## 5 Results and Discussion
### \(\mathcal{F}_{inter}\) Cross-Lingual Experiments
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Experiment Label**} & \multicolumn{5}{c}{**Average EER per Signature Dataset**} \\ \cline{2-6}  & **CEDAR** & **MCYT** & **GPDS300** & **BANGLA** & **HINDI** \\ \hline \(\frac{\Psi_{\mathbf{X},\mathbf{Y}}}{LFW2}\mathcal{E}(J,100,DS)\) & 2.021 & 2.534 & 2.290 & 0.709 & 1.420 \\ \hline \(\frac{\Psi_{\mathbf{X},\mathbf{Y}}^{\dagger}}{LFW2}\mathcal{E}(J,0,SV)\) & 0.531 & 3.957 & 2.108 & **0.531** & 0.972 \\ \hline \(\frac{\Psi_{\mathbf{X},\mathbf{Y}}^{\dagger}}{LFW2}\mathcal{E}(J,0,DS)\) & 0.973 & 4.048 & 1.800 & 0.888 & 1.493 \\ \hline \(\frac{\Psi_{\mathbf{X},\mathbf{Y}}^{\dagger}}{LFW2}\mathcal{E}(J,100,SV)\) & 1.064 & 2.586 & 3.444 & 0.995 & 1.668 \\ \hline \(\frac{\Psi_{\mathbf{X},\mathbf{Y}}^{\dagger}}{LFW2}\mathcal{E}(J,100,DS)\) & 2.123 & 3.735 & 2.671 & 2.210 & 2.534 \\ \hline \multicolumn{6}{c}{Common pole—LFW1, a = 8} \\ \hline \(\frac{\Psi_{\mathbf{X},\mathbf{Y}}^{\dagger}}{LFW1}\mathcal{E}(J,0,SV)\) & 0.864 & 4.037 & 1.861 & 0.885 & 1.544 \\ \hline \(\frac{\Psi_{\mathbf{X},\mathbf{Y}}^{\dagger}}{LFW1}\mathcal{E}(J,0,DS)\) & 0.846 & 2.991 & 1.171 & 0.790 & 2.721 \\ \hline \(\frac{\Psi_{\mathbf{X},\mathbf{Y}}^{\dagger}}{LFW1}\mathcal{E}(J,100,SV)\) & 1.115 & 3.536 & 2.064 & 0.853 & 1.767 \\ \hline \(\frac{\Psi_{\mathbf{X},\mathbf{Y}}^{\dagger}}{LFW1}\mathcal{E}(J,100,DS)\) & 1.775 & 2.603 & 1.638 & 0.718 & 2.578 \\ \hline \end{tabular}
\end{table} 
Table 6: _Cont._RDV approach, the SVM classifier, and the \(a=8\) segment index to ensure fairness and robustness through all datasets and the \(\mathcal{F}_{intra}\) protocol. A comparative inspection of the results indicates that the _LFW1_/_TFW1_ serial protocol has superior (i.e., lower) verification error rates when compared to the parallel _LFW2_/_TFW2_ one. Moreover, by inspection of Figure 12 it is also evident that the verification error rates can drop much more for the local _LFW1_/_TFW1_ protocol for higher values of the segment index \(a>8\). Figure 12: Average \(ER_{SF}^{user}\) (%) for the \(\mathcal{F}_{inter}\) and LFW1/TFW1 experimental setup for all datasets. TR denotes the learning dataset \(D_{i}\), while TS denotes all the remaining testing datasets \(D_{j\
eq i}\). The AIRM measure is used. As Figure 12 and Tables 7 and 8 illustrate, the poor verification performance exhibited by both classifiers when the BENGALI and HINDI datasets are employed for learning purposes is discernible. Specifically, the BENGALI and HINDI subsets demonstrate suboptimal performance when their learned verifier models are evaluated against the CEDAR, MCYT, and GPDS300 dataset. This deficiency in the performance can be attributed to the fact that the Bengali and Hindi SPD points are derived from corresponding binary images, which consequently gives rise to covariance matrices with their first line and column equal to zero, apart from the first variance, which is set to one. On the other hand, this is not observed when the verifiers learn from gray-scale signatures emerging from the CEDAR, MCYT, and GPDS300 datasets. Therefore, it can be inferred that higher generalization necessitates the utilization of gray-scale images in lieu of binary images. In summary, we provide the following assertions:  
* The common pole RDV \(\Psi^{I}_{\mathbf{X},\mathbf{Y}}\) accompanied by the local _LFWI/TFWI_ protocol provides lower verification error rates. * For the case of testing signatures emerging from fixed a priori acquisition conditions and signature styles (e.g., Western, Asian) as in the \(F_{intra}\) protocol, the use of the \(\omega^{-0\%RF}\) seems to be more efficient. On the other hand, in the case of having unknown a priori acquisition conditions and signature styles as in the \(F_{inter}\) protocol, the use of the \(\omega^{-100\%RF}\) seems to be more efficient. * For the \(F_{inter}\) protocol and the local _LFWI/TFWI_, efficiency seems to be an increasing function of segment index \(a\).