# An Oversampling Method for Class Imbalance Problems on Large Datasets
## 2 Related Work
Then, when a neighbor of the majority class is selected to generate a synthetic object, the random number (\(r\)) is computed as in SLS and adjusted as \(r^{\prime}=r(sl_{n}/k)\) where \(sl_{n}\) is the safe level of the selected neighbor. NDO [35] generates synthetic objects around each object of the minority class by adding a fraction of the standard deviation of the values of each feature. This portion of the standard deviation is computed by dividing the standard deviation by the square root of the number of objects in the minority class, and multiplying the result by a random number. The random number is generated by a normal distribution with the mean of 0 and standard deviation of 1. SMOTE-RSB* (S-RSB*) [13] first applies SMOTE, and then only keeps as synthetic objects the objects that belong to the lower approximation of the minority class, according to the Rough Set Theory. \(K\)-means-SMOTE (\(K\)-means-S) [24] applies \(K\)-means for clustering the training set and then selects the clusters with an Imbalance Ratio (IR) lower than a given threshold. Finally, \(K\)-means-SMOTE applies SMOTE on those selected clusters. The amount of oversampling for each cluster is computed based on the sparsity and density values of the minority class objects. Following this idea, A-SUWO [25] first group the training set but apply Complete-Linkage Hierarchical Clustering and then apply SMOTE over each cluster. Farthest SMOTE (Farthest-S) [27] uses a similar approach to that of SMOTE, but rather than using the \(k\)-nearest neighbors, it uses the \(k\)-farthest neighbors. To generate a synthetic object, Geometric-SMOTE (G-SMOTE) [28] first randomly selects an object of the minority class as the center of a hyper-spherical region and, also randomly selects one of its nearest neighbors computed in the whole training set to define the size of the hyper-spherical region based on the distance between the two selected objects. Then, the synthetic object is randomly generated as a point inside of the hyper-spherical region; the generation of synthetic objects is repeated as many times as synthetic objects to be generated. SMOTE-SF (S-SF) [29] selects a subset of features to handle with high-dimensional datasets (a high number of features). The selection of the subset of features is performedby applying a feature ranking method (many methods are studied in their work). Then, SMOTE-SF generates synthetic objects similar to SMOTE but only until it reaches the number specified by an input parameter. In the literature, other methods that are not based on computing the \(k\)-nearest neighbors for generating synthetic objects have been also proposed. However, these methods use computationally expensive techniques such as particle swarm optimization [22], self-organizing maps [23], multi-objective swarm fusion [26], genetic algorithms [31], differential evolution [32], deep generative models and variational autoencoders [33], and feature correlation computing [29]; among others for generating synthetic objects. Therefore, these methods are time-consuming and are unsuitable for large datasets with imbalanced classes. From the above review of oversampling methods, we can see that with the exception of NDO, most oversampling methods are based on the search for the \(k\)-nearest neighbors or other slow techniques. This makes them time-consuming when applied on large datasets with imbalanced classes. Therefore, in the next section, we propose a fast oversampling method for class imbalance problems on large datasets.