Higher-Order Computational Model for Novel Neurons - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 90

4.3.4 Model-2

Another neuron architecture for complex-valued signals has been defined by an
aggregation function which is also a functional of input signals. Before integration,
the signals are preprocessed through summation and radial basis operations. Such
processed information is integrated in desired proportion ( ), linearly

in theRSS (Rbf-Sigma-Sigma)model. The compensatory parameters

ʳ : ʻ

specify
the contribution of radial basis and summation subfunctions to take into account the
vagueness involved. The union or algebraic sum are inserted in the formulas for
modeling linear operation, expressed here as a

ʳ and ʻ

b . The novel neuron
constructed with this operation is named as RSS. The net potential of this neuron is
defined by following aggregation function:

↕ b = 1 + a +

exp

2

W m Z T W RB ʩ m ( z 1 , z 2 ... z L ) = ʻ m × ʳ m × − Z −

m

(4.13)

The output of this neuron may be expressed as: Y m = f C (ʩ m ( z 1 , z 2 ... z L ))

4.3.5 Learning Rules for Model-2

Consider a three-layer network (L-M-N) based on RSS neuron, similar to network
of RSP neuron. All weights, bias, and input-output signals are complex numbers.
Let Z z L ] be the vector of input signals and Z T = [ z 1 , z 2 ... is transpose of vector

= w 1 m , w Lm is a vector of weights from inputs ( l Z. W m w 2 m ... = 1 ... L )to

Lm is a vector
of weights from inputs to radial basis part of m th RSS neuron. w 0 is a bias and
z 0 =

= w RB

summation part of m th RSP neuron and W RB
m

w RB
2 m

w RB

1 m ,

...

+

j is the bias input. The error gradient and weight update rules for various
weights of a feedforward network of the proposed neuron can be derived as follows:
Let V m be net potential of m th RSS neuron in the hidden layer then fromEq. ( 4.13 )

1

+ ʳ m exp

2

V m = ʻ m W m Z T W RB − Z − + w 0 m z 0 (4.14)

m

From Eq. ( 3.3 ) , the output of a neuron in the hidden layer can be expressed as

f V m + jf V m

Y m =

(4.15)

Output of a neuron in the output layer ( n = 1 ... N ) of considered network is

M

Y n = f C ( V n ) = f C w mn Y m + w 0 n z 0 (4.16)

m = 1