## 5 Results and Discussion  
### \(\mathcal{F}_{intra}\) Intra-Lingual Experiments  
We initiate this section by presenting a thorough evaluation of the proposed inference 5 \(\times\) 2 intra-lingual fold schemes. From the aforementioned material exposed so far, we have an abundant number of experiment cases, given the fact that there are (a) two kinds of classifiers (SVM, DSC-BSF); (b) two kinds of RDVs, \(\Psi_{\mathbf{X,Y}}\) (local pole) and \(\Psi_{\mathbf{X,Y}}^{\mathbf{I}}\) (common pole), and corresponding vectors \(v_{\mathbf{X,Y}}\) or \(dv_{\mathbf{X,Y}}\); (c) two ways to fuse the \(v_{\mathbf{X,Y}}\) or \(dv_{\mathbf{X,Y}}\) vectors and thus create the experimental setups _LFWI_, _TFWI_ (serial) and _LFW2_, _TFW12_ (parallel); (d) three measures (i.e., AIRM, Stein, Jeffrey) for the creation of the RDVs \(\Psi_{\mathbf{X,Y}}\) and \(\Psi_{\mathbf{X,Y}}^{\mathbf{I}}\) (e) two ways to form the \(\omega^{-}\) learning set \(\omega_{\mathbb{T}_{\mathbb{R}}\text{ or }\mathbb{V}}^{-100\% RF}\) (or \(\omega_{\mathbb{T}_{\mathbb{R}}\text{ or }\mathbb{V}}^{-0\% RF}\)); and (f) five datasets. To avoid misperception, Table 3 provides an indicative subset of the labels used in order to characterize the experimental setups. We make use of the subsequent terminology \(\underset{Fusion_{\text{final}}}{RDV_{\text{final}}}\mathcal{E}(SPD_{measure}, \omega_{way}^{-},\Delta)\) in order to label the experiments according to the design parameters. For example, \(\underset{LFWI}{\Psi_{\mathbf{X,Y}}}\mathcal{E}(S,0,SV)\) denotes an experiment with local pole \(\Psi_{\mathbf{X,Y}}\) RDV,  
Figure 6: Depiction of the TFW1 testing protocol. For a pair of signature images, a set of 14 covariance matrices are evaluated and fed as pairs to the trained model verifier in order to evaluate the local scores. Sorting and averaging created a stack of fourteen levels \(D_{a}\in\mathbb{R}^{Q^{\pm}\times N_{\text{REF}}}\) between all possible pairs \(\mathbb{Q}^{\pm}\times\mathbb{N}_{REF}\). The final vector \(FSV\big{(}a|\mathbb{Q}^{\pm}\big{)}\in\mathbb{R}^{|Q^{\mp}|}\) is evaluated by taking the minimum distance of any \(\mathbb{Q}^{\pm}\) over all \(\mathbb{N}_{REF}\). Figure 8: \(\mathcal{F}_{intra}\) and LFW1 experimental setup: average \(EER_{SF}^{user}\) (%) MCYT dataset. Commenting on the content of Figures 7-11, a number of useful comparisons can be deducted regarding the \(EER_{SF}^{user}\) efficiency with respect to the following design pa rameters: (a) SVM vs. DSC-BFS, (b) local pole \(\Psi_{\mathbf{X},\mathbf{Y}}\) vs. common pole \(\Psi_{\mathbf{X},\mathbf{Y}}^{\mathbf{I}}\) RDVs, (c) \(\omega^{-100\%RF}\) vs. \(\omega^{-0\%RF}\), and (d) the use of AIRM, Stein, or Jeffrey measure for the formation of the RDVs content. * With respect to the employment of the SVM or the DSC-BFS as the signature verifier, it is evident that all datasets exhibit superior performance under the SVM classifier when compared to the DSC-BFS in terms of average \(EER_{SF}^{user}\). Furthermore, the SVM module demonstrates higher robustness with respect to SPD measures A, S, and J. This is evidenced by a higher proportion of cases exhibiting lower \(EER_{SF}^{user}\) results in comparison to the DSC-BFS cases. * With respect to the use of the local \(\Psi_{\mathbf{X},\mathbf{Y}}\) or common pole \(\Psi_{\mathbf{X},\mathbf{Y}}^{\mathbf{I}}\) RDVs highlighted in Figures 7-11 it is evident that, with the notable exception of the HINDI dataset, SVM verifier and \(\omega^{-0\%RF}\), clearly the common pole \(\Psi_{\mathbf{X},\mathbf{Y}}^{\mathbf{I}}\) RDV provides the best average \(EER_{SF}^{user}\) in all cases. A possible explanation for the higher discriminative capabilities of the common pole \(\Psi_{\mathbf{X},\mathbf{Y}}^{\mathbf{I}}\) RDV approach is that, in the local \(\Psi_{\mathbf{X},\mathbf{Y}}\) approach, the RDVs are created without having fixed poles, thus making the conditioned class outputs of the \(\left(-\right)_{\mathcal{M}}\) operator somehow incompatible with each other.