# A Decision Tree for Rockburst Conditions Prediction
## 3 Methods
### Data Evaluation  
A key problem with ML algorithms is their complexity. Thus, according to different proposals, ML algorithms are assessed by relying on accuracy. The confusion matrix is a classification process that contains the evaluation metrics, such as recall, F1, and precision. This makes it easier to access and more reliable. The performance of different distinct data-driven models will be evaluated and compared using seven metrics: Recall, Precision, F1, Accuracy (ACC), Specificity (SP), Matthew Correlation Coefficient (_MCC_), and Area Under the Receiving Operating Characteristic (ROC) Curve (AUC). Additionally, the interpretability of the models is assessed through sensitivity analysis--the relative importance of input variables to the output variable--rockburst condition. The equations and definitions of the metrics are as follows.  
The recall measures the proportion of cases of a certain class correctly identified by the model. Therefore, recall is given by:  
\[recall=\frac{\textit{TruePositive}\ (TP)}{\textit{TruePositive}\ (TP)+\textit{FalseNegative}(FN)} \tag{1}\]  
On the other hand, precision measures the correctness of the model when it predicts a certain class. Precision is given by:  
\[precision=\frac{\textit{TruePositive}\ (TP)}{\textit{TruePositive}\ (TP)+\textit{FalsePositive}(FP)} \tag{2}\]  
The harmonic mean of precision and recall is a class of F1 score (F1). It is also a measure of the performance of the model's classification ability. The F1 score is considered a better indicator of the classifier's performance than the regular accuracy measure.  
\[F1=2\cdot\frac{\textit{precision}\cdot\textit{recall}}{\textit{precision}+ \textit{recall}} \tag{3}\]  
Furthermore, the accuracy criterion defines the percentage of the data in the correct place. The closer the value is to one, the higher the accuracy and reliability.  
\[ACC=\frac{TP+FN}{TP+TN+FP+FN} \tag{4}\]  
Specificity can be defined as the algorithm's ability to predict the True Negative of each category available. It is also known as the True Negative Rate (TNR).  
\[SP=\frac{TN}{FP+TN} \tag{5}\]  
\[MCC=\frac{(TP\cdot TN)-(FP\cdot FN)}{\sqrt{(TP+FP)\cdot(TP+FN)\cdot(TN+FP) \cdot(TN+FN)}} \tag{6}\]  
AUC calculates the area under the ROC curve. The higher the AUC, the better the model classifier. Therefore, the AUC for a perfect classifier is 1. In all, the higher the metric values, the better the prediction. This goes for all the metrics selected. _MCC_ ranges in the interval \(-1\), \(+1\), with extreme values \(-1\) and \(+1\) reached in the case of perfect misclassification and perfect classification, respectively, while _MCC_ = 0 is the expected value for the coin-tossing classifier.  
Figure 4: Decision tree schematic of metamorphic rock.  
Figure 3: DT for igneous rock.  
Figure 5: Decision tree schematic of sedimentary rock.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Rockburst Condition** & **Precision** & **Recall** & **F1** & **AUC** & **ACC** & **SP** & **MCC** \\ \hline None & 0.70 & 0.57 & 0.63 & 0.83 & 0.88 & **0.95** & **0.61** \\ Light & 0.57 & 0.63 & 0.60 & 0.75 & 0.75 & 0.80 & 0.41 \\ Moderate & 0.64 & **0.69** & 0.66 & 0.75 & 0.76 & 0.80 & 0.37 \\ Strong & **0.77** & 0.68 & **0.72** & **0.86** & **0.90** & **0.95** & 0.52 \\ \hline Average & 0.67 & 0.64 & **0.65** & 0.80 & **0.82** & 0.88 & 0.48 \\ \hline \end{tabular}  
NB : Best Value in Bold.  
\end{table}
Table 6: Metrics for Unique-DT Model.