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In-Depth Information
subject to:
P
(
Y
I
=
y
I
)
P
(
Y
c
=
y
c
|
Y
I
=
y
I
)
f
k
∑
y
I
P
=
(
f
c
|
f
k
)
,
k
∈ {
0
}∪
I
,
(2.89)
P
(
f
k
)
I
. In addition,
P
where
c
(
·
)
represents the empirical probabilities directly estimated from the training samples,
f
c
=
∈
C
and
c
∈
I
because
P
(
Y
c
=
1
|
Y
I
=
1
)
≡
1for
c
∈
1 otherwise. Using a matrix-based
representation, solving the above optimization leads to the result that
Y
c
and
f
k
=
Y
k
when
k
=
0 and
f
k
=
N
−
1
P
=
M
×
×
f
(2.90)
where
=
P
P
Ya
|
C
/
I
|
Y
I
t
P
(
Y
a
1
|
Y
I
)
,
P
(
Y
a
2
|
Y
I
)
,...,
(2.91)
⊡
P
f
a
1
|
⊤
P
P
(
f
a
1
|
f
0
)
(
f
a
1
|
f
I
1
)
···
f
I
|
I
|
⊣
P
f
a
2
|
⊦
P
P
(
f
a
2
|
f
0
)
(
f
a
2
|
f
I
1
)
···
f
I
|
I
|
M
=
(2.92)
.
.
.
.
.
.
P
f
a
|
C
/
I
|
f
I
|
I
|
P
f
a
|
C
/
I
|
f
0
P
f
a
|
C
/
I
|
f
I
1
···
⊡
⊤
1
1
···
1
P
f
I
1
|
⊣
⊦
P
(
f
I
1
|
f
0
)
1
···
f
I
|
I
|
N
=
(2.93)
.
.
.
.
.
.
P
f
I
|
I
|
f
0
P
f
I
|
I
|
f
I
1
···
1
f
0
,
t
f
=
f
1
,...,
f
I
|
I
|
(2.94)
and
|
C
/
I
|
=
{
a
1
,
a
2
,...,
a
|
C
/
I
|
}
.
2.5.4
Experimental Result
In the experiment, four methods summarized in Table
2.15
were compared. A total
of 200 classes of images was selected from the COREL image collection, with 50
images in each class. The resulting 10,000 images and the vendor-defined categories
were used as the database and the ground truth for evaluating the performance. From
the database, 10 queries are selected from each of the 200 classes, resulting in 2,000
queries being selected, each of which is composed of two different images. Under
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