robert zack dissertation work also see

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


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


Standard Biometric ROC Curve


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


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


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?


Vector Difference Authentication Model

Transforms biometric samples from a many-class problem feature space into a two-class problem in feature-distance space


ROC Curve Derivation fromm-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


ROC Curve Derivation from unweighted

m-matching, k Nearest Neighbors

W1

W2

W3

W4W5

W6

Q

B1B2

W7 W8

W9

B4

B3

B5

B6

B7

B8

k = 7m = 4

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).


ROC Curve Derivation from weighted m-matching, k Nearest Neighbors

W1

W2

W3

W4W5

W6

Q

B1B2

W7 W8

W9

B4

B3

B5

B6

B7

B8

k = 7m = 4

•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


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.


Keystroke Biometric ROC curves: unweighted and weighted methods for

k = 10, 15, 20


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


ROC Curve Derivation using Distance Threshold from Questioned Sample


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

robert zack dissertation work also see

Documents