# 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
This may lead to some important samples in the boundary region being incorrectly processed due to their high sensitivity. UA-KF, on the other hand, only employs KNN to address noise issues in minority-class samples. In contrast, FDUS eliminates the influence of outliers far from the classification boundary through spatial compression throughout the entire KNN data preprocessing process. This enables FDUS to perform well in terms of noise and sensitivity. **Ensemble learning and undersampling across the majority class**. In order to compare FDUS with ensemble learning methods that do not partition in the majority class, we chose RUS. Regarding the average results of the AUC, F-measure, and G-mean evaluations, FDUS performs exceptionally well, with 7.80%, 5.59%, and 6.37% higher values compared to RUS. Meanwhile, 20, 15, and 16 data sets dominate, respectively. Because random undersampling is performed directly on the majority class without partitioning, the balanced majority class obtained may not necessarily match the original sample distribution well, which could lead to a worse score than that obtained with FDUS. **Comparison with cluster-based undersampling methods. ** We chose Centers_NN and CBIS for a comparison of their performance. Regarding the average results of the AUC, F-measure, and G-mean evaluations, FDUS exceeds Centers_NN by 4.50%, 4.58%, and 4.60%, respectively. It also exceeds CBIS by 3.43%, 2.49%, and 3.23%, respectively. The number of data sets in which FDUS outperforms Centers_NN is 19, 18, and 19, respectively, and the number of data sets in which FDUS surpasses CBIS is 20, 16, and 15, respectively. The Centers_NN and CBIS methods use the NN and AP algorithms, respectively, to cluster the majority class and obtain the sample distribution characteristics. However, during undersampling, they operate within the entire class sample space. As a result, some samples that are distant from the classification boundary are retained; their number is \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Data Set** & **FDUS** & **Tomek** & **US** & **RUS** & **RBU** & **Centers** & **CBIS** & **UA-KF** \\ \hline abalone-17\_vs\_7-8-9-10 & 0.7782 & 0.7547 & 0.7066 & 0.7169 & 0.7033 & 0.7164 & 0.7423 & 0.7244 \\ car-vgood & 0.7827 & 0.2727 & 0.7093 & 0.9064 & 0.8722 & 0.8063 & 0.7783 & 0.8722 \\ dermatology-6 & 1 & 0.9493 & 0.9354 & 0.9382 & 0.9199 & 0.9732 & 0.9627 & 0.9199 \\ ceoill & 0.8387 & 0.8785 & 0.8098 & 0.8375 & 0.8812 & 0.8551 & 0.8723 & 0.8644 \\ glass-0-1-6\_vs\_4-5-6 & 0.8923 & 0.8667 & 0.7700 & 0.9318 & 0.8582 & 0.7991 & 0.9442 & 0.8582 \\ glass-0-1-6\_vs\_5 & 1 & 0.9177 & 0.8063 & 0.8214 & 0.8619 & 0.9197 & 0.8947 & 0.8385 \\ iris0 & 0.9895 & 0.9707 & 0.9434 & 0.9477 & 0.9042 & 0.9675 & 0.9228 & 0.9375 \\ k-vs\_k-three\_vs\_eleven & 0.9618 & 0.7799 & 0.7948 & 0.9629 & 0.8991 & 0.9348 & 0.9517 & 0.8991 \\ led7 digit-0-2-4-5-6-7-8-9\_vs\_1 & 0.8633 & 0.6654 & 0.7297 & 0.9346 & 0.7652 & 0.8607 & 0.8625 & 0.7652 \\ new-hybrid1 & 0.9867 & 0.9195 & 0.8494 & 0.9491 & 0.9323 & 0.9543 & 0.9631 & 0.8564 \\ page-blocks0 & 0.9051 & 0.8924 & 0.8741 & 0.8113 & 0.8901 & 0.8873 & 0.9085 & 0.8473 \\ segment0 & 0.9874 & 0.8930 & 0.9524 & 0.9059 & 0.9581 & 0.9386 & 0.9534 & 0.8934 \\ shuttle-0-vs\_c4 & 0.9633 & 0.8902 & 0.8574 & 0.8752 & 0.9584 & 0.9459 & 0.9259 & 0.9162 \\ vehicle0 & 0.9455 & 0.9006 & 0.8112 & 0.8622 & 0.8928 & 0.8621 & 0.9372 & 0.9059 \\ vehicle2 & 0.9162 & 0.8945 & 0.9429 & 0.9296 & 0.8672 & 0.8452 & 0.9414 & 0.8672 \\ vowel0 & 0.8989 & 0.9004 & 0.8711 & 0.7973 & 0.8968 & 0.8667 & 0.8958 & 0.8427 \\ winequality-white\_3\_vs\_7 & 0.9333 & 0.7697 & 0.7275 & 0.7229 & 0.7574 & 0.7178 & 0.7704 & 0.7202 \\ wisconsin & 0.9183 & 0.8792 & 0.8706 & 0.8013 & 0.8821 & 0.8257 & 0.8769 & 0.7809 \\ yeast-0-5-6-7-9\_vs\_4 & 0.7385 & 0.7169 & 0.7087 & 0.6943 & 0.7057 & 0.7274 & 0.7143 & 0.7062 \\ yeast5 & 0.9367 & 0.8238 & 0.8727 & 0.8078 & 0.9365 & 0.9133 & 0.9193 & 0.8247 \\
**Average** & 0.9118 & 0.8268 & 0.8097 & 0.8559 & 0.8671 & 0.8660 & 0.8869 & 0.8420 \\ \hline \hline \end{tabular}
\end{table}