1. Biometric ROC Curves Methods of Deriving Biometric Receiver Operating Characteristic Curves from the Nearest Neighbor Classifier Robert Zack dissertation work Also see Pace University CSIS Technical Report No. 268, November 2009 PDF Version

2. Biometric ROC Curves Receiver Operating Characteristic (ROC) Curves – A Quick Review Used for binary decisions Signal detection – signal / no signal Medical diagnosis – disease / no disease Biometric authentication – you are the person you claim to be / you are not In biometrics the ROC curve varies from FAR=1 & FRR=0 at one end to FAR=0 & FRR=1 at other FAR = False Accept Rate – the rate an imposter is falsely accepted FRR = False Reject Rate – the rate the correct person is falsely rejected

3. Biometric ROC Curves Standard Biometric ROC Curve

4. Biometric ROC Curves ROC curves easily obtained from parametric classification techniques As t varies from 0 to infinity. For a specific t, you get a specific point on the ROC. FAR varies from 0 to 1 and FRR from 1 to 0

5. Biometric ROC Curves Nearest Neighbor Non-Parametric Classification Technique Makes no assumptions about the data Data are not drawn from or fitted to probability distributions Test samples are classified based on distances to training samples No standard method of obtaining ROC curves

6. Biometric ROC Curves Nonparametric - k Nearest Neighbor (kNN) Pattern Classification Procedure Underlying prob. density function is: unknown and no form assumed Go directly to decision a function here k=5 Use odd numbers and take the majority Now, how can we get ROC curve?

7. Biometric ROC Curves Vector Difference Authentication Model Transforms biometric samples from a many-class problem feature space into a two- class problem in feature-distance space

8. Biometric ROC Curves ROC Curve Derivation from m-matching, k Nearest Neighbors Two procedures: vary m from 0 to infinity Unweighted m-match kNN (m-kNN) equal weight on all within-class matches Weighted m-match kNN (wm-kNN) heavier weights applied to closer matches first investigated linear weighting k, k-1, k-2, …, 1

9. Biometric ROC Curves ROC Curve Derivation from unweighted m-matching, k Nearest Neighbors W=Within B=Between Authenticate if m of the kNN within-class. m varies from 0 to k for points on ROC curve. All W’s are equal in weight. If m=0, all users accepted (FAR=1,FRR=0) If m=7, few users accepted (FAR=small, FRR=large).

10. Biometric ROC Curves ROC Curve Derivation from weighted m-matching, k Nearest Neighbors Authenticate if W choices > weighted match (m) m varies from 0 to n n= k(k+1)/2. Here, 7+6..+1=28 weights of m vary from 7 to 1, with the closest having the highest weight. For every m, you have a FAR/FRR pair on ROC curve If n=0, all users accepted (FAR=1,FRR=0) If n=28, few users accepted FAR=small and FRR=large

11. Biometric ROC Curves FAR and FRR versus threshold m for unweighted m-kNN procedure for k = 10 DeskCopy (left) and LapFree (right) plots of FAR and FRR versus the threshold m for the unweighted m-kNN procedure for k = 10.

12. Biometric ROC Curves Keystroke Biometric ROC curves: unweighted and weighted methods for k = 10, 15, 20

13. Biometric ROC Curves ROC Curve Derivation using Distance Threshold from Questioned Sample When t = 0, no user authenticated, at ∞ all users authenticated Threshold t starts at 0, increments by 0.1, data exhausted at t=5 EER is about 15 at t=2 Key Finding: threshold method performs poorly

14. Biometric ROC Curves ROC Curve Derivation using Distance Threshold from Questioned Sample

15. Biometric ROC Curves Future Work Investigate two types of enrollment Weak enrollment (for which the system was designed) – the individuals being tested are not part of the training (initial enrollment) group, although reference enrollment samples are used in the authentication process Strong enrollment – the individuals being tested are part of the training (initial enrollment) group, and additional reference (enrollment) samples are used in the authentication process