# A Selective Dynamic Sampling Back-Propagation Approach for Handling the Two-Class Imbalance Problem
## 1 Introduction  
In recent years, the class imbalance problem has been a hot topic in machine learning and data-mining [1; 2]. It appears when the classifier is trained with a dataset where the number of samples in one class is lower than the samples in the other class, this and produces an important deterioration in the classifier performance [3; 4]. The common methods handled with the class imbalance problem have been the re-sampling methods (under-sampling and over-sampling) [2; 5; 6], mainly due to the independence of the underlying classifier [7]. One of the most well-known over-sampling methods is the Synthetic Minority Over-sampling Technique (SMOTE). This generates artificial samples of the minority class by interpolating existing instances that lie close together [8]. The development of other samplings has been motivated: borderline-SMOTE, Adaptive Synthetic Sampling (ADASYN), SMOTE editing nearest neighbor, safe-level-SMOTE, Density-Based Synthetic Minority Over-sampling TEchnique (DBSMOTE), SMOTE + Tomek's Links [9], among others (see [1; 7; 10]). An interest has been observed for finding the best samples to build the classifiers. For example, borderline-SMOTE has been proposed to over-sample only the minority samples near the class decision borderline [11]. Accordingly, in [12], the safe-level-SMOTE is proposed, to select minority class instances from the safe level region, and then, these samples are used to generate synthetic instances. ADASYN has been developed to generate more synthetic data from minority class samples that are harder to learn than those from minority class samples, which are easy to learn [13]. In a similar way, SPIDER approaches (framework that integrates a selective data pre-processing with the Ivotes ensemble method) over-sampling locally only for those minority class samples that are difficult to learn and includes a removing or relabeling process of noisy samples from the majority class [14; 15]. The above discussed approaches have in common that they use the \(K\) nearest neighbors rule as the basis, and they are applied before the classifier training stage. On the other hand, the under-sampling methods have shown effectiveness to deal with the class imbalance problem (see [7; 8; 10; 16; 17; 18; 19]). One of the most successful under-sampling methods has been the random under-sampling, which eliminates random samples from the original dataset (usually from the majority class) to decrease the class imbalance, however, this method loses effectiveness when removing significant samples [7]. Other important under-sampling methods including a heuristic mechanism are: the neighborhood cleaning rule, from Wilson editing [20], one-sided selection [21], Tomek links [22] and the Condensed Nearest Neighbor rule (CNN) [23]. Basically, the aim of the cleaning mechanism is: (i) to eliminate samples with a high likelihood of being noise or atypical samples or (ii) to eliminate redundant samples in CNN methods. In the same way as the above approaches, we apply these methods before the training process. They employ the \(K\) nearest neighbors rule (except the Tomek links methods) as the basis. Another important alternative to face the class imbalance has been the Cost Sensitive (CS) approach, which has become one of the most relevant topics in machine learning research in recent years [24]. They consider the costs associated with misclassifying samples, i.e., CS methods use different cost matrices describing the costs for misclassifying any particular data sample [10]. The over- and under-sampling could be a special case of the CS techniques [25]. Anther CS method is threshold-moving, which moves the output threshold toward inexpensive classes, such that samples with higher costs become hard to misclassify. It is applied in the test phase and does not affect the training phase [24]. Ensemble learning is an effective method that has increasingly been adopted to combine multiple classifiers and class imbalance approaches to improve the classification performance [2; 4; 5].