# An Undersampling Method Approaching the Ideal Classification Boundary for Imbalance Problems
## 2 Related Work
### Cluster-Based Sampling Methods  
In contrast to random sampling, the cluster-based undersampling method can preserve the distribution characteristics of the data set by dividing the majority class into groups of similar samples through cluster analysis; as a result, the data characteristics of the majority class are maintained as long as the samples are drawn from these different groups to form a new, balanced data set.  
[PERSON] et al. [16] used Kmeans to cluster the majority classes and then randomly sampled the representative objects from clusters of the majority classes according to the proportion of the number of each cluster. [PERSON] et al. [17] set the number of clusters in the majority class to the same number of samples in the minority class; they then used the center point of these clusters and the minority class to form a new data set. [PERSON] et al. [18] proposed a clustering-based combination method named CBIS that first uses the AP algorithm to perform clustering in the majority class and then uses sample selection techniques to obtain a new data set; it then achieves the final results via ensemble learning. Herein, the number of clusters is adaptively obtained. [PERSON] et al. [19] utilized the hierarchical clustering of undersampled fused random forests. The proposed method clusters the majority of samples using a hierarchical clustering algorithm, undersamples each cluster to achieve the balance of data samples, and then constructs a random forest. Compared to the method comprising random undersampling combined with random forest (RF), it improves the prediction accuracy by 16% and the F-value by 17%. [PERSON] and [PERSON] [20] proposed a new method that enables the self-organizing mapping of boundary regions to be described using a normal distribution, and that addresses high-dimensional imbalance problems. This method has been shown to perform well on two high-dimensional data sets used in industrial fault detection. [PERSON] et al. [8] performed clustering in the majority class such that there were no minority samples in the convex hull of each cluster. They believe that this approach can preserve the data distribution in the feature space and achieve good results. [PERSON] et al. [21] presented an algorithm that uses the adaptive clustering method combined with AdaBoost to eliminate the majority of samples with minor contributions; this method therefore aids in the classification process. [PERSON] et al. [22] adopted a two-stage method that aims to overcome the problem of imbalance by combining DBSCAN and a graph-based process to filter noisy objects in the majority class. [PERSON] and [PERSON] [23] used the k-prototypes clustering algorithm to partition majority-class samples and perform initial undersampling, followed by resampling using ADASYN, NearMiss-2, and SMOTETomek. This method has achieved good results when applied to imbalanced large truck collision data.  
The majority of the above-mentioned studies present methods that aim to accurately obtain the number of clusters in the majority class. This is, however, a paradox, because if the data of the majority class can be clearly distinguished from each other, then it is more reasonable to divide the majority class into several classes so that a majority class no longer exists. In addition, these methods mainly focus on preserving the data structure of the majority class, and ignore the fact that the boundary points have a greater impact on the construction of the classification model.