# Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
## 3 Model Construction and Optimal Selection of Dataset Balancing Methods
### Construction of Optimized Model  
During the training process of the predictive model, it was not trained on raw data. To eliminate the differences between different feature scales and prevent features with larger value ranges from having a disproportionate impact on model training, it is necessary to normalize the initial dataset [37,38]. Normalization methods include min-max scaling and standardization, with this study primarily selecting the former. Min-max scaling achieves normalization by linearly transforming each feature value according to the following formula:  
\[x^{\prime}=\frac{x-min(x)}{max(x)-min(x)} \tag{15}\]  
where \(x\) represents the original feature value and \(\min(x)\) and \(\max(x)\) are the minimum and maximum values of that feature, respectively. Using this method, each feature value was scaled to a range of 0 to 1. This approach not only balances the impact of different features on the model, but also speeds up the convergence of gradient descent during the training process, improving the overall performance and stability of the model. Additionally, normalized data are better suited to the assumptions of various machine learning algorithms, ensuring that the model performs better during training and prediction. K-fold cross-validation is widely used in the field of machine learning algorithms [39,40] and can be divided into model selection and model evaluation based on its purpose. When using the LSSVM, SVM, and ELM models, this study employed ten-fold cross-validation to select the best hyperparameter combination for predicting the stability of mine pillars. For the LSSVM and SVM models, the RBF function was used as the kernel function, so the hyperparameters to be determined were \(\gamma\) and \(\sigma\), whereas the ELM model's hyperparameter was the number of hidden layer units, n. This study used a grid search to systematically evaluate the performance of different hyperparameter combinations, and the parameter values are listed in Table 2.  
When using datasets with five different feature combinations, the optimal combinations for the two hyperparameters \(\gamma\) and \(\sigma\) of the LSSVM model were concentrated in the range of \([2^{-4},2^{4}]\). For the SVM model, the optimal position for the penalty parameter (also known as the regularization parameter), \(\gamma\), is \([2^{3},2^{5}]\), and for \(\sigma\) is \([2^{-6},2^{-8}]\). The ELM model achieved the best prediction performance with a hidden layer neuron count between 20 and 60. The basic principle of the LSSVM is described in the Materials and Methods Section, and it is evident that the selection of hyperparameters significantly affected the performance of the model. The default LSSVM model generally employs a simple one-by-one search method for hyperparameter selection, which is ineffective in terms of the search range and precision. Therefore, the emergence of intelligent algorithms has effectively addressed this \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Hyperparameter** & **Range of Values** \\ \hline LSSVM & \(\gamma\) & \(\{2^{-8},2^{-6},2^{-4},2^{-2},2^{0},2^{2},2^{4},2^{6},2^{8}\}\) \\ SVM & \(\sigma\) & \(\{10,20,30,40,50,60,70\), \\ ELM & \(n\) & 80, 90, 100, 200, 300, 400, \\  & & 500, 600, 700, 800, 900, 1000] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Range of values for model hyperparameter grid search. problem [41, 42]. Algorithms such as the GA and PSO simulate evolutionary or physical processes in nature, enabling efficient search and optimization in a larger parameter space. These algorithms utilize population search and random selection mechanisms, allowing the exploration of a wider range of parameter combinations and finding global optimal solutions to avoid local optima. The flowchart of the SABO-LSSVM prediction model is shown in Figure 7.  
The specific process of mine pillar stability state recognition based on the SABO-LSSVM model is as follows:  
Step 1. Prepare the dataset for model training and perform pre-processing.