# Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
## 2 Materials and Methods
### Oversampling Methods  
Imbalanced data are often encountered in the practical applications of machine learning, where the accuracy of the minority class, which has a smaller proportion, is often not ideal. Therefore, oversampling algorithms were used. The role of oversampling methods in addressing imbalanced data problems is to increase the number of samples in the minority class, balance the sample distribution across different classes, and improve the performance of the classifiers [35; 36]. They can enhance the classification accuracy of the minority class, prevent information loss, and strengthen the robustness and generalization ability of the model. However, oversampling methods must be carefully selected and combined with other processing techniques to avoid issues, such as overfitting and increased sensitivity to noise.  
Common oversampling algorithms include synthetic minority oversampling (Smote), adaptive synthetic sampling (Adasyn), and random oversampling (Ros). Smote increases the number of samples in the minority class by synthesizing new samples in the feature space rather than simply duplicating existing samples, which differentiates it from Ros's random generation of samples, and the principle of smote is shown in Figure 5. The specific method involves randomly selecting minority class samples and generating new sample points between their nearest neighbors, thereby expanding the distribution of minority class samples and improving the classifier's ability to recognize the minority class.  
Figure 4: Principle of the operation process \(\overset{\rightarrow}{\boldsymbol{v}}\) in the SABO algorithm.  
The Adasyn algorithm is an improvement of the Smote algorithm. Unlike Smote, Adasyn adaptively generates new samples by focusing on minority class samples that are difficult to classify. Specifically, Adasyn determines the number of new samples to be generated based on the density of the minority class samples, generating more samples in regions that are challenging to classify.  
In methods for balancing datasets, in addition to oversampling the minority class, under-sampling can be applied to boundary and noisy data. Tomek-Smote sampling is an approach that combines these two concepts. It was originally proposed by [PERSON] et al. in 2003, and often achieves better model accuracy than under-sampling alone. The key concept of this sampling method is Tomek Links [36], an under-sampling technique developed by [PERSON] in 1976. It is inspired by the condensed nearest neighbors (CNN) and primarily balances the dataset by removing sample pairs (also known as Tomek Links pairs) with the smallest Euclidean distance between different classes. Principle of the Tomek Links is shown in Figure 6.  
As shown in the illustration, the data group within the blue circles represents the Tomek Links pairs. During the under-sampling process, the samples removed from Class 2 included both the newly generated samples from Smote and the original samples located at the decision boundary. This approach helps reduce the noise introduced by oversampling algorithms and cleans up confused samples between classes, making it more beneficial for the model's predictions.