Why Temporal Persistence of Biometric Features, as Assessed by the Intraclass Correlation Coefficient, Is So Valuable for Classification Performance
Abstract
:1. Introduction
2. Prior Work
2.1. Prior Work on Permanence in Biometrics
2.2. How This Work Differs from Our Earlier Article
…“each subject (dataset) serves as his or her (its) own control. This typically gives within-subjects designs considerably more power than between-subjects designs. That is, this makes within-subjects designs more able to detect an effect of the independent variable than are between-subjects designs.” (online statistics book: http://onlinestatbook.com/2/research_design/designs.html#:~:text=An%20advantage%20of%20within%2Dsubjects,levels%20of%20performance%20are%20controlled.&text=That%20is%2C%20this%20makes%20within,than%20are%20between%2Dsubjects%20designs).
3. Creation and Analysis of Synthetic Datasets
3.1. Creation of Synthetic Data
3.2. Creation of Sets of Features with Varying Degrees of Persistence
Algorithm 1 Creating Synthetic Features. |
Input: N (subjects), K (features), Output: 3-dimensional () feature matrix with desired correlation structure for for Set where Z is a random standard normal deviate. Set for for for Set ; where W is a random normal deviate with mean = 0 and standard deviation = For each feature j, treat as a single vector of length and apply a z-score transform to ensure mean = 0 and standard deviation = 1 |
3.3. Biometric Performance Assessment
3.4. Plotting Similarity Score Distributions for Each Band
3.5. Discussion of Results
4. Evaluation of the SBA Dataset
4.1. Description of the SBA Dataset
4.2. Biometric Assessment of SBA Dataset
4.3. Results with SBA Dataset
5. Evaluation of the Gait1 Dataset
5.1. Description of the Gait1 Dataset
5.2. Biometric Assessment of the Gait1 Dataset
5.3. Results with Gait1 Dataset
6. Comparing Synthetic and Real Data Results
6.1. Discussion of Results
6.2. Relationship between ICC Band and Median Intercorrelation between Features
6.3. Relationship between the IQR of Impostor Distributions and Median Intercorrelation
6.4. The Effects of Decorrelation
7. General Discussion
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
ECG Electrocardiogram EER Equal Error Rater |
ICC Intraclass correlation coefficient IQR Interquartile Range |
PDF Probability density function |
ROC Receiver Operating Characteristic |
Appendix A. R Code to Create Datasets of Synthetic Features
*********************************************** R Code to Create Datasets of Synthetic Features *********************************************** # Load relevant libraries library(mise) library(lme4) library(matrixStats) mise() # Clear out variables # Close all previous connections closeAllConnections() n<-1000 # Number of Subjects k<-10 # Number of Features s<-2 # Number of Sessions. For~Biometrics, s = 2. ICC_Target<-0.7 # Target ICC # Fill feature matrix with zeros Feature_Matrix <- array(0,dim=c(n,k,s)) # Generate standard normal data for first session of # all features Feature_Matrix[,,1] <- rnorm(n*k,0,1) # Set session 2 measurements equal to the first # session measurements Feature_Matrix[,,2] <- Feature_Matrix[,,1] # At this