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artificial neural network. The learning algorithms in complex domain derived from
anyEF( E
:
−→
C
R ) explicitly minimize only the magnitude error.
3.3.2.1 Quadratic Error Function
The quadratic EF ( E
R ) for practical data analysis in real domain is
developed by mean squared error, which is given by
:
R
−→
e i
E
=
(3.5)
n
The complex quadratic EF ( E
:
C
−→
R ) is defined to be
ʵ i ʵ i
E
=
(3.6)
n
where n is the number of outputs and superscript
represents the complex conjugate
of variable. This is widely accepted as the standard EF (Bose and Liang 1996). Its
plane and surface plots are given in Fig. 