Database Reference
In-Depth Information
Table 2.10
Summary of the RBF network learning with randomly selected centers,
applied to image retrieval
Input:
N
i
The training samples
=
{
x
i
}
1
for a given query
x
q
=
Output:
The final retrieval set, containing
k
-relevant samples
=
S
k
Initialization:
Number of RBF centers
N
m
Setting RBF width to a positive constant,
=
˃
i
≤
1
,
i
=
1
,...,
N
m
Repeat:
User provides class label
l
i
,
i
=
1
,···,
N
,
l
i
∈{
0
,
1
}
N
M
i
N
i
Select RBF center
{
z
i
}
ↂ {
x
i
}
=
1
=
1
t
:
ʻ
=
G
t
G
−
1
y
Calculate weights
ʻ
=[
ʻ
1
,...,
ʻ
N
m
]
where
G
=
K
ij
exp
x
i
z
j
2
−
K
ij
=
−
,
i
=
1
,...,
N
;
j
=
1
,...,
N
m
2
j
2
˃
t
y
=[
y
1
,...,
y
i
,...,
y
N
]
,
y
i
ₐ
l
i
T
, calculate
f
N
m
i
=
1
For
n
=
1
,
2
,...,
(
x
n
)=
∑
ʻ
i
K
(
x
n
,
z
i
)
Obtain
k
-nearest neighbor:
x
q
)=
x
x
k
)
f
f
S
k
(
|
(
x
)
≥
(
where
S
k
is the set of top
k
ranked samples.
N
i
=
1
{
x
i
}
ₐ
S
k
(
x
q
)
Until:
User is satisfied with the retrieval result.
2.4.3
Adaptive Radial-Basis Function Network
Problems in adaptive image retrieval are considered as a special case for function
approximation. The characteristics of learning are quite different. First, the training
data size for image retrieval is very small compared to the general approximation
strategy. Second, the training samples available for image retrieval are highly
correlated, i.e., each sample is selected from a specific area of the input space and
is near to the next, in the Euclidean sense. When the training samples are highly
correlated, the choice of centers is the most important factor. The BRF network
will be ill-conditioned, owing to the near-linear dependency caused by some centers
being too close together [
44
].
In order to circumvent the environmental restrictions in image retrieval, an
adaptive learning strategy for the RBF network is introduced and referred to as
adaptive RBF network (ARBFN). This is a special network for learning in image
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