## 5 Results: ROC-Based Measures
### ROC-curves  
Here we calculate and plot entire ROC-curves for several numbers of features and gallery sizes. In Figure 9 we plot the ROC-curves for the synthetic data. In Figure 10 we plot the ROC-curves for the FaceNet data. These ROC-curves facilitate the comparison between entire curves as a function of gallery size.  
As a general matter, entire ROC-curves do not appear to change as a function of gallery size. Since the ROC-curves are based on the characteristics of the genuine and similarity score distributions, it makes sense that the ROC-curves do not change. With increases in gallery size, the distributions will become more well defined, and the median and inter-quartile range (IQR) should become increasingly stable. However, there is no basis for predicting a change in the central tendency or spread of these distributions as gallery size increases.  
Figure 8: **(Top)**: In addition to mean EER, we also evaluated the mean false rejection rate (FRR) at a false positive rate of 0.01%. Here we plot these error rates (mean of 30 repetitions) versus gallery size (1000, 2000, 4000, 8000, 16,000, 32,000, 64,000 subjects) for synthetic data (Band 8). Data shown for 5, 10, 15 and 20 features. The average error rates (shown to the right of the last dot) across gallery size are illustrated with dotted lines. There was some instability at small gallery sizes, but otherwise, the mean error rate did not change as a function of gallery size. **(Bottom)**: FRR at FAR = 0.0001%. Here we plot these error rates (mean of 30 repetitions) versus gallery size (1000 to 10,000 in steps of 1000 subjects) for FaceNet PCA components. Data shown for 5, 10, 15 and 20 PCA components. The average error rates (shown to the right of the last dot) across gallery size are illustrated with dotted lines. The mean error rate did not change as a function of gallery size.  
Figure 9: ROC-curves for synthetic data (Band 8). Curves for 3, 8, 15 and 20 features. Each curve was evaluated at gallery sizes of 2000, 10,000 and 100,000 subjects. Each curve is the average over 30 repetitions. (**A**) illustrates the entire 3 ROC-curves for 3 features. (**B**) illustrates the same data in (**A**) zoomed in on the lower error rates for enhanced visibility. (**C**) illustrates the entire 3 ROC-curves for 8 features. (**D**) illustrates the same data in (**C**) zoomed in on the lower error rates for enhanced visibility. (**E**) illustrates the entire 3 ROC-curves for 15 features. (**F**) illustrates the same data in (**E**) zoomed in on the lower error rates for enhanced visibility. (**G**) illustrates the entire 3 ROC-curves for 20 features. (**H**) illustrates the same data in (**G**) zoomed in on the lower error rates for enhanced visibility. Note that the ROC-curves are essentially overlapping across gallery size.  
Figure 10: ROC-curves for FaceNet PCA components. Plots for 2, 5, 12 and 30 PCA components are displayed. Each curve was evaluated at 1000 and 10,000 subjects. Each curve is the average over 30 repetitions. (**A**) illustrates the entire 2 ROC-curves for 2 features. (**B**) illustrates the same data in (**A**) zoomed in on the lower error rates for enhanced visibility. (**C**) illustrates the entire 2 ROC-curves for 5 features. (**D**) illustrates the same data in (**C**) zoomed in on the lower error rates for enhanced visibility. (**E**) illustrates the entire 2 ROC-curves for 12 features. (**F**) illustrates the same data in (**E**) zoomed in on the lower error rates for enhanced visibility. (**G**) illustrates the entire 2 ROC-curves for 30 features. (**H**) illustrates the same data in (**G**) zoomed in on the lower error rates for enhanced visibility. Note that the ROC-curves are essentially overlapping across gallery size.