Computational Intelligence - February 2017 - 25

where P = [p 1, p 2, f, p n] and Q = [q 1, q 2, f, q n] are probability
distr ibutions. The KL divergence is a positive value,
D (P Q ) $ 0 . If the distributions are the same then the KL
divergence is zero; the closer they are, the smaller the value of
D (P Q ) . Hence, the divergence can be computed for any pair
of Doddington's categories.
In Figure 9, the risks of traveler 04882 (which is on the
watchlist) are evaluated in the KL metric over Doddington's
landscape. In addition to the Doddington's categories, we plot
the KL measures of traveler 04882 at Phase I (04882d62), Phase
II (04882d61), and total. KL measure is in agreement with the
Bayesian inference results (Figure 7) because both methods
show that the traveler is most likely a sheep, less likely a wolf/
lamb, and least likely a goat.
D. Extended Experiment

Consider how the Doddington's detector (Figure 4) operates in
the scenario of two-phase watchlist inference. We have selected
six travelers who are 'Wolves/Lambs,' six 'Goats,' and six 'Sheep.'
The results are reported in Figure 10, where "Phase I" contains
the Doddington's evidence calculated for the non-cooperative
traveler; "Phase II" contains the Doddington's evidence calculated for the cooperative traveler without taking into account
the evidence from Phase I; and "Accumulated" contains the
Doddington's evidence evaluated for the traveler who transitioned to Phase II from Phase I, using the likelihood evidence
from Phase I (Equation 2).
Figure 10 addresses the scenario when the traveler is on the
watchlist. Such a traveler should always be directed to manual
control, and the role of the Doddington's detector is to assist
the border personnel in estimating the potentially dangerous
cases such as intentional impersonation and misidentification
aiming at deceiving the watchlist check.
Scenario I
Travelers in the 'Wolves/Lambs' category on the watchlist (first
session in Figure 10). Consider a typical 'Wolf/Lamb' traveler.
The risk of impersonation is detected at Phase II with a probability of 0.1842. This means that 18 out of 100 individuals on
watchlists will be suspected of impersonation. The two-phase
approach is worthless for security purposes: it decreases the
probability of the detection of impersonation from 0.1842 to

Likelihood

X: 434.1
Y: 0.002559

2
0

100
200
300
400
'Sheep' - Genuine Score
(a)

500

0.015 X: 103.8
Y: 0.01055
0.010
X: 434.1
Y: 1.162e-147

0.005
0

100
200
300
400
'Goat' - Genuine Score
(b)

× 10-3
6 X: 103.8
Y: 0.002585
4
2
0

500

X: 434.1
Y: 0.0002764

pj
qj

× 10-3
X: 103.8
Y: 0.002634

Likelihood

KL divergence = D (P Q ) = / p j log 2

Likelihood

posterior probability intervals are calculated using theory from
[65]. In this scenario with probability intervals, traveler 04882
has a 66.7-100% probability of being a 'Sheep,' a 0.0-31.4%
probability of being a 'Goat' and a 0.0-3.97% probability of
being a 'Wolf/Lamb.'
A useful measure for evaluating the Doddington's landscape
given the similarity of probability distributions is the KullbackLeibler (KL) divergence, or cross-entropy. It is defined by the
equation [66]:

100
200
300
400
'Wolf/Lamb' - Genuine Score
(c)

500

figure 5 likelihood functions of the doddington's classes with respect
to the score threshold; and genuine likelihood. the solid-gray curve marks
the lower and upper bound for the likelihood functions; whereas, the
dash-black curve represents the point probabilities for the likelihood functions. each vertical line represents the different "qualities" of photos used
for authentication: red represents low-quality photos and green is for
high-quality photos. the low scores indicate a potential for false rejects.

Phase I

Phase II

(a)

(b)

figure 6 modeling the two-phase watchlist check scenario: (a): noncooperative traveler waiting for service in front of an automated border control machine; (b): cooperative traveler following the
regulations for face acquisition (subject from the frgc database [61]).

0.0568. This is because the Doddington's detector failed at
Phase I (probability 0.0069, non-cooperative (low-quality
images) traveler).

February 2017 | Ieee ComputatIonal IntellIgenCe magazIne

Table of Contents for the Digital Edition of Computational Intelligence - February 2017