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Here, the Chi square statistic was used as the dissimilarity measure of two LBP-TOP
histograms computed from the components:
L
Q
i
)
2
(
P
i
−
χ
P,Q
=
(2)
P
i
+
Q
i
i
=1
where
P
and
Q
are two CSF histograms, and
L
is the number of bins in the histogram.
3
Multi-classifier Fusion
We consider a
C
-class classification problem. A pattern described by CSF is, in general,
a p-dimensional vector
X
. It is associated with a class label which can be represented
by
ω
t
∈{
1
)
represents the probability of the pattern
X
belonging to a given
i
-th class, given that
X
was observed. It is then natural to classify the pattern by choosing the
j
-th class with
largest posteriori probability:
...,C
}
. Consider also the a posteriori probability function
P
(
ω
t
=
i
|
X
P
(
ω
t
=
j
|
X
)= max
i∈{
1
,...,C}
P
(
ω
t
=
i
|
X
)
(3)
Some studies [19,20] show better classification can be obtained if multiple classifiers
are used instead of a single classifier. Consider that we have
R
classifiers (each repre-
senting the given pattern by a distinct measurement vector [19]), which are denoted as
D
k
,k
,...,R
, for the same pattern
X
.Inthe
k
-th single classifier, its outputs are
approximated by a posteriori probabilities
P
=1
(
ω
t
=
i
|
X
)
,i.e.
P
(
ω
t
=
i
|
D
k
)=
P
(
ω
t
=
i
|
X
)+
ε
i
(
X
)
(4)
where
ε
i
(
represents the error that a single classifier introduces.
From Eqn. 4, we consider a classifier that can approximate the a posteriori proba-
bility function
P
X
)
is small. According to Bayesian theory, the
pattern
X
should be assigned to the
i
-th class provided the a posteriori probability of
that interpretation is maximum:
Assign
X
(
ω
t
=
i
|
X
)
,when
ε
i
(
X
)
→{
ω
t
=
j
}
if
P
(
ω
t
=
j
|
X, D
1
,...,D
R
)= max
i∈{
1
,...,C}
P
(
ω
t
=
i
|
X, D
1
,...,D
R
)
(5)
Fig. 3.
The structure of multi-classifier fusion
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