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Table 4.1 Comparison of training and testing performance for Wine Data problem
S. No.
Training
Neuron
Network
Average
MSE
Testing
algorithm
type
epochs
training
error (%)
R -MLP
13-6-1
45,000
0.0065
2.8
1
R BP
R RPN
(
d
=
0
.
85
)
13-4-1
35,000
0.0034
2.8
R RSS
13-2-1
40,000
0.0039
2.8
R RSP
13-2-1
29,000
0.0040
2.8
R MLP
13-5-1
2,000
0.0047
2.8
2
R RPROP
R RPN
(
d
=
0
.
85
)
13-4-1
2,000
0.0019
1.4
R RSS
13-2-1
2,000
0.0032
2.8
R RSP
13-2-1
2,000
0.0028
1.4
C MLP
13-3-1
35,000
0.0034
1.4
3
C BP
C RPN
(
d
=
0
.
85
)
13-1-1
17,000
0.0026
1.4
C RSS
13-1
20,000
0.0039
2.8
C RSP
13-1
15,000
0.0029
1.4
C MLP
13-1-1
2,000
0.0012
0.0
C RPN ( d = 1 . 1 )
4
C RPROP
13-1-1
1,500
0.0011
0.0
C RSS
13-1
1,500
0.0027
1.4
C RSP
13-1
1,500
0.0020
0.0
the ionosphere. The targets were free electrons in the ionosphere. Simulations use
first 200 instances for training and remaining 150 instances for testing. Table 4.2
presents comparative performance of different networks with training algorithms viz
R BP , C BP (
μ
+
ʷ =
0
.
004) and R RPROP , C RPROP (
=
0
.
5
=
1
.
2
min
=
10 ( 6 ) max
1). Results clearly mention that a RPN-based net-
work achieve minimum test error with least training epochs when implemented in a
complex domain.
=
0
.
003
0
=
0
.
4.4.2 Complex Domain Problems
4.4.2.1 Approximation of Vector Operations
A complex number corresponds to a vector with the coordinates as its components. In
fact a complex number ' z ' is referred as a radius vector from the origin to the point
that represents ' z '. The vector interpretation of complex number is very useful in
analyzing various geometrical relationships on a plane. The set of complex number
is well equipped with basic algebraic operations. The summation (SUM), subtraction
(SUB), multiplication (MULT), and Quotient (QUOT) of two complex number is a
complex number and is very helpful in defining different vector operations in the two
dimensional space. This experiment is conducted to design a learningmachine, which
 
 
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