# Improving Graphite Ore Grade Identification with a Novel FRCNN-PGR Method Based on Deep Learning
## 4 Experimental Results and Analysis
### Experiment Results  
The total loss function and learning rate changes during model training are shown in Figure 13.  
In Figure 13, the loss value curve, indicated by the red line, is observed to be decreasing in tandem with the learning rate curve, depicted by the blue line, as the number of iterations of FRCNN-PGR is augmented. The decreasing trend of both parameters is sustained until they eventually stabilize. Figure 14 illustrates the changes in mAP during model training, wherein a gradual increase in mAP is observed with the continuation of training iterations until it ultimately reaches a stable state.  
Figure 13: Changes in total loss function and learning rate.  
The ROC curves of different models in each grade category are shown in Figure 15.  
The Receiver Operating Characteristic (ROC) curve is a graphical representation that elucidates the interdependence between sensitivity and specificity in a given classification model. Upon meticulous scrutiny of Figure 15, it is evident that the model in question has undergone a series of enhancements, resulting in a gradual amplification in the Area Under Curve (AUC) value. This surge in the AUC value unequivocally signifies that the predictive performance of our model has been consistently ameliorated over time.  
The comparison between the different models (FR-CNN, FR-CNN + RGA, FR-CNN + FPN, FR-CNN + RGA + FPN, and FRCNN-PGR) and the experimental results are shown in Table 3, and the FPR and FNR of each model in different graphite ore grade categories are shown in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**FR-CNN (ResNet50)**} & \multicolumn{1}{c}{**FR-CNN + RGA**} & \multicolumn{1}{c}{**FR-CNN + FPN**} & \multicolumn{1}{c}{**FR-CNN + RGA + FPN**} & \multicolumn{1}{c}{**FRCNN-PGR (Our)**} \\ \cline{2-11}
**Grade** & **FPR** & **FNR** & **FPR** & **FNR** & **FPR** & **FNR** & **FPR** & **FNR** \\ \hline
0–5\% & 11.80 & 22.67 & 11.42 & 16.67 & 8.12 & 15.33 & 6.18 & 14.67 & 4.83 & 13.33 \\
5–10\% & 9.23 & 30.38 & 9.80 & 31.01 & 11.00 & 26.58 & 9.82 & 24.05 & 8.64 & 22.15 \\
10–15\% & 9.17 & 23.52 & 8.96 & 24.60 & 9.37 & 30.48 & 8.75 & 26.20 & 7.71 & 21.39 \\
15–20\% & 10.89 & 13.95 & 9.88 & 9.88 & 10.69 & 8.14 & 10.48 & 4.65 & 9.88 & 3.80 \\ Macro-average & 10.27 & 22.63 & 10.02 & 20.54 & 9.80 & 20.13 & 8.81 & 17.39 & 7.77 & 15.17 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The results of FPR and FNR (unit: %).  
Figure 14: Changes in mAP during training.  
The comparative data displayed in Table 3 evinces a discernible augmentation in the precision and recall rates of the primary model of the faster R-CNN algorithm for the recognition of graphite mine images, as a direct consequence of employing the FRCNN-based model.  
Figure 15: The ROC curves of different models.  
PGR algorithm. The data further suggest that the mean average precision (mAP) has increased by 5.3%, whilst the recall rate has surged by 1.9%. Moreover, upon scrutinizing the false positive rate (FPR) and false negative rate (FNR) values, alongside the macro-average values of both the native and FRCNN-PGR models, as presented in Table 4, it can be inferred that our proposed model yields superior performance, overall. Furthermore, the macro-average value exhibits a progressive decrease, which further substantiates our model's enhanced performance. Finally, Figure 16 illustrates the outcomes of the graphite mine image recognition, based on the FRCNN-PGR model.