# Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
## 4 Results and Discussion
### Performance of Different Balancing Methods  
The oversampling methods used in this study were the Smote and Adasyn algorithms. Additionally, a balancing method that combines an under-sampling algorithm, called the Tomek-Smote sampling method, was employed. These methods were applied to balance the dataset of the SABO-LSSVM model under the M-3 parameter combination. The results of each method are shown in Figure 11.  
It can be observed from Figure 11 that the SABO-LSSVM model performed poorly in predicting the second-class (unstable) samples when using the unbalanced (Default) dataset. Out of the 14 samples, eight were incorrectly predicted, resulting in an accuracy of only 42.86% for this class. This indicates that an imbalanced dataset can lead to inconsistent prediction results for different classes, as the samples from the minority class contribute less information during model training, resulting in significantly lower accuracy compared with other classes. Therefore, various oversampling algorithms can be employed to supplement an imbalanced dataset with new samples, thereby achieving a balanced representation of each class. After applying the Smote and Adasyn algorithms for oversampling, there was a noticeable improvement in the ability of the model to identify unstable pillar samples. The number of incorrectly predicted samples from the second class was reduced from eight to two, and the accuracy increased to 85.71%. Thus, by supplementing samples from the minority class, the information provided to the model was enhanced, resulting in improved prediction accuracy. However, after oversampling, some of the originally correctly predicted samples from the other two classes were misclassified. For example, in the \"stable\" and \"failed\" pillar samples, one sample from each class was predicted as unstable after oversampling, whereas these samples were correctly predicted in the default dataset's model predictions. This also highlights the negative impact of oversampling, as it introduces noise into the dataset. To balance the sample representation while removing noise, this study explored the use of the Tomek-Links-improved Smote algorithm, the Tomek-Smote balancing method. This method removes abnormal samples caused by dataset recombination from a Smote-balanced dataset, thereby reducing the noise introduced during the balancing process. From the graph, it can be observed that the Tomek-Smote algorithm, compared to the Smote algorithm, corrected one misclassified sample in both the \"stable\" and \"failed\" pillar samples due to noise. This suggests that Tomek Link under-sampling, when applied, removed the noise samples introduced by Smote, effectively improving the prediction accuracy of these two classes. In order to quantitatively analyze the performance of different balancing algorithms in the model, various evaluation metrics must be calculated, as shown in the table. The quantitative analysis of different models primarily included an overall and classification evaluation. The overall evaluation calculated the metrics for all samples, whereas the classification evaluation considered metrics for each specific pillar sample class. In the classification evaluation, precision and recall were calculated for each class to assess the model's ability to distinguish between positive and negative samples in different classes. Precision and recall had mutually exclusive relationships. If only precision is considered to be increased by predicting samples with a high probability as positive, it may lead to missing positive samples with lower probabilities, resulting in a decrease in recall. To strike a balance between the two, the F1 score was calculated to provide a comprehensive assessment of the classification performance of the model [44]. For ease of understanding, we list the meaning of the relevant indicators and how to calculate. Table 5 shows meaning of confusion matrix, and Table 6 shows formulas and meanings of model performance metrics.