# An Undersampling Method Approaching the Ideal Classification Boundary for Imbalance Problems
## 1 Introduction  
In the era of big data, classification has become an increasingly important learning task in various data mining and analysis applications, including bankruptcy prediction [1], stroke prediction [2], fraud detection [3], and fault diagnosis [4]. Generally speaking, the classification algorithms employed in machine learning are designed to deal with balanced data classification problems. In reality, however, the data collected in practical applications are usually imbalanced, i.e., the number of samples representing different classes is unequal. For example, in a binary classification problem, there are 10 samples in one class and 500 in the other class. When the two types of data overlap one another, the classification algorithm may treat these 10 samples as noise data. It is therefore difficult to predict the minority-class samples when using classification algorithms, as the algorithm tends to learn the characteristics of the majority-class data; this results in the minority-class samples being misclassified as majority-class samples. For example, in practical applications such as cancer prediction, there are far more normal cells than cancer cells. However, there would be serious consequences if the cancer cells were to be misclassified as normal cells.  
It is well known that imbalanced problems can be solved via two methods of research: one is oversampling [5; 6], whereby data sets are balanced via the random generation of samples for the minority class, and the other is undersampling, whereby data sets are balanced by performing partial sampling in the majority class and the number of samples selected is therefore reduced [7; 8; 9]. Although both methods have enabled significant research results to be obtained, we will focus on the undersampling method in this paper.  
Great success has been achieved by conducting random sampling and removing samples from the majority class to maintain the balance of data sets [7; 9]. Experiments conducted by [10], [11], and [12] proved that not all data have a significant effect on the classification model, and that the contribution of some data is even negligible. Researchers have screened data based on the borderline [13], sensitivity [14], and distribution of data overlap [7] to obtain a new, balanced data set; these methods, unfortunately, may compromise the original distribution characteristics of the data set. Therefore, the cluster-based undersampling technique emerged; for example, [8] obtained good results showing that the majority class was partitioned into clusters. It is clear that regardless of the data sampling method used, it will eventually affect the generation of the classifier, and then affect the shape of the classification boundary. Therefore, our goal is to find an undersampling method that makes the distribution of samples conform to that at the ideal classification boundary.  
The main contributions of this paper are as follows:  
1. Identifying a sampling area that is more consistent with the ideal classification boundary shape via the performance of segmentation after clustering and space compression;
2. Ensuring that the distribution of the sampled data coincides with the sample distribution at the ideal classification boundary by optimizing the number of classifiers obtained and performing undersampling during ensemble learning;
3. Demonstrating that the proposed method has a clear effect via the performance of experiments using 20 data sets.  
In the remainder of this paper, Section 2 discusses related works, Section 3 gives a detailed description of our proposed model, and Section 4 presents extensive experimental results in order to justify the effectiveness of our method. The conclusions and future research directions are outlined in Section 5.