## 4 Process and Result
### Comparision of Different Models  
To demonstrate the superiority of the proposed method, we compare the proposed joint algorithm with similar decision and classification algorithms like Decision Trees (DT), Random Forests (RF) [65], Support Vector Machines (SVM), Random Forests based on calssification and regression tree (CART-RF) [66; 67; 68; 69]. We did not use any pre-trained models, but trained each model from scratch. When we select the parameters of traditional machine learning algorithm, we take into account the number of data features and avoid overfitting, as we can see in Table 10. Then we perform experimental simulations of these models to be compared as well as the model proposed in this paper using Matlab. The results are presented in the following Table 11. In the classification results, this study uses common evaluation indicators to judge the superiority of the model: Train Acc, Test Acc, Precision, Recall, and F\({}_{1}\) Score. TP, TN, FP, FN are required to explain the above indicators, so confusion matrix is introduced, as shown in Figure 6. The specific performance is described as follows: \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithms** & **Parameters** \\ \hline \hline \multicolumn{3}{c}{Node splitting evaluation criteria = gini} \\ \multicolumn{3}{c}{Feature division point selection criteria = random} \\ \multicolumn{3}{c}{Minimum samples for internal node splitting = 2} \\ \multicolumn{3}{c}{Minimum samples in leaf nodes = 1} \\ \multicolumn{3}{c}{Maximum leaf nodes = 2} \\ \multicolumn{3}{c}{Maximum depth of the tree = 15} \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Selected parameters of each algorithm. Figure 5: Fitting curve of multiple linear regression equation. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Relic Number** & **A1** & **A2** & **A3** & **A4** & **A5** & **A6** & **A7** & **A8** \\ \hline Identification & High & Lead & Lead & Lead & Lead & High & High & Lead \\ type & potassium & barium & barium & barium & barium & potassium & potassium & barium \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Identification results. TP (True Positive): The true value of the data is high potassium, and the predicted value is also high potassium. TN (True Negative): The true value of the data is lead barium, and the predicted value is also lead barium. FP (False Positive): The true value of the data is high potassium, but it is incorrectly predicted as lead barium. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms** & **Train Acc** & **Test Acc** & **Precision** & **Recall** & **F\({}_{1}\) Score** \\ \hline DT & 0.862 & 0.873 & 0.806 & 0.791 & 0.798 \\ RF & 0.958 & 0.924 & 0.872 & 0.866 & 0.869 \\ CART-RF & 0.962 & 0.951 & 0.929 & 0.941 & 0.935 \\ SVM & 0.850 & 0.909 & 0.869 & 0.830 & 0.849 \\ JMLA & 0.979 & 0.976 & 0.975 & 0.976 & 0.975 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Results of model experiments. Figure 6: Confusion matrix (1: high potassium, 0: lead barium). FN (False Negative): The true value of the data is lead barium, but it is incorrectly predicted as high potassium. Accuracy is the simplest and most clear index for evaluating classification models, but it is a good measurement standard only when the proportion of samples in each category of the data set is fairly balanced, as shown in Equation (41):  
\[\text{Accuracy}=\frac{TP+TN}{TP+FP+TN+FN} \tag{41}\]  
Precision represents the proportion of samples that are actually positive in the predicted positive example. As shown in Equation (42):  
\[\text{Precision}=\frac{TP}{TP+FP} \tag{42}\]  
Recall represents the proportion of the actual number of positive samples in the total positive samples among the predicted positive samples. As shown in Equation (43):  
\[\text{Recall}=\frac{TP}{TP+FN} \tag{43}\]  
F\({}_{1}\) Score is a weighted average of accuracy rate and recall rate, which is a synthesis of both. The value of the F\({}_{1}\) Score determines the robustness of the model.