# An Undersampling Method Approaching the Ideal Classification Boundary for Imbalance Problems
## 3 Proposed Method
### Undersampling That Enables Close-Fitting Data Distribution at the Ideal Classification Boundary
In these experiments, we used a 5-fold cross validation method to carry out the experiment and repeat it 20 times. Herein, the average of 20 experimental results is used as the final result. **Benchmark methods** As mentioned in Section 2, we use five of the latest imbalanced undersampling methods and two classic algorithms; these are listed below as our benchmark methods:

1. **NB-Tomek**[7] This method accurately identifies and eliminates overlapping instances of imbalanced data sets; therefore, the visibility of minority instances is maximized, and the excessive elimination of data is minimized, thereby reducing information loss. 2. **USS**[14] This method calculates the sensitivity of majority-class samples. Low-sensitivity examples are considered as either noisy or safe examples, and high-sensitivity examples are regarded as critical examples. It performs undersampling in the majority-class samples via sensitivity. 3. **RUS**[33] This method randomly selects the same number of samples from the majority class as that from the minority class, and then obtains a classifier by using AdaBoost. 4. **RBU**[34] This method uses the Gaussian kernel function to calculate the mutual class relationship between majority-class samples and minority-class samples based on the mutual-class potential, and achieves a balance between the two classes through the diffusion kernel radius. Finally, the naive Bayes classifier is applied to achieve classification. * **Centers_NN**[17] This method conducts the clustering learning of most classes in an imbalanced data set, and the nearest neighbors of the cluster center of the undersampling clustering are used for the classification learning of the imbalanced data set. * **CBIS**[18] This method uses the AP algorithm to cluster the data of the majority class; it then uses the IS3 [35] method to select samples from the majority class subsets of each cluster and combines them with the minority-class samples to form a training set. Ensemble learning is then used to obtain the classifier. * **UA-KF**[12] This method performs noise filtering on minority-class data, randomly undersamples majority-class data, and finally uses AdaBoost for ensemble learning. **Parameters and Metrics** In our proposed method, we set \(k=15\) in the kNN filtering step, and use five CART trees as weak classifiers in the AdaBoost step. It is believed that if the ratio of majority-class samples to minority-class samples exceeds 1.5, then the data are imbalanced; therefore, we set the ratio of the sampled data to 1.5 (majority class vs. minority class). In an imbalanced data set, the accuracy of classification is biased to the data of the majority class, and therefore the results are not considered to be accurate. In this work, we use the F-measure, AUC, and G-mean, which are commonly used in research on imbalance in order to evaluate the experimental performance [36; 37; 38]. Herein, the AUC can be obtained by calculating the area of the ROC, which is a curve showing the relationship between the _False Positive Rate_ and _True Positive Rate_. The formula is as follows. \[False\ Positive\ Rate=\frac{FP}{FP+TN} \tag{5}\]

\[True\ Positive\ Rate=\frac{TP}{TP+FN} \tag{6}\]

\[False\ Negative\ Rate=\frac{TN}{TN+FP} \tag{7}\]

\[Precision=\frac{TP}{TP+FP} \tag{8}\]

\[Recall=\frac{TP}{TP+FN} \tag{9}\]