7) & 89.4 (4) & 80.8 (6) & 88.8 (9) & 98.8 (5) & **90.9** (1) & 88.9 (4) \\ Penhead & 74.2 (5) & 76.9 (7) & 76.9 (7) & 78.8 (7) & 79.4 (2.5) & **79.7** (1) & 79.1 (4) \\ Penndigit & 0.0 (7) & 77.8 (5) & 33.3 (7) & **72.8** (1) & 71.9 (2) & 71.0 (7) & 70.9 (4) \\ Segment & 79.3 (7) & 79.3 (7) & 79.7 (5) & 82.5 (4) & 83.3 (2) & **83.4** (1) & 82.8 (5) \\ Staleg & 45.8 (7) & 69.2 (1) & 67.7 (2) & 59.1 (9) & 59.2 (4) & 62.8 (5) & 59.2 (4.5) \\ Urbanlander & 37.3 (7) & 40.9 (6) & **66.7** (1) & 49.9 (9) & 52.7 (2) & 49.2 (4) & 46.8 (5) \\ Vehicle & 31.3 (7) & 43.9 (2) & **47.0** (1) & 40.8 (3) & 39.1 (6) & 41.7 (3) & 39.3 (5) \\ Wilt & 74.0 (7) & 92.8 (6) & 94.4 (5) & **95.4** (1) & 95.3 (2) & 95.2 (4) & 95.3 (2.5) \\ Wine & 94.7 (5) & 94.1 (7) & 96.7 (6) & 97.3 (9) & 97.7 (2) & 98.2 (1) \\ Winogually-end & 0.0 (7) & 15.9 (4) & 0 (7) & 15.9 (4) & **19.6** (1) & 14.2 (6) & 16.9 (2) \\ Winogually-while & 0.0 (7) & 97 (5) & 0.0 (7) & **13.0** (1) & 11.5 (9) & 10.7 (4) & 12.3 (2) \\ \hline Mean accuracy & 41.4 & 41.3 & 56.1 & 62.9 & **63.1** & 62.8 & 62.1 \\ Average rank & 6.4 & 4.7 & 5.0 & 3.1 & 2.8 & 3.2 & 3.8 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Minimum accuracy per class of standard bagging, UnderBagging, SMOTEBagging and margin-based bagging with four margins.