## 2 Related Works
### Ensemble-Based Imbalanced Data Classification Methods
#### 2.2.2 Bagging Based Ensemble Learning  
Bagging significantly outperforms boosting over noisy and imbalanced data [62]. Moreover, bagging techniques are not only easy to develop, but also powerful when dealing with class imbalance if they are properly combined [5]. Most of the related works in the literature indicate good performance of bagging extensions versus the other ensembles [50; 63]. OverBagging [8] is a method for the management of class imbalance that merges bagging and data preprocessing. It increases the cardinality of the minority class by replication of original examples (random oversampling), while the examples in the majority class can be all considered in each bag or can be resampled to increase the diversity. This method outperforms original bagging in dealing with binary imbalanced data problems [5]. SMOTEBagging has been proposed to deal with multi-class imbalance problems [8]. It creates each bag to be significantly different. A SMOTE resampling rate (a) is set in each iteration (ranging from 10% in the first iteration to 100% in the last, always being multiple of 10) and this ratio defines the number of minority class instances (\(a\cdot N_{maj}\)) randomly resampled (with replacement) from the original data-set in each iteration. The rest of the minority class instances are generated by the SMOTE algorithm. The reported results show that this method can get better performance than OverBagging for both binary class and multi-class imbalance problems [5; 63]. [PERSON] and [PERSON] proposed a Neighbourhood Balanced Bagging [26] for binary class imbalance problems. In this method, the sampling probabilities of training examples are modified according to the class distribution in their neighbourhood. Then it consists in keeping a larger size of bootstrap samples by a probability-based oversampling. Their experiments prove that their extended bagging is significantly better than OverBagging and SMOTEBagging. UnderBagging was first proposed by [PERSON] et al. [38]. In this method, the number of the majority class examples in each bootstrap sample is randomly reduced to the cardinality of the minority class. Simple versions of undersampling combined with bagging are proved to work better than more complex solutions such as EasyEnsemble and BalanceCascade [26; 50; 64]. Another popular extended version of bagging is Roughly Balanced Bagging (RBBag) [65]. It results from the critics of the original UnderBagging algorithm and its variants which use exactly the same number of majority and minority class examples in each bootstrap sample. Instead of fixing a constant sample size, RBBag equalizes the sampling probability of each class. For each iteration, the size of the majority class in the bootstrap sample is set according to the minority class binomial distribution. The class distribution of the resulting bootstrap samples may be slightly imbalanced and it varies over iterations. This approach is more consistent with the nature of the original bagging and better uses the information about the minority examples. Both under-sampling bagging extensions outperform SMOTEBagging and OverBagging for binary class imbalance problems in [26]. However, the performances of the two methods were not tested for multi-class imbalance learning. Neighbourhood Balanced Bagging has another version [26]. The difference with the presented method in the previous section is in reducing the sample size with a probability-based undersampling. The reported experiments prove that this method is competitive with RBBag for binary-class imbalance tasks and outperforms the first version that involved an oversampling scheme. [PERSON] et al. proposed a resampling bagging algorithm [22] which is another version of UnderOverBagging [8; 66], a combination of UnderBagging and OverBagging. In that method, small classes are oversampled and large classes are undersampled. The resampling scale is determined by the ratio of the minimum class size and the maximum class size.