## 2 Creation and Analysis of Synthetic Data Sets
### Biometric Performance Assessment for Synthetic Features  
All of the synthetic analyses for this report are based on Band 8 (\(0.8<ICCs\leq~{}0.9\)). This was chosen because in our face recognition data set, described below, all of the features had ICCs in this range as well. A synthetic dataset with 50 features, and 100,000 subjects studied on 2 sessions with ICC in Band 8 was constructed. Biometric performance was evaluated using various numbers of features. Given very low or non-existent inter-correlations between features, the number of features is a proxy for biometric performance. Higher numbers of features always produce better biometric performance. The number of features ranged from 2 to 20 for both synthetic and FaceNet data, depending on the goal of the analysis. The precise number is always provided for each analysis. These features were randomly selected from the full set of 50 features. For one analysis of the synthetic data, we employed gallery sizes of of 1000, 2000, 4000, 8000, 16,000, 32,000 or 64,000 subjects. For other types of analysis, gallery sizes were 1000,  
Figure 2: (**A**) Frequency histogram of ICCs for 1000 features with an \(ICC_{Target}=0.7\). This was from a synthetic data set with 10,000 subjects. (**B**) Frequency histogram of correlations between 1000 features for 10,000 subjects, two sessions, with an \(ICC_{Target}=0.7\). Note that the median and maximum are of the absolute value of the correlations. 10,000 or 100,000 subjects. We employed the cosine distance metric, since we have shown in an earlier (unpublished) report that the best biometric performance was produced with this choice (Link to unpublished report: [[https://www.doi.org/10.13140/RG.2.2.17510.06727](https://www.doi.org/10.13140/RG.2.2.17510.06727)]([https://www.doi.org/10.13140/RG.2.2.17510.06727](https://www.doi.org/10.13140/RG.2.2.17510.06727)), (accessed on 20 October 2022)). The resulting distance measures were scaled to go from 0 to 1 and then they were reflected (1 - distance) to compute similarity scores. The Rank-1 IR for a data set represents how often (what percent of the time) the greatest similarity score for a probe subject was for the same subject in the gallery. A \"genuine\" distribution of similarity scores was constructed from the similarity scores for each subject and their self. All other similarity scores were considered impostors. Applying different decision thresholds to the genuine and impostor similarity scores yields false acceptance and false rejection rates. These can be plotted as a receiver operating characteristic (ROC) curve. The EER is the point on this curve at which the false acceptance rate (FAR) and the false rejection rate (FRR) are equal. The number of similarity scores is equal to (gallery size)\({}^{2}\). However, we can only do exact ROC analyses in computer memory for up to 20,000 subjects. Therefore we created software which estimates ROC-based measures for much larger sample sizes, and which does not hold all of the similarity scores in memory. We will call the large scale procedure for estimating ROC-based measures BIG_ROC. Python code is available at [[https://digital.library.txstate.edu/handle/10877/16141](https://digital.library.txstate.edu/handle/10877/16141)]([https://digital.library.txstate.edu/handle/10877/16141](https://digital.library.txstate.edu/handle/10877/16141)), (accessed on 20 October 2022). Download big_roc-master_12_04_2019.zip. The core of this analysis is the computation of the genuine and impostor distribution frequency histograms. All the ROC-based statistics are computed from these two histograms. First, both frequency histograms are initialized to zero. We use 1000,000 bins of equal size. Cosine similarity scores can assume values from 0 to 1, so each bin has a width of 1/1000,000. Then both histograms are computed from genuine and impostor similarity scores of subjects from session 1 and session 2. The similarity scores are calculated iteratively, in batches of 1000 subjects from each session per batch (1000,000 similarity scores at a time).