# Ocular Biometrics Recognition by Analyzing Human Exploration during Video Observations
## 5 Experiments and Results
### Experimental Phase #2: Soft-Biometrics Identification
Thus, the global stability is defined as the average of the \(Stability(C_{i})\), i.e., (Equation (10)):  
\[Stability=\frac{1}{t_{s}}\sum_{i=1}^{t_{s}}Stability(C_{i}) \tag{10}\]  
The discriminability, instead, is defined as in Equation (11):  
\[Discriminability=\frac{1}{2K}\sum_{i=1}^{K}\sum_{j=1}^{K}\frac{t_{i}}{K}d(c_{i}, c_{j})^{2} \tag{11}\]  
where \(c_{i}\) and \(c_{j}\) are the average computed, respectively, on the points composing the clusters \(i\) and \(j\), and \(K\) the number of subjects. Results are plotted in Figure 12. It is worth noting that stability monotonically increases while considering more components, whereas the discriminability value decreases while less than about 50 components are retained, before slightly increasing again. This suggests that the trade-off between stability and separability is to retain a number of components that are almost in the middle of the range [0-50]. Since strictly related works in the state of the art dealt with the task of identification as a whole (clips and sessions were not separated [20] or not available [43]), a similar operation has been performed in the UserWGaze dataset by joining all sequences and afford a fair comparison. Figure 13 reports the SPCA, t-SNE, and classification analysis on the whole dataset. In this case, 28 components are retained. In particular, the 2D representation of the first two principal components is in Figure 13a, the embedding obtained with the t-SNE using the proposed pipeline is in Figure 13b), and a comparison of SVM and k-NN classifiers is in Figure 13c). It can be observed that, even if sometimes SVM is more accurate, in most of the cases the k-NN based approach outperforms the SVM classifier, included when 28 components are chosen. Since the analysis of soft biometrics discriminability is usually carried out using hit/penetration plots, in Figure 14 the top-N accuracy varying the number of classes for different values of k of the k-NN classifier is reported. To get this plot, different values of k have been tested in order to have continuous confidence outcomes instead of the discrete ones (0 or 1). The plot confirms, once again, that the gaze patterns provide useful information to discriminate soft biometrics. Figure 12: Stability (**a**) and discriminability (**b**) plots while varying the number of retained SPCA components. A final comparison with some leading methods in the state of the art is resumed in Table 2. In particular, five previous works have been compared and the most relevant performance and used benchmark dataset are reported for each of them. Some additional notes have been also added to highlight the pro and cons of each work. The table clearly shows that the accuracy in subject identification is comparable with that in the works [18, 36, 42] where, as depicted in the last column reporting notes, initialization, calibration, or expensive eye tracker are required. In addition, the proposed approach outperforms the work in [20], despite it removes the constraint of the previous work of using an RGBD sensor. The pipeline in [43] has been also compared and its results have been reproduced using the UserWGaze dataset. It can be observed that the maximum accuracy reached in [43] is higher but, in that work, authors used an a posteriori analysis, presenting a method that is not fully automated. In fact, authors employed the rank, but it needs the class label for a query vector. If the pipeline in [43] is reproduced applying the fully automatic approach, it is possible to observe how our solution is more accurate. Finally, two general considerations may be made: (1) it is here useful also to remark again that, differently from all the comparing approaches, in this paper, a new benchmark dataset is provided with both facial images and extracted gaze tracks, and (2) the proposed work describes the whole computer vision pipeline that works on raw images and provides evidence of the biometrics identification using extracted gaze tracks.