point, Both session measurements match for # each feature (for each individual) and ICC = 1.0. # There is perfect # agreement. We need to add # noise to features to obtain a lower ICC. The # noise we add will have a mean of 0 and a # SD = SD_Noise, calculated as: SD_Noise<-sqrt((1-ICC_Target)/ICC_Target); # Add this noise to all features Feature_Matrix <- Feature_Matrix + rnorm(n*k*s,0,SD_Noise) # Now we vertically concatenate the sessions # to get a single matrix of dimension n*s x k Both_Sessions <- rbind(Feature_Matrix[,,1],Feature_Matrix[,,2]) # Get the column Means FeatureMeans<-colMeans(Both_Sessions) cat(sprintf(’Column Means: 1:%0.3f 2:%0.3f 3:%0.3f 4:%0.3f 5:%0.3f 6:%0.3f 7:%0.3f 8:%0.3f 9:%0.3f 10:%0.3f\n’, FeatureMeans[1],FeatureMeans[2],FeatureMeans[3],FeatureMeans[4], FeatureMeans[5],FeatureMeans[6],FeatureMeans[7],FeatureMeans[8], FeatureMeans[9],FeatureMeans[10])) FeatureSDs<-colSds(Both_Sessions) # Get the column SDs. cat(sprintf(’Column SDs: 1:%0.3f 2:%0.3f 3:%0.3f 4:%0.3f 5:%0.3f 6:%0.3f 7:%0.3f 8:%0.3f 9:%0.3f 10:%0.3f\n’, FeatureSDs[1],FeatureSDs[2],FeatureSDs[3],FeatureSDs[4], FeatureSDs[5],FeatureSDs[6],FeatureSDs[7],FeatureSDs[8], FeatureSDs[9],FeatureSDs[10])) # Create a Subject Number vector Subject<-c(seq(1:n),seq(1,n)) # Now we create a Session Vector Session<-vector(mode=’numeric’,length = 0) Session[1:n]<-1; Session[(n+1):(n*2)]<-2; # Horizontally concatenate the Subject Vector, # the Session vector and the feature data into a # single dataframe. Feature_DF <-data.frame(Subject,Session,Both_Sessions) names(Feature_DF)<-c("Subject","Session","Feat01","Feat02","Feat03", "Feat04","Feat05","Feat06","Feat07","Feat08", "Feat09","Feat10") cat(sprintf(’\nWhich directory will the data be written to: %s\n\n’,getwd())) FeatureFileName<-paste0(’SynthFeatSet_NSess_2_ICC_Targ_’, as.character(ICC_Target*10),’_NFeat_’,as.character(k),’_NSubs_’, as.character(n),’.csv’) #Write out a .csv file with the synthetic features write.csv(Feature_DF,FeatureFileName,row.names = FALSE) # Below we illustrate how to compute the ICC using # variance components. auto <- function(x) as.data.frame(VarCorr(lmer(x~(1|Feature_DF$Subject) + (1|Feature_DF$Session),REML = TRUE, na.action=na.omit))) lmer_results_apply<-apply(Feature_DF[,1:k+2], 2, auto) ICCs<-vector(mode=’numeric’, length=k) for (i in 1:k){ a<-unlist(lmer_results_apply[i]) VarSub=as.numeric(a[10]) VarSession=as.numeric(a[11]) VarErr=as.numeric(a[12]) TotalVariance<-sum(VarSub,VarSession,VarErr) ICCs[i]<-VarSub/TotalVariance cat(sprintf(’For Feature %2.2d, VarSubject = %0.3f, VarSession = %0.3f, VarErr = %0.3f, TotVar = %0.3f, ICC = %0.3f\n’, i,VarSub,VarSession,VarErr,TotalVariance,ICCs[i])) } ICC_DF<-data.frame(ICCs) names(ICC_DF)<-c("ICC") ICCFileName<-paste0(’SynthFeatSet_ICCs_NSess_2_ICC_Targ_’, as.character(ICC_Target*10),’_NFeat_’,as.character(k),’_NSubs_’, as.character(n),’.csv’) # Write out .csv file with ICCs write.csv(ICC_DF,ICCFileName,row.names = FALSE)
Appendix B. Variability in Similarity Score and EER Estimates
Median of | Minimum of | Maximum of | Median of | Minimum of | Maximum of | |
---|---|---|---|---|---|---|
Medians of | Medians of | Medians of | Medians of | Medians of | Medians of | |
