Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 93

K w

S

j

' w w (3.4)

i

w

i

where K is a positive learning parameter determining the speed of convergence to
the minimum.

w 0 bias

X 0 = 1

x 1

w 1

x 2 u j

output

w 2

Summing
Element

f ( u j )

:
:

y j

x n

w n

f' ( u j )

weights

desired
output

-

Learning rate

+

Training
Algorithm

d j

Summing
Element

Product

Figure 3.12. Backpropagation training implementation for a single neuron

Now, taking into account that from (3.3) follows:

,

e dy df u (3.5)

j j j j j

where

n

u ¦ x .

j i i

i 0

By applying the chain rule

K ww

Se

j j

' ww w (3.6)

i

ew

j i

to Equation (3.5) we get

w e w e w u

j j j

'
w

we K K e (3.7)

i j j

w w u w w

i j i

This can further be transformed to