# Cost-Sensitive Variational Autoencoding Classifier for Imbalanced Data Classification
## 2 Related Work
### Research on Imbalanced Data Classification at the Data Level  
At the data level, classification is mainly used to change the distribution of training data by sampling the original data to eliminate or reduce data imbalance, including over-sampling and under-sampling methods.  
The over-sampling method improves the classification performance of minority classes by increasing the number of minority samples. The simplest method is to copy minority samples directly. The disadvantage of this method is that it simply copies minority samples without adding any new information to minority classes, which may lead to overfitting. The improved over-sampling method solves the above problems to some extent by addingrandom Gaussian noise to minority classes to generate new synthetic samples. For example, the SMOTE algorithm proposed by [PERSON] et al. is a classic over-sampling method [7]. SMOTE generates a new minority sample without repetition by randomly selecting samples of the same kind of close neighbours for interpolation, which can overcome the overfitting problem of the random over-sampling method to some extent. However, the SMOTE method also has several problems, such as over-generalization, sample overlap, and noise. To solve the above problems, several improved methods have been developed based on SMOTE, such as Borderline-SMOTE [8] and SMOM [9]. In [10], the classification performance of minority classes is addressed by selecting suitable neighbours in the minority classes with which to increase the number of minority classes and generate new synthetic samples using the firefly algorithm. Reference [11] proposed a method that combines over-sampling technology and instance selection techniques to classify imbalanced data streams. The method selects data streams from different classes to form data chunks using the over-sampling technique, and then selects the data chunks for classifier learning using the instance selection techniques. Reference [12] proposed a density-based mixed sampling method that deletes high-density samples from the majority classes and samples low-density samples from the minority classes. This eliminates the noise in the two classes and maintains the structural balance of the classes to the maximum extent, improving the performance of the classifier.  
In contrast, the under-sampling method improves the classification performance of the minority classes by reducing the number of majority-class samples. The simplest method is to remove some majority-class samples randomly to reduce the size of the majority class, which has the disadvantage of some important information of the majority class being lost and existing information not being able to be fully utilized [13]. Therefore, many improved under-sampling methods have been proposed. [PERSON] and [PERSON] proposed a one-sided sampling method to remove noise, boundary, and redundant samples in the majority-class samples. The basic idea of the algorithm is to divide the majority samples into noise, boundary, and safety samples, and to delete the boundary and noise samples from the majority samples without deleting useful samples as much as possible in order to achieve a better classification performance than random under-sampling [14]. In [15], an under-sampling algorithm based on clustering was proposed. First, the training set is divided into several clusters using a clustering method, and each cluster contains a certain number of majority and minority classes. For each cluster, all of the minority classes are removed, and the majority classes in the cluster are undersampled according to certain rules. Finally, the samples taken from each cluster are combined to obtain a new training set.