Genuine | Genuine | Genuine | Impostor | Impostor | Impostor | |
Similarity | Similarity | Similarity | Similarity | Similarity | Similarity | |
Band | Scores | Scores | Scores | Scores | Scores | Scores |
0 | 0.489 | 0.482 | 0.493 | 0.461 | 0.452 | 0.466 |
1 | 0.542 | 0.536 | 0.553 | 0.461 | 0.456 | 0.469 |
2 | 0.599 | 0.592 | 0.610 | 0.462 | 0.454 | 0.470 |
3 | 0.654 | 0.647 | 0.658 | 0.464 | 0.453 | 0.470 |
4 | 0.708 | 0.700 | 0.714 | 0.459 | 0.452 | 0.468 |
5 | 0.764 | 0.758 | 0.767 | 0.463 | 0.457 | 0.466 |
6 | 0.818 | 0.811 | 0.822 | 0.462 | 0.458 | 0.472 |
7 | 0.868 | 0.864 | 0.874 | 0.458 | 0.454 | 0.470 |
8 | 0.924 | 0.920 | 0.928 | 0.461 | 0.450 | 0.476 |
9 | 0.973 | 0.969 | 0.981 | 0.461 | 0.450 | 0.471 |
Median of | Minimum of | Maximum of | Median of | Minimum of | Maximum of | |
---|---|---|---|---|---|---|
IQRs of | IQRs of | IQRs of | IQRs of | IQRs of | IQRs of | |
Genuine | Genuine | Genuine | Impostor | Impostor | Impostor | |
Similarity | Similarity | Similarity | Similarity | Similarity | Similarity | |
Band | Scores | Scores | Scores | Scores | Scores | Scores |
0 | 0.168 | 0.159 | 0.175 | 0.168 | 0.166 | 0.171 |
1 | 0.164 | 0.154 | 0.177 | 0.168 | 0.165 | 0.169 |
2 | 0.156 | 0.148 | 0.161 | 0.168 | 0.165 | 0.170 |
3 | 0.148 | 0.139 | 0.153 | 0.167 | 0.165 | 0.170 |
4 | 0.134 | 0.124 | 0.140 | 0.168 | 0.166 | 0.171 |
5 | 0.115 | 0.109 | 0.126 | 0.167 | 0.166 | 0.169 |
6 | 0.096 | 0.087 | 0.103 | 0.167 | 0.164 | 0.168 |
7 | 0.072 | 0.067 | 0.078 | 0.169 | 0.165 | 0.170 |
8 | 0.045 | 0.042 | 0.049 | 0.168 | 0.163 | 0.171 |
9 | 0.017 | 0.013 | 0.019 | 0.168 | 0.164 | 0.171 |
Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | |
---|---|---|---|---|---|---|
Band | Synthetic | Synthetic | SBA | SBA | Gait1 | Gait |
0 | 43.95 | 47.20 | 47.39 | 49.33 | ||
1 | 36.10 | 38.08 | 41.84 | 43.59 | ||
2 | 27.20 | 29.47 | 34.90 | 37.64 | ||
3 | 20.40 | 21.98 | 30.18 | 31.96 | ||
4 | 13.70 | 15.95 | 25.84 | 29.02 | 31.25 | 34.27 |
5 | 8.00 | 10.00 | 20.47 | 22.82 | 25.00 | 28.57 |
6 | 4.10 | 5.20 | 17.45 | 21.19 | 19.30 | 25.44 |
7 | 1.50 | 2.15 | 10.61 | 16.14 | 15.56 | 18.96 |
8 | 0.23 | 0.60 | 6.71 | 10.91 | 10.51 | 16.47 |
9 | 0.00 | 0.01 |
Median of | Minimum of | Maximum of | Median of | Minimum of | Maximum of | |
---|---|---|---|---|---|---|
Medians of | Medians of | Medians of | Medians of | Medians of | Medians of | |
Genuine | Genuine | Genuine | Impostor | Impostor | Impostor | |
Similarity | Similarity | Similarity | Similarity | Similarity | Similarity | |
Band | Scores | Scores | Scores | Scores | Scores | Scores |
0 | 0.502 | 0.491 | 0.515 | 0.488 | 0.482 | 0.490 |
1 | 0.554 | 0.539 | 0.565 | 0.488 | 0.482 | 0.494 |
2 | 0.621 | 0.607 | 0.641 | 0.490 | 0.486 | 0.494 |
3 | 0.680 | 0.660 | 0.694 | 0.489 | 0.484 | 0.493 |
4 | 0.735 | 0.706 | 0.752 | 0.487 | 0.484 | 0.492 |
5 | 0.805 | 0.785 | 0.818 | 0.488 | 0.484 | 0.489 |
6 | 0.847 | 0.840 | 0.855 | 0.487 | 0.485 | 0.491 |
7 | 0.899 | 0.893 | 0.908 | 0.487 | 0.482 | 0.490 |
8 | 0.939 | 0.934 | 0.943 | 0.487 | 0.478 | 0.491 |
Median of | Minimum of | Maximum of | Median of | Minimum of | Maximum of | |
---|---|---|---|---|---|---|
