# Predicting the Pillar Stability of Underground Mines with Random Trees and C4.5 Decision Trees
## 4 Development of Prediction Models  
In this paper, the C4.5 decision tree and random tree algorithms were used to develop models for predicting underground mine pillar stability. The input variables were the width of the pillar (\(W\)), height of the pillar (\(H\)), \(W\)/\(H\) ratio, the pillar stress (\(\sigma_{p}\)), and uniaxial compressive strength of the rock (\(\sigma_{ucs}\)). Pillar stability (PS) (dependent variable) was the sole output variable. The train-and-test approach, which is one of the most widely used techniques for establishing the predictive performance of ML algorithms for a given database, was used to develop the models. In this research study, the dataset used by [PERSON] et al. [18] was used as the training and testing dataset for the proposed models. The working procedure for pillar stability prediction using the proposed models is shown in Figure 4.  
To develop the proposed models, C4.5 DT and random tree algorithms are implemented based on training data on the Waikato Environment for Knowledge Analysis (WEKA) tool. The training dataset in ARFF form (attribute relation file format) was loaded in WEKA to train the adopted models which are subsequently tested by using a testing dataset based on the given training dataset. The optimal value of the C4.5 DT model parameters, including the confidence factor and the minimum number of  
Figure 4: Working procedure for the prediction of pillar stability using a random tree and C4.5 decision tree (DT). Figure 3: Decision tree induced by the C4.5 algorithm [24]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Random Tree (RT)** & **C4.5 Decision Tree (DT)** \\ \hline Attributes available at each decision node & Random subset & All \\ Attributes selected at each decision node & Best among a random subset & Highest information gain among all \\ Trees count & One & One \\ Samples of data used for the training & All & All \\ Classification final result & Based on the leaf node reached & Based on the leaf node reached \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Differences between a random tree and a C4.5 decision tree. instances per leaf, were calculated by the trial-and-error method to achieve the highest classification accuracy. The C4.5 DT algorithm's optimal value for confidence factor was 0.25 and that of the minimum instances per leaf was found to be 2. Figures 5 and 6 represent the random tree and C4.5 DT models based on the training dataset. As shown in the figure, the size of the random tree is 11 including a root node, 4 internal nodes, and 6 leaves, while the size of the C4.5 DT was 5 including a root-node, 1 internal node, and 3 leaves. The leaf node shows the stable and the failed class of underground mines. The value in the parentheses with each leaf node denotes the number of cases at that leaf. It is evident that for leaves, few instances are misclassified, which are clearly specified after a slash (see Figures 5 and 6). The performance of the trained pillar stability models was estimated using a number of statistical classification evaluation criteria such as counts of true-positive (TP), true-negative (TN), false-positive (FP), and false-negative (FN). These counts together form the confusion matrix shown in Table 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Predicted Class**} \\ \hline \hline  & & Failed & Stable \\ \hline \multirow{2}{*}{Actual class} & Failed & TP & FN \\  & Stable & FP & TN \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Confusion matrix for the binary class problem. Figure 5: The random tree for prediction of underground mines pillar stability. Figure 6: Decision tree model generated by the C4.5 algorithm for prediction of underground mines pillar stability. Consider that the failure of the underground mine pillar is actually positive then TP and TN represent the number of failed and stable instances that were predicted correctly. FN and FP occur when the outputs are incorrectly predicted as negative and positive, respectively.