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Table 4.3 Training and testing performance for approximation of vector operations
C MLP
C RPN ( d
=
1
.
05) C RSS
C RSP
Algorithm
C BP
C RPROP C BP
C RPROP C BP
C RPROP C BP
C RPROP
Network
2-18-4 2-18-4
2-18-4 2-18-4
2-10-4 2-10-4
2-10-4 2-10-4
Parameters
130
130
130
130
114
114
114
114
MSE
(training)
0
.
0010 0
.
0015
0
.
0014 0
.
00057
0
.
0021 0
.
0029
0
.
0013 0
.
0021
SUM 0
.
0008 0
.
0007
0
.
0022 0
.
0020
0
.
0009 0
.
0007
0
.
0006 0
.
0005
MSE
SUB 0
.
0009 0
.
0010
0
.
0026 0
.
0020
0
.
0018 0
.
0009
0
.
0010 0
.
0007
(testing) MULT 0
.
0098 0
.
0010
0
.
0072 0
.
0014
0
.
0092 0
.
0004
0
.
0033 0
.
0003
QUOT 0
.
0029 0
.
0074
0
.
0022 0
.
0010
0
.
0063 0
.
0008
0
.
0013 0
.
0006
SUM 0
.
9983 0
.
9983
0
.
9796 0
.
8838
0
.
9954 0
.
9876
0
.
9975 0
.
9984
Correlation
SUB 0
.
9986 0
.
9963
0
.
9786 0
.
9858
0
.
9958 0
.
9890
0
.
9971 0
.
9980
MULT 0
.
1296 0
.
9063
0
.
1886 0
.
8758
0
.
1454 0
.
9376
0
.
1748 0
.
9812
QUOT 0 . 1096 0 . 1463
0 . 0241 0 . 0218
0 . 0554 0 . 1196
0 . 2780 0 . 3179
SUM 0
.
0009 0
.
0007
0
.
0021 0
.
0022
0
.
0010 0
.
0007
0
.
0006 0
.
0005
Error
SUB 0
.
0009 0
.
0009
0
.
0022 0
.
0020
0
.
0013 0
.
0009
0
.
0010 0
.
0007
.
.
.
.
.
.
.
.
variance MULT 0
0094 0
0009
0
0072 0
0014
0
0082 0
0035
0
0030 0
0003
QUOT 0 . 0041 0 . 0084
0 . 0044 0 . 0021
0 . 0043 0 . 0022
0 . 0013 0 . 0015
AIC
6.14
6.13
6.22
6.18
6.07
5.58
6.47
6.86
Average
epochs
10,000 2,000
10,000 2,000
10,000 2,000
10,000 2,000
functions. The convolution version of complex 2D Gabor functions have the follow-
ing form:
(
x 2
2
1
2
e
x 1 /ʻ)
+
/
2
˃
e 2 ˀ j ( u 0 x 1 + v 0 x 2 )
g
(
x 1 ,
x 2 ) =
(4.37)
2
2
ˀʻ˃
Here,
ʻ
is the aspect ratio,
˃
is the scale factor, and ( u 0 ,
v 0 ) aremodulation parameters.
When
ʻ =
1, the g
(
x 1 ,
x 2 )
becomes circularly symmetric. Thus, the Gabor function
to be approximated is
e x 1 + x 2 / 2 ( 0 . 5 )
2 e 2 ˀ j ( x 1 + x 2 )
1
g
(
x 1 ,
x 2 ) =
(4.38)
2
2
ˀ(
0
.
5
)
Shin and Ghosh [ 47 ] and Li [ 48 ], considered either imaginary or real part of
above function in their simulations. But this section uses complete 2DGabor function
for approximation. For training, 100 input points were randomly selected from an
evenly spaced 10
5. Similarly, 900 input points were
randomly selected for testing froman evenly spaced 30
×
10 grid on
0
.
5
x 1 ,
x 2
0
.
×
30 grid on
0
.
5
x 1 ,
x 2
0
.
5. Figure 4.2 presents the real and imaginary part of 2D Gabor function for this
 
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