## 3 Ensemble-Based Methods
A separate classifier is introduced for each example in the training set, thus having \(k\) numbers of a classifier for each iteration of the training set. From the bagging family, the most prominent methods reported in the literature are random forest, which is a flexible and easy-to-use ensemble-based machine-learning algorithm. Most of the time random forest gives very good results, even without hyper-tuned parameters. Because of its simplicity, it can be widely used for both regression and classification tasks. A variation of the bagging scheme, UnderBagging [2], under samples the underlying subset of the instance before the bagging iteration for multi-class imbalance problems by keeping all the minority class samples in each iteration. Another variation of bagging schemes is random forest [5], where the base classifier trained via the bootstrap samples of the underlying training dataset has been randomly reduced to a small subset of dataset samples. In voting-based ensemble methods, predictions from various individual models are combined. In the voting method using an ensemble approach, two or more component models were created separately with a dataset, following an ensemble model to wrap the previously created models and the prediction of those models then aggregated. The resulting model was used to predict new data. Assuming that we have \(L\), bootstrap samples (approximations of \(L\) independent datasets) of size \(B\) are denoted in Equation (7):  
\[\{z_{1}^{1},z_{2}^{1},z_{B}^{1}\},\{z_{1}^{2},z_{2}^{2},z_{B}^{2}\},\{z_{1}^{L },z_{2}^{L},z_{B}^{L}\} \tag{7}\]  
where \(z_{b}^{l}\equiv b\)th observation of the \(l\)th bootstrap sample. We can fit \(L\) almost independent weak learners (one on each dataset) as given in Equation (8):  
\[w_{1}(.),w_{2}(.),\ldots\ldots,w_{L}(.) \tag{8}\]  
All the weak learners of Equation (8) are then combined into some kind of averaging process to obtain an ensemble model with a lower variance. For example, we can define our strong model given in Equation (9):  
\[S_{L}(.)=arg_{k}^{l=1}max[card(l\mid w_{l}(.)=k)] \tag{9}\]  
Apart from accuracy improvements and being accuracy oriented, most of the standard techniques for creating ensembles face difficulties in identifying the subset of the dataset with the minority class. To cope with such difficulties, special attention has to pay to designing ensemble algorithms to handle the class imbalance problem. The effective combination of imbalanced learning, ensemble learning techniques with a base learner, and sampling strategies to confront the imbalance class issue put forward many possible proposals for prominent results in the literature by putting aside the conventional categories such as cost-based and kernel-based methods in the imbalanced domain [56]. Regardless of the popularity, versatility, and effectiveness of ensemble methods (by using an independent baseline classifier) as compared to cost-sensitive and improved algorithm-based methods, in an ensemble process, however, transforming dissimilar classifiers by ensuring their stability and regularity using the underlying training dataset is still a crucial factor for ensured accuracy while dealing with the multi-class classification problems. All the symbols used in this article are described in Table 2.