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Table 2.12
Comparison of RBF learning methods
Method
Learning algorithm
N
p
i
X
+
=
{
x
i
}
ARBFN
Table
2.11
, RBF centers: using positive samples in
1
; RBF width:
=
Eq. (
2.54
)
EDLS [
43
]
The weight and bias of the second layers were calculated by the least squares
criterion; RBF centers: using all samples in
N
p
i
=
1
N
n
i
=
1
; RBF width:
x
i
}
x
i
}
{
∪{
˃
=
0
.
8 for all RBF units
N
p
i
=
1
N
n
i
=
1
using the orthogonal least
square method. The RBF center selection starts zero centers, and new centers
were iteratively picked in the subsequent selection procedure. Each time, the
network's mean square error was checked and compared to the pre-defined
tolerance set at 0.0001; RBF width:
x
i
}
x
i
}
OLS [
44
]
RBF centers: selecting from
{
∪ {
˃
=
0
.
8 for all RBF units
Table 2.13
Average precision rate (%) as a
Pr
(
Iter
.
)
function
of
iteration,
,
obtained
by
retrieving 35 queries, using Corel dataset
Method
Iter. 0
Iter. 1
Iter. 2
Iter. 3
ARBFN
44
.
82
80
.
72
90
.
36
92
.
50
EDLS
44
.
82
50
.
18
43
.
39
43
.
04
OLS
44
.
82
66
.
07
73
.
21
76
.
61
retrieved set was associated with the RBF centers [Eq. (
2.43
)], using a one-to-one
correspondence. This is named as EDLS (exact design network using the least
squares criterion). For both methods, the final RBF network model can be written as:
i
=
1
ʻ
i
exp
N
m
2
−
x
−
z
i
f
(
x
j
)=
ʻ
0
+
(2.79)
i
2
˃
where
N
m
=
16 for the OLS learning method,
since the size of retrieved samples is set to 16 at each feedback iteration.
The query image set used here is identical to the experiments reported in
Sect.
2.3.3
. Precision (
Pr
) was recorded after each query iteration. Table
2.13
summarizes the average precision results,
Pr
16 for the EDLS method, and
N
m
≤
, as a function of iteration, taken
over the 35 test queries. It can be seen from the results that the ARBFN significantly
improved the retrieval accuracy (up to 92 % precision). The first iteration showed
an improvement of 35.9 %. The ARBFN outperformed the OLS (76.61 %) and the
EDLS. This result confirms that the ARBFN learning strategy offers a better solution
for the construction of an RBF network for adaptive image retrieval, compared to
the two standard learning strategies.
Both the OLS and the EDLS strategies usually perform well under the opposite
condition, where the training samples are sufficiently large [
46
], and where the
data samples may not correlate closely to each other. In this experiment, it
was observed that the EDLS achieved improvement after the first iteration (i.e.,
Pr
(
Iter
.
)
(
Iter
.
=
1
)=
50
.
2 %), because the retrieved data at
Iter
.
=
0 usually has a low
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