# Multimodal Biometric Template Protection Based on a
## 4 Experiments
### Hyperparameter Analysis  
In this section, we explore the impact of the two essential hyperparameters, \(q\) and \(m\), used in CSMoFN, where \(q\) determines the range of elements of the PSMoT hash vector and \(m\) is the hash vector size. We set \(m=256,\ 512,\ 1024,\ 2048,\ \text{and}\ 4096,\ \text{and}\ q=8,\ 16,\ 32,\ \text{and}\ 64\). Table 2 shows the performance on the six datasets at various settings of \(m\) and a fixed value of \(q=32\). For all datasets, it can be seen that the smaller the value of \(m\), the lower the accuracy performance, which implies a loss of information. As \(m\) increases, the degree of information loss decreases, which leads to a lower EER. For Table 3, we set \(m=4096\) and checked the performance for different values of \(q\). We can observe that although the parameter \(q\) does not have a significant effect on the overall accuracy performance, medium (i.e., \(q=32\)) and small values (such as \(q=8\)) give a slightly higher EER. However, it is better to set \(q\) to a larger value to enhance the security, as a larger \(q\) increases the complexity of a brute-force guessing attack on a hash vector. Figure 7 shows the EER (%) performance for \(m\) and \(q\), while Figure 8 shows the ROC curve and area under the curve (AUC) for six datasets with \(m=4096\) and \(q=32\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Testing Set**} \\ \cline{2-9}  & \multicolumn{1}{c}{**Training**} & \multicolumn{1}{c}{**AR**} & \multicolumn{1}{c}{**Ethnic**} & \multicolumn{1}{c}{**Facesrub**} & \multicolumn{1}{c}{**IMDB**} & \multicolumn{1}{c}{**Pubfig**} & \multicolumn{1}{c}{**YTF**} \\ \hline No. of subjects & 1054 & 126 & 325 & 530 & 2129 & 200 & 1595 \\ No. of images & 166,737 & 700 & 1645 & 31,066 & 40,241 & 9220 & 150,259 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of training and testing datasets. As discussed in Section 3.4, the MDC module reshapes the PSMoT hash vector with size \(m\) to a matrix \(\mathbf{V}^{\prime}\) with size \(k\times n\), and hence \(m=k\times n\). Note that the size of the final hash vector (CB template) is \(k\), with the value of \(k\) dependent on \(m\) and \(n\). For this experiment, we examine two combinations of \(k\) and \(n\), i.e., \((k,\ n)=(128,\ 16)\) and \((256,\ 8)\) with a fixed value of \(m=2048\). The EER is shown in Table 4. We observe that \((256,\ 8)\) outperforms \((128,\ 16)\), which implies that \(k=256\) is a better choice than \(k=128\). It is worth noting that the EERs for the PSMoT hash vector (without reshaping) and \((256\ \times 8)\) are \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Equal Error Rate (EER) (\%)**} \\ \hline \multirow{2}{*}{\(\mathbf{q}=\mathbf{32}\)} & \multicolumn{6}{c}{\(\mathbf{m}\)} \\ \cline{2-6}  & **256** & **512** & **1024** & **2048** & **4096** \\ \hline
**AR** & 11.99 & 8.36 & 7.47 & 6.74 & 5.64 \\
**Ethnic** & 14.66 & 11.51 & 9.49 & 8.58 & 7.40 \\
**Facescrub** & 6.81 & 4.55 & 3.20 & 2.42 & 2.12 \\
**IMDB Wiki** & 14.84 & 10.52 & 8.03 & 6.55 & 5.97 \\
**Pubfig** & 12.43 & 8.81 & 6.69 & 5.44 & 4.56 \\ YTF & 22.55 & 19.05 & 16.61 & 15.16 & 14.33 \\ \hline
**Average** & 13.88 & 10.47 & 8.58 & 7.48 & 6.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy of the model for various values of \(m\) and \(q=32\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Equal Error Rate (EER) (\%)**} \\ \hline \multirow{2}{*}{\(\mathbf{m}=\mathbf{4096}\)} & \multicolumn{4}{c}{\(\mathbf{q}\)} \\ \cline{2-5}  & **8** & **16** & **32** & **64** \\ \hline
**AR** & 6.99 & 5.76 & 5.64 & 5.63 \\
**Ethnic** & 7.29 & 7.21 & 7.40 & 8.05 \\
**Facescrub** & 2.09 & 2.26 & 2.12 & 2.02 \\
**IMDB Wiki** & 6.17 & 6.01 & 5.97 & 5.91 \\
**Pubfig** & 4.94 & 4.31 & 4.56 & 4.62 \\
**YTF** & 14.44 & 14.84 & 14.33 & 14.05 \\ \hline
**Average** & 6.99 & 6.73 & **6.67** & 6.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Accuracy of the model for various values of \(q\) and \(m=4096\).