## 4 Results and Discussion
### Data Refinement
#### 4.4.1 Selection  
1. **Keep energies above the threshold. ** Before processing, in the training data set for the \(5\times 5\times 36\) sample, there are just 11.37% non-zero values. Using different threshold values, for the described method, the percent of non-zero values decreases: for threshold value 0.1 GeV to 5.99%, for 0.5 GeV to 1.67%, for 1 GeV to 1,01%, and finally for threshold value 2 GeV to 0.6%. As is visible in Table 9, as the threshold value increases, accuracy slightly drops, and there is an increase in FNR value for the threshold values higher than 0.5. Therefore, forthcoming tests are not carried out for those threshold values. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Threshold** & **acc** & **prec** & **rec** & **f1** & **AUC** & **fpr** & **fnr** \\ \hline
0.1 & 0.9698 & 0.9604 & **0.9800** & 0.9701 & **0.9875** & 0.0404 & **0.0200** \\
0.1 & 0.9689 & 0.9678 & **0.9700** & 0.9689 & **0.9812** & 0.0322 & **0.0300** \\
0.5 & 0.9737 & 0.9790 & 0.9681 & 0.9736 & **0.9875** & 0.0207 & 0.0319 \\
0.5 & 0.9713 & 0.9782 & 0.9641 & 0.9711 & **0.9812** & 0.0215 & 0.0359 \\
0.939913 & 0.9744 & **0.9845** & 0.9641 & **0.9742** & **0.9875** & **0.0152** & 0.0359 \\
0.851953 & **0.9717** & **0.9826** & 0.9604 & **0.9713** & **0.9812** & **0.0170** & 0.0396 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The results for the QCNN and QMLP (gray background) with different threshold values. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Threshold** & **acc** & **prec** & **rec** & **f1** & **AUC** & **fpr** & **fnr** \\ \hline
0.1 & **0.9722** & 0.9800 & 0.9641 & **0.9720** & 0.9844 & 0.0196 & 0.0359 \\
0.1 & 0.9674 & 0.9647 & **0.9704** & 0.9675 & 0.9835 & 0.0356 & **0.0296** \\
0.5 & 0.9706 & 0.9711 & **0.9700** & 0.9705 & **0.9851** & 0.0289 & **0.0300** \\
0.5 & **0.9676** & 0.9685 & 0.9667 & **0.9676** & 0.9823 & **0.0315** & 0.0333 \\
1 & 0.9693 & 0.9774 & 0.9607 & 0.9690 & 0.9826 & 0.0222 & 0.0393 \\
1 & 0.9667 & 0.9684 & 0.9648 & 0.9666 & **0.9851** & **0.0315** & 0.0352 \\
2 & 0.9578 & **0.9870** & 0.9278 & 0.9565 & 0.9657 & **0.0122** & 0.0722 \\
2 & 0.9556 & **0.9858** & 0.9244 & 0.9541 & 0.9643 & 0.0133 & 0.0756 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The QCNN and QMLP (gray background) results with different thresholds applied on energy/pixel values. 2. **Keep layer maximum (single sample per layer). ** The models where just one value per image layer is kept show no drop in classification precision compared with base quantized versions, according to results shown in Table 10.
3. **Capping. ** Data capping is performed by using different values (2, 4, 8, 16). For QMLP, there is no notable difference in metrics, but for QCNN, there is an improvement in FNR for all capping values (Table 11), no matter which capping value is chosen. The impact of the applied capping value on the model's accuracy is shown in Figure 13(a) and on FPR in Figure 13(b). 4. **Reduction in longitudinal profile. ** The complete HGCAL image contains 5 \(\times\) 5 \(\times\) 36 = 900 pixels per image, resulting in 2807 parameters for QCNN (respectively 7353 for QMLP). Here, QCNN is used as a classifier. As a result of reducing the longitudinal profile following procedures described in Section 4, the number of model parameters is drastically decreased. The described solutions are examined and results are shown in Table 12 :  
* The QCNN model using a full HGCAL image has 2807 parameters, and with this approach (E+Hf), the number of parameters is reduced to 1673. * This approach (3 Eh+Hf) replaces the full HGCAL image (5 \(\times\) 5 \(\times\) 36) with a 5 \(\times\) 5 \(\times\) 4 image, decreasing the NN parameter numbers to 1079.