# A New Under-Sampling Method to Face Class Overlap and Imbalance  
[PERSON]  
1 Facultad de Ingenieria, Universidad Autonoma del Estado de Mexico, Cerro de Coatepec s/n, Ciudad Universitaria, Toluca 50100, Mexico; [EMAIL_ADDRESS] (A.G.-P.); [EMAIL_ADDRESS] (R.M.V.) [PERSON]  
1 Facultad de Ingenieria, Universidad Autonoma del Estado de Mexico, Cerro de Coatepec s/n, Ciudad Universitaria, Toluca 50100, Mexico; [EMAIL_ADDRESS] (A.G.-P.); [EMAIL_ADDRESS] (R.M.V.) [PERSON]  
the classes are approximately equal (i.e., all classes have a similar amount of data), which makes most classifiers more likely to produce a large number of misclassifications [10]. Class noise, which refers to mislabeled instances, can also lead to incorrect classification decisions, especially when combined with class imbalance [11]. The presence of both noise and class imbalance can significantly affect the classification process: mislabeling from the minority class to the majority class increases the imbalance ratio in the data set, whereas mislabeling from the majority class to the minority class produces an even higher difficulty to correctly classify the positive instances [12]. Both class overlap and noise have been commonly tackled through the application of data filtering methods, which are intended to identify and remove mislabeled and atypical data and also to clean possible overlapping between classes [13, 14]. The different strategies to address the class imbalance problem are usually categorized into four groups [7, 15]:  
1. Algorithmic-level methods. These consist in internally biasing the discrimination-based process so as to compensate for the class imbalance. 2. Data-level methods. These perform some sort of data preprocessing with the aim of reducing the imbalance ratio. 3. Cost-sensitive methods. These incorporate distinct misclassification costs into the classification process and assign higher misclassification costs to the errors on the minority class. 4. Ensemble-based techniques. These consist of a combination between an ensemble algorithm and either the data-level or the cost-sensitive approaches. In the first one, data preprocessing is performed before training the classifier, whereas in the second one, the low cost guides the use of the ensemble algorithm. Conclusions about what is the best solution for the class imbalance problem are divergent, but the data-level methods are likely the most investigated because they are not classifier-dependent, do not need any algorithmic adaptation to the data sets, and can be easily implemented for any problem [16]. Thus, focusing on the data-level approach, resampling methods consist of adjusting the data set size with the aim of balancing the class distribution, either by decreasing the number of majority class instances (under-sampling) or increasing the number of minority class instances (over-sampling). A hybrid resampling approach consists of combining both over-sampling and under-sampling strategies. As remarked by several authors, under-sampling methods may throw away many potentially useful data as a result of ignoring most of majority class, whereas the over-sampling methods can lead to overfitting on the minority class and an increase in complexity and execution time [17]. On the other hand, it is worth pointing out that the resampling methods have been also used to face the imbalance problem together with class overlap and/or the presence of noisy and borderline instances in the data set [8, 18, 19, 20, 21], a common situation that has motivated the research presented in this paper. Although most traditional resampling methods are based on the \(k\) nearest neighbor (\(k\)NN) rule [22, 23, 24], clustering algorithms have been demonstrated to be even a more powerful strategy for addressing the class imbalance problem [16, 25, 26] because they may reduce the risk of removing potentially useful data and, therefore, they can achieve better results than the \(k\)NN-based resampling methods.