Higher-Order Computational Model for Novel Neurons - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 89

f V m + jf V m

Y m =

(4.4)

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 (4.5)

m = 1

Update equation for learning parameters in output layer

f ( ( f ( ( ʔ w mn = ʷ Y m ( ( e n ) V n )) + j ( e n ) V n ))) (4.6)

f ( ( f ( ( ʔ w 0 n = ʷ z 0 ( ( e n ) V n )) + j ( e n ) V n ))) (4.7)

The update equations for learning parameters between input and hidden layer are as
follows:

z l ʻ m 1 V ˀ m ʓ m

ʾ m

N

w lm = ʔ + + j (4.8)

exp

2 z l −

lm

2 N

w RB
lm

W RB
m

w RB ʔ = − Z −

ʓ m (ʳ m ) 1

+ V ˀ m − (ʳ m ) V ˀ m

+ ʾ m (ʳ m ) 1 + V ˀ m + (ʳ m ) V ˀ m

(4.9)

Z T 1 V ˀ m ʓ m

N W m

ʾ m ʔʻ m = + + j (4.10)

exp

2 1

V ˀ m ʓ m ʾ m

N

W RB
m

ʔʳ m = − Z − + + j (4.11)

z 0 ʓ m

ʾ m

N

ʔ

w 0 m =

+

j (4.12)

N

n = 1 { (

ʓ m f ( ( V m )) f ( ( where = e n ) V n )) ( w mn )

f ( ( + ( e n ) V n )) ( w mn ) }

N

ʾ m f ( ( V m )) f ( ( and =

1 { (

e n ) V n )) ( w mn )

n =

f ( ( − ( e n ) V n )) ( w mn ) }