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neuron models can be obtained as its special cases by varying the value of
d
. These
are as follows:
When
d
=
1the
C
RPN model turn out to be conventional neuron (
C
MLP), then
from (
4.27
)
n
Y
(
z
1
,
z
2
...
z
n
;
w
1
,
w
2
...
w
n
)
=
f
C
w
k
z
k
(4.28)
k
=
0
which is the conventional neuron
2
model proposed in real and complex domain as
cases apply.
Now, considering all variables in real domain, when
d
ₒ
0 then (
4.25
) and (
4.27
)
yield:
f
n
x
w
k
k
Y
(
x
1
,
x
2
...
x
n
;
w
1
,
w
2
...
w
n
)
=
lim
d
M
=
(4.29)
ₒ
0
k
=
0
which is a multiplicative neuron proposed in [
41
] whose functional capability is
proved there in.
When
d
=−
1 then Eq.
4.27
yields:
f
1
k
=
0
Y
(
x
1
,
x
2
...
x
n
;
w
1
,
w
2
...
w
n
)
=
(4.30)
w
k
x
k
which is a harmonic neuron model proposed in [
42
].
When
d
=
2 then from Eq.
4.27
:
f
1
/
2
n
w
k
x
k
Y
(
x
1
,
x
2
...
x
n
;
w
1
,
w
2
...
w
n
)
=
(4.31)
k
=
0
This is a neuron model which is conceptually similar to the quadratic neuron pre-
sented in [
20
,
43
].
4.3.7 Learning Rules for Model-3
Consider, a three-layer network (L-M-N) of
C
RPN model, first layer consists of
L inputs (
l
=
1
...
L
), second and output layer has M (
m
=
1
...
M
) and N
2
In this topic, a neuron with only summation aggregation function is referred to as a 'conventional
neuron' and a standard feedforward neural network with these neurons is referred to as as 'MLP'
(multilayer perceptron).
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