## 5 Results: ROC-Based Measures
### Similarity Score Distribution Metrics  
ROC-curves are based on genuine and impostor similarity score distributions. We were interested in evaluating changes in similarity score distributions as a function of gallery size. To this end, we evaluated the median and IQR of both genuine and impostor distributions as a function of number of features and gallery size. The results for synthetic data are presented in Figure 11 and for FaceNet data in Figure 12. All dots are means and each mean is associated with an SD error bar. Often, the SD was so small that it was not visible. For synthetic data, this was especially the case for the impostor IQR (Figure 11D. The effect of number of features was extremely strong with no overlap. Of these 4 plots, this statement was only true for Figure 11D. In Figure 11A, note the very narrow range, and the large degree of overlap of medians from the genuine distributions. In Figure 11C, again note the very narrow range, and the large degree of overlap of medians from the impostor distributions. The pattern in Figure 11B resembles that in Figure 11D, but the effect was relatively weak. From this analysis we conclude that, as features are added and biometric performance improves, it was mostly the change in the spread of the impostor distribution that was driving the biometric results, at least for synthetic data.  
The results for the FaceNet data are presented in Figure 12. For each plot, the dot represents the mean and the SD error bars are also plotted. Often, the SD was so small that it was not visible. There are many more invisible error bars in Figure 12 than in Figure 11. Although there was very little overlap in all the plots, notice the range in Figure 11D and compare it to the other ranges. Clearly the effect of number of features on the impostor IQR was remarkable compared to all the other metrics. From this analysis we conclude that, as features are added and biometric performance improves, it was mostly the change in the spread of the impostor distribution that is driving the biometric results for the FaceNet data.  
Figure 11: (**A**) Median of the genuine similarity score distributions for synthetic data. Data are for the Band 8 data set with 4, 8, 15 and 20 features. Each dot is based on 30 repetitions. The error bars are at \(\pm 1\)\(SD\). The numbers at the top of each plot are the average EERs across the gallery sizes represented. (**B**) IQR of the genuine similarity score distributions for the same data in (**A**). (**C**) Median of the impostor similarity score distributions. (**D**) IQR of the impostor similarity score distributions.  
To compare the contribution of each distribution metric (median and IQR) to EER, we performed a stepwise linear regression. The dependent variable was the mean EER for all features sets. The independent variables were the medians and IQRs of the two distributions. We did this analysis for both synthetic and face recognition data sets. For both data sets, the first independent variable entered into the model was for the impostor IQR (synthetic: \(p=2\ *10^{-15}\), \(r^{2}=0.998\); real: \(p=1.8\ *10^{-6}\), \(r^{2}=0.979\)). This is consistent with the idea that the decrease in impostor IQR with increasing features was the driving force behind the lower EERs obtained.  
Note that the particular patterns we see in Figures 11 and 12 may be related to the distance metric (cosine) that we have employed. In the future, we hope to evaluate the role of distance metric and other design elements on the pattern of these similarity score medians and IQRs as performance improves.