IQRs of | IQRs of | IQRs of | IQRs of | IQRs of | IQRs of | |
Genuine | Genuine | Genuine | Impostor | Impostor | Impostor | |
Similarity | Similarity | Similarity | Similarity | Similarity | Similarity | |
Band | Scores | Scores | Scores | Scores | Scores | Scores |
0 | 0.249 | 0.252 | 0.230 | 0.234 | 0.285 | 0.293 |
1 | 0.256 | 0.238 | 0.220 | 0.233 | 0.275 | 0.257 |
2 | 0.244 | 0.251 | 0.231 | 0.238 | 0.272 | 0.271 |
3 | 0.244 | 0.265 | 0.212 | 0.243 | 0.261 | 0.293 |
4 | 0.243 | 0.256 | 0.228 | 0.249 | 0.274 | 0.267 |
5 | 0.219 | 0.266 | 0.189 | 0.253 | 0.233 | 0.282 |
6 | 0.184 | 0.313 | 0.169 | 0.292 | 0.206 | 0.332 |
7 | 0.120 | 0.302 | 0.104 | 0.293 | 0.147 | 0.357 |
8 | 0.078 | 0.308 | 0.074 | 0.299 | 0.093 | 0.362 |
Median of | Minimum of | Maximum of | Median of | Minimum of | Maximum of | |
---|---|---|---|---|---|---|
Medians of | Medians of | Medians of | Medians of | Medians of | Medians of | |
Genuine | Genuine | Genuine | Impostor | Impostor | Impostor | |
Similarity | Similarity | Similarity | Similarity | Similarity | Similarity | |
Band | Scores | Scores | Scores | Scores | Scores | Scores |
4 | 0.758 | 0.739 | 0.769 | 0.493 | 0.492 | 0.497 |
5 | 0.827 | 0.800 | 0.834 | 0.494 | 0.491 | 0.496 |
6 | 0.871 | 0.852 | 0.892 | 0.496 | 0.493 | 0.499 |
7 | 0.902 | 0.888 | 0.910 | 0.492 | 0.489 | 0.494 |
8 | 0.950 | 0.941 | 0.952 | 0.493 | 0.491 | 0.494 |
Median of | Minimum of | Maximum of | Median of | Minimum of | Maximum of | |
---|---|---|---|---|---|---|
IQRs of | IQRs of | IQRs of | IQRs of | IQRs of | IQRs of | |
Genuine | Genuine | Genuine | Impostor | Impostor | Impostor | |
Similarity | Similarity | Similarity | Similarity | Similarity | Similarity | |
Band | Scores | Scores | Scores | Scores | Scores | Scores |
4 | 0.319 | 0.280 | 0.369 | 0.366 | 0.340 | 0.379 |
5 | 0.249 | 0.234 | 0.277 | 0.377 | 0.348 | 0.407 |
6 | 0.190 | 0.161 | 0.236 | 0.414 | 0.374 | 0.441 |
7 | 0.144 | 0.119 | 0.164 | 0.391 | 0.367 | 0.403 |
8 | 0.087 | 0.071 | 0.107 | 0.433 | 0.400 | 0.478 |
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Friedman, L.; Stern, H.S.; Price, L.R.; Komogortsev, O.V. Why Temporal Persistence of Biometric Features, as Assessed by the Intraclass Correlation Coefficient, Is So Valuable for Classification Performance. Sensors 2020, 20, 4555. https://doi.org/10.3390/s20164555
Friedman L, Stern HS, Price LR, Komogortsev OV. Why Temporal Persistence of Biometric Features, as Assessed by the Intraclass Correlation Coefficient, Is So Valuable for Classification Performance. Sensors. 2020; 20(16):4555. https://doi.org/10.3390/s20164555
Chicago/Turabian StyleFriedman, Lee, Hal S. Stern, Larry R. Price, and Oleg V. Komogortsev. 2020. "Why Temporal Persistence of Biometric Features, as Assessed by the Intraclass Correlation Coefficient, Is So Valuable for Classification Performance" Sensors 20, no. 16: 4555. https://doi.org/10.3390/s20164555
APA StyleFriedman, L., Stern, H. S., Price, L. R., & Komogortsev, O. V. (2020). Why Temporal Persistence of Biometric Features, as Assessed by the Intraclass Correlation Coefficient, Is So Valuable for Classification Performance. Sensors, 20(16), 4555. https://doi.org/10.3390/s20164555