# Data Sampling Methods to Deal With the Big Data Multi-Class Imbalance Problem
## 1 Introduction  
The huge amount of data continuously generated by digital applications is an important challenge for the machine learning field [1]. This phenomena is not only characterized by the volume of information, but also by the speed of transference and the variety of data; i.e., the big data characteristics [2; 3]. Concerning to the volume of information, a dataset belongs to big data scale when it is difficult to process with traditional analytical systems [4]. In order to efficiently seize the large amount of information from big data applications, deep learning techniques have become an attractive alternative, because these algorithms generally allow toobtain better results than traditional machine learning methods [5; 6]. Multi-Layer Perceptron (MLP), the most common neural network topology, has been also translated to the deep learning context [7]. Deep Learning MLP (DL-MLP) incorporates two or more hidden layers in its architecture [8], which increases the computational cost of processing large size and high dimension datasets. Nevertheless, this disadvantage can be overtaken by using modern efficient frameworks, such as Apache-Spark [9] or Tensor-Flow [10]. Thus, the high performance, robustness to overfitting, and high processing capability of these deep neural networks can be exploited. Machine learning and deep learning algorithms are strongly affected by the class imbalance problem [11; 12; 13; 14; 15]. The latter refers to some difficulties that appear when the number of samples in one or more classes in the dataset is fewer than another class (or classes), thereby producing an important deterioration of the classifier performance [16]. In the literature, many studies dealing with this problem have been reported [17]; in particular, the data sampling methods such as Random Over-Sampling (ROS), which replicate samples from the minority class, and Random Under-Sampling (RUS), which eliminate samples from the majority class. These methods bias the discrimination process to compensate the class imbalance ratio [18]. Data sampling methods have important drawbacks, such as longer training times and over-fitting, which are more likely to occur when minority samples are replicated. Additionally, the loss of information is common when many samples are removed from majority classes, potentially dismissing useful information for the classifier [19; 20; 21]. Then, more \"intelligent\" sampling, methods including a heuristic mechanism, have been developed [17; 22; 23]. Synthetic Minority Over-sampling Technique (SMOTE) is a heuristic over-sampling algorithm. It generates artificial samples from the minority class by interpolating existing instances that lie close together. Nowadays, it is one the most popular data sampling methods [1] and it has motivated the development of other over-samplings algorithms [24]. Similarly, under-sampling methods have been incorporate a heuristic component [25], some of the most outstanding examples being the Tomek's Links (TL) [26], Editing Nearest Neighbor (ENN) [27], and Condensed Nearest Neighbor rule (CNN) [28], among others [22; 29; 30; 31; 32; 33]. Another way to deal with the class imbalance problem has been through the Cost Sensitive (CS) approach [34], which has become an important topic in deep learning research in recent years [13; 14; 15; 35]. CS considers the costs associated with misclassifying samples; i.e., it uses different cost matrices describing the costs of misclassifying any particular data sample [29]. The over and under-sampling could be a special case of CS techniques [34; 36].