## 2 Related Work  
There is an extensive literature focused on this problem, which is very common in many domains. In this section, we include a brief survey of some representative work that addresses the improvement of imbalanced data classification by using both internal and external algorithms. Solutions at the internal level include some techniques such as modifying existing classification algorithms, one-class classification and cost-sensitive methods. Some internal strategies such as instance weighting can be used either outside this classification to give more weight to minority class instances or within cost-sensitive methods [14]. Another option to reduce the bias toward majority class instances is to calibrate the prediction probability of the algorithms to align it with prior probabilities. The aim of algorithm modification is to make the resulting classifier more suitable for class imbalance distributions. In order to achieve this objective, a process of learning from these distributions is performed prior to the induction of the classification model. A well-known classifier that has been adapted to process imbalanced datasets is SVM. Some modifications of this algorithm are Z-SVM [18], GSVM and GSVM-RU [19]. Z-SVM aims to increase the G-mean values by moving the position of the hyperplane of the original algorithm. GSVM and GSVM-RU are based on granular computing, consisting of splitting the problem into a sequence of granules and building SVMs on some of these granules. GSVM-RU also uses SVM for undersampling, which makes it suitable for high imbalance problems. Fuzzy classification is another approach proposed for some authors to deal with the problem of imbalanced data. In [20], a fuzzy-based classifier is presented where fuzzy sets representing the classes are created from the relative class frequency distributions. Hierarchical fuzzy rules (HFR) and a genetic algorithm are combined in [21] to classify imbalanced datasets. Some variations of SVM based on fuzzy sets have been proposed to deal with the problem of classification of nonbalanced data [22; 23]. A less popular alternative is to resort to one-class classifiers that are focused on classifying instances of a target class, ignoring all other classes [24]. These methods are generally based on similarity measures between examples of the target class. In the class imbalance scenario, this approach has been applied in some works in the literature [25; 26; 27] where the minority class is considered the target class and the majority class as the outlier. Although only the minority class is learned, examples from the majority class can also be used for training. This approach is also combined with resampling strategies [28]. Cost-sensitive learning is an internal technique based on considering the misclassification cost, which has been the subject of more studies in the literature. In [29], the impact of imbalance on classifiers is analyzed when the misclassification costs are unequal. The work of [30] includes an effective framework that integrates an evaluation measure into the objective function of cost-sensitive SVM directly to increase the performance by improving misclassification cost criteria. The use of an uneven cost matrix in an approach based on neural networks and fuzzy logic is presented in [31]. One of the problems of cost-sensitive learning is the frequent unavailability of the cost matrix, thus this drawback has also been addressed in some work. Some authors propose to create artificial cost values when cost values cannot be obtained [32]. The problem of overfitting is also analyzed in the literature on these methods [33], concluding that this drawback associated with oversampling strategies also occurs with cost-sensitive methods. On the other hand, both approaches present similar performance when dealing with the class imbalance problem [34].