## 5 Experimental Results and Analysis
### Experimental Setup
Moreover, our extracted CRP data have an estimated proportion of 1's(p) at 0.4928 and a Shannon entropy (H) of 0.9794, which is quite close to the ideal values of 0.5 and 1. Figure 13: Intra-HD: Variation of PUF output to the same challenge across conditions. Figure 14 is a confusion matrix (also known as an error matrix), which is a visual representation of classification algorithm performance. It is one of the key evaluation tools used to assess how well a model performs. From this matrix, several performance metrics can be derived, such as precision, recall, and F1 score. The top left cell represents the number of true positives (TPs), indicating correctly predicted positive instances. The cell below TP shows false positives (FPs), which are negative instances incorrectly classified as positive. The top-right cell corresponds to false negatives (FNs), representing positive instances that were mistakenly predicted as negative. The bottom right cell indicates the true negatives (TNs), referring to correctly identified negative instances. The confusion matrices for four selected classifiers are used to derive model performance metrics, as shown in Table 4, using Equations (20)-(24). \[\text{Accuracy}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{FP}+\text{FN}+ \text{TN}} \tag{20}\]  
\[\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{21}\]  
\[\text{Recall}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{22}\]  
\[\text{False Discovery Rate (FDR)}=\frac{\text{FP}}{\text{FP}+\text{TP}} \tag{23}\]  
\[\text{F1-Score}=2\cdot\frac{\text{Precision}\cdot\text{Recall}}{\text{ Precision}+\text{Recall}} \tag{24}\]  
In ML, parameters are generally categorized into model parameters and hyperparameters. Model parameters are learned from the training data, whereas the user predefines hyperparameters before the training process begins [135]. Hyperparameters influence what the model can learn and significantly affect its ability to generalize to unseen data [136]. Table 5 lists the tuning details of ML models used in our work. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Regression** & **TP** & **TN** & **FP** & **FN** & **Accuracy** & **Precision** & **Recall** & **FDR** & **F1-Score** \\ \hline LR & 94,021 & 89,470 & 58,170 & 58,161 & 0.612 & 0.617783 & 0.6178195 & 0.393999 & 0.617801 \\ \hline RF & 148,545 & 143,658 & 3982 & 3637 & 0.974588 & 0.973893 & 0.976101 & 0.026971 & 0.974996 \\ \hline MLP & 146,580 & 142,454 & 5186 & 5602 & 0.964019 & 0.965829 & 0.9631888 & 0.035126 & 0.964507 \\ \hline GB & 94,021 & 89,470 & 58,170 & 58,161 & 0.612 & 0.617783 & 0.6178195 & 0.393999 & 0.617801 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimation of PUF confusion matrix. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Hardware Platforms** & **Uniformity** & **Intra-HD** & **Uniqueness** & **Ref.** \\ \hline Artix\(\mathcal{\gamma}\) FPGA & 51.22\% & - & 50.81\% & [128] \\ \hline Xilinx XC2S200 FPGA & 49\% & 5\% & 45–50\% & [129] \\ \hline Virtex-5 FPGA & 54.78\% & - & 4.7\% & [130] \\ \hline Virtex-5 FPGA & 42.34\% & - & 36.75\% & [131] \\ \hline Artix-7 FPGA & 57.64\% & - & 51.34\% & [132] \\ \hline Artix-7 FPGA & 51.84\% & - & 46.21\% & [133] \\ \hline HSPICE 65 nm ptm & 55.69\% & 11.36\% & 42.12\% & [134] \\ \hline Cyclone IV & 49.28\% & 10.81\% & 38.6\% & Proposed APUF \\ \hline \hline \end{tabular}
\end{table} 
Table 3: CRPs performance metrics of APUF-Variants.