# Data Sampling Methods to Deal With the Big Data Multi-Class Imbalance Problem
## 1 Introduction
In neural networks, CS can be performed on several ways [37]: (a) cost-sensitive classification, where the learning process is not modified and only the output probability estimates for the network are adjusted during the testing stage; (b) adapting the output of the network, unlike the last one, the neural network output is appropriately scaled; (c) adapting the learning rate, meaning to include a constant factor that modify the learning rate value; (d) minimization of the misclassification costs or loss function (in deep learning), where the loss function is corrected by introducing the factor that compensates the classification errors or the class imbalance. Reference [11] presents a novel focal loss to deal with the class imbalance problem on dense object detection. It can be seen as a CS approach which applies a modulating term (weighting factor) to the cross entropy loss in order to focus learning on hard negative examples and addressing the class imbalance. The weighting factor can be set by inverse class frequency or treated as a hyper-parameter to be set by cross validation. Reference [13] proposes a cost-sensitive deep neural network which can automatically learn (during training) robust feature representations for both the majority and minority classes. Ensemble learning is an effective method that combines multiple classifiers and class imbalance approaches to improve the classification performance on several applications [38; 39; 40]. Reference [41] proposes a solution for breast cancer diagnosis: to use decision trees and Multi-Layer Perceptrons as base classifiers in order to build an ensemble similar to the Easy Ensemble algorithm, and sub-samplingmethods to deal with the class imbalance problem. In [42], an ensemble of support vector machines is used, where the maximum margin is adopted to guide the ensemble learning procedure for multi-class imbalance classification. In [14], a hybrid optimal ensemble classifier framework that combines under-sampling and cost sensitive methods is proposed. The combination of deep learning and an ensemble classifier has been performed. For example, in [43], a software bug prediction is presented. It has two stages: deep learning (auto-encoder) and ensemble learning, and it was noticed to be able to deal with the class imbalance and over-fitting problem. In big data scenarios, the conjunction of ensembles and clustering methods has been proposed, as was demonstrated by [44], where ensembles with datasets preprocessed by clustering and sampling methods were built. Moreover, the use of clustering and sampling techniques to deal with the class imbalance problem has been increased [45; 46; 47]. In the machine learning context, extensive and comprehensive reviews about of ensembles and class imbalance problem have been performed [30; 38; 39]. It has seen that big data class imbalance approaches have been addressed by adaptation of traditional techniques, mainly sampling methods [21; 44]. However, recent studies show that some conclusions from machine learning are not applicable to the big data context; for example, in machine learning is common that SMOTE performs better than ROS [24], but in big data some results do not show this trend [1; 48]. In addition, only a few works have been addressed to deal with the class imbalance in big data by using \"intelligent\" or heuristic sampling techniques [17; 49]. Thus, more studies are need in order to test methods that traditionally present good performances in machine learning (such as the random and heuristic sampling algorithms) at the big data scale. The potential of traditional sampling methods on deep learning neural networks in the big data context is studied in this work. The main contributions of this research are: (a) This paper is focused in dealing with multi-class imbalance problems, which have hardly been investigated [50; 51; 52] and they are critical issues in the field of data classification [45; 53].