A Neural Approach to Cursive Handwritten Character Recognition Using Features Extracted from Binarization Technique - Complex System Modelling and Control Through Intelligent Soft Computations - page 747

The back-propagation algorithm applies a correction

D w ji ð n Þ

to synaptic weights

which is proportional to partial derivative o eð n Þ
o w ji ð n Þ

w ji ð n Þ which can be written as:

o eð n Þ

Þ ¼ o eð

n Þ

Þ : o

e j ð n Þ

Þ : o

y j ð n Þ

Þ : o

v j ð n Þ

ð 6 Þ

w ji ð n e j ð n y j ð n v j ð n w ji ð n Þ

o o o o o

Diffrentiating Eq. ( 2 ) with respect to e j ð n Þ

Þ
o e j ð n Þ ¼

o eð

n

e j ð n Þ ð 7 Þ

Differentiating Eq. ( 1 ) w.r.t. y j ð n Þ

e j ð n Þ

o

Þ ¼

1 ð 8 Þ

y j ð n

o

Differentiating Eq. ( 5 ),

y j ð

Þ

o n

Þ ¼ / j ð v j ð n ÞÞ

ð 9 Þ

v j ð n

o

Differentiating Eq. ( 4 ) w.r.t. w ji ð n Þ

o v j ð n Þ
o

Þ ¼

y i ð n Þ ð 10 Þ

w ji ð n

Using Eqs. ( 7 - 10 ) in Eq. ( 6 ),

o eð

n Þ

Þ/ j ð

Þ ¼

e j ð n v j ð n ÞÞ y i ð n Þ ð 11 Þ

w ji ð n

o

The correction w ji ð n Þ applied to w ji ð n Þ is de ned by

D

o eð

Þ

n

D w ji ð n Þ¼g

w ji ð n Þ

o

ð 12 Þ

Þ/ j ð ¼ g e j ð n v j ð n ÞÞ y i ð n Þ

¼ gd j ð n Þ y i ð n Þ

Thus the weight updates for output unit can be represented as

w ji ð n Þ¼gd j ð n Þ y i ð n Þ ð 13 Þ

D

where g is a constant called learning rate parameter, d is local gradient and is a

derivative of error with respect to v j and y is the input.