Chapter 5 Basic System Errors (Alireza Tavakkoli).
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Transcript of Chapter 5 Basic System Errors (Alireza Tavakkoli).
Chapter 5
Basic System Errors
(Alireza Tavakkoli)
2
Outline
• Matching
• The Receiver Operating Curves (ROC)
• Error Conditions Specific to Biometrics
• Negative Authentication
• Trade-offs
3
Matching
• Definition
• Notations:Biometric Uniqueness
4
Matching Scores
• Similarity measure Prob (B=B’)– Higher match score Higher Prob.
• Similarity d(B’,B)– [0,Inf.) [0,1]
5
The Tail of Two Errors
• Hypothesis Test and Errors:
• Two Errors:– False Match (Type I)– Flase Non-match (Type II)
NonMatchHhypothesisAlternate
MatchHhypothesisNullThe
a
:
: 0
6
Score Distributions
Hard Decision
Reliability of s
7
FMR and FNMR
x
y
a
xFNMRdsHspxF
yFMRdsHspyG
0|
1|
T
s m
T
s
T
nTs nTs a
dsspdsHspTFNRM
dsspdsspdsHspFMR
0|)(
1|
8
Estimating Error from Data
• Access to G(y) & F(x)
• Estimation:
• Need to be studied more
N
jjj
i
M
ii
sN
sN
sG
sM
sM
sF
1
1
#11ˆ
#11ˆ
YY
XX
9
Error Rates of Match Engines
• FM and FNM – Accept/Reject Object
• FA and FR– Accept/Reject Null Hypothesis
10
Positive Authentication
• Errors in Pos. Authentication:– False Accept (FA)– False Reject (FR)
• Problems:– FA Security Breach– FR Convenience Problems
11
ROC
T
TTROC
TTT
1,0
0,1
FNMR,FMRROC
- Design vs Application
- Security vs Convenience
FMR ↑ FNMR ↓
12
Variations of ROCs
Semi-log plots
Log-log plot
13
Using the ROC Curve
• Comparing matchers– Tradeoff between FMR & FNMR.– Specific Threshold FMR(T)/FNMR(T)
14
Expressing Quality of ROC
• The Equal Error Rate:
• d-prime:
• Expected Overall Error
• Cost Function
15
Expressing Quality of ROC
• The Equal Error Rate:
16
Expressing Quality of ROC
• d-prime:
22'
nm
nmd
17
Expressing Quality of ROC
• Expected Overall Error
TEE
pp
pTFNMRpTFMRTE
T
GI
GI
min
1
)(
min
18
Expressing Quality of ROC
• Cost Function
GFAGFNM PFMRCPFNMRCCost 1
19
Error Conditions Specific to Biometrics
• FTAFTEFTU Significant Cost.
• FTA:
• FTE:
• Manual vs Automatic Authentication
• CMC or RPM
20
Negative Authentication
• Negative Hypotheses:
• The Two Errors:– Falsely missing B– Incorrectly matching B
and B’.
21
Negative Authentication
• Detection Theory Terminology:– False Negative– False Positive
22
Trade Offs
• Different Errors Different Outcomes– False Accept Security Breach.– False Reject Inconvenience.
• Convenience vs Security• Cost vs Security• Cost of Negative Authentication
23
Convenience vs Security
• Convenience of a Biometric
• Convenience of Implementation
FAR1
FRR1
Security
eConvenienc
24
Cost vs Security in Pos. Auth.
• Why it is important
– FRR ↑ Service denial Exception handling
• Dynamic Authentication Protocol
FRRCost
25
Cost of Negative Authentication
• Screening:
• Higher FPR&FNR Inconvenient to all
FPR
FNR1
Cost
Security
26
Neg. Vs Pos. Authentiocation
27
• Questions?