# Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
## 2 Materials and Methods
### Feature Correlation Analysis  
In machine learning classification tasks, conducting feature correlation analysis is crucial, as it helps identify and eliminate redundant or unnecessary features, reduces data dimensionality, simplifies the model, and reduces computational resource consumption [28; 29]. In research using machine learning to predict mine pillar stability, several scholars have tested different combinations of features in their datasets. [PERSON] et al. [25] selected six features: pillar width (W), pillar height (H), aspect ratio of the pillar (K), uniaxial compressive strength of the rock (UCS), pillar stress (\(\sigma\)), and pillar strength (\(\sigma_{\text{p}}\)). [PERSON] and [PERSON] et al. [2] chose seven features, including pillar width (W), pillar height (H), aspect ratio of the pillar (K), pillar constraint (C\({}_{\text{pav}}\)), uniaxial compressive strength of the rock (UCS), pillar stress (\(\sigma\)), and pillar strength (\(\sigma_{\text{p}}\)), for mine pillar state recognition. They compared the effects of different feature  
Figure 1: Boxplots of the features in the mine pillar dataset. (**a**) Pillar width (m), (**b**) pillar height (m), (**c**) ratio of width and height, (**d**) pillar constraint (MPa), (**e**) uniaxial compressive strength (MPa), (**f**) pillar stress (MPa), and (**g**) pillar strength (MPa).  
combinations on various discriminant criteria using feature elimination. [PERSON] et al. [14] selected five features: pillar width (W), pillar height (H), pillar aspect ratio (K), uniaxial compressive strength of the rock (UCS), and pillar stress (\(\sigma\)). These features were used as evaluation indicators in the quantitative theory II discriminant model, and the results showed that this combination performed well in practical applications and had certain engineering significance.  
The present study investigated all seven mine pillar indicators and utilized correlation analysis to identify redundant features. To assess the correlation between different sets of features, the Pearson correlation analysis method [30; 31] was employed to calculate the correlation coefficients between each pair of features. Outliers in the data can significantly affect the correlation analysis. Before conducting correlation analysis, it is advisable to replace outliers with the mean value within each group. To check for the presence of outliers, boxplots were generated using SPSS software (v.26).  
The intergroup correlation coefficients and scatter plots are shown in the figure. From the Figure 2, it can be observed that the groups with higher correlation coefficients included \"UCS-\(\sigma_{\text{p}}\)\", \"K-C\({}_{\text{pav}}\)\", and \"W-H\". The absolute values of the correlation coefficients were 0.88, 0.81, and 0.59, respectively. The first two groups exhibited a strong correlation relationship, while the \"W-H\" group showed a moderately strong correlation relationship.  
Based on correlation analysis, we identified features that exhibited strong correlations. These highly correlated features provided redundant information as inputs for the predictive model. To simplify the model, it was necessary to eliminate redundant features. The selection process involved considering the correlation coefficients between each set of features and class labels and removing the one with weak correlation. Through the selection of redundant features, this study attempted to use five parameter combinations, namely, M-1, M-2, M-3, M-4, and M-5, as the dataset for the predictive model and explore their impact on predictive performance. The specific parameters of these combinations are listed in Table 1.  
Figure 2: Scatter plots and correlation analysis of mine pillar feature data (The green circles represent stable samples, the yellow circles represent unstable samples, and the red circles represent failed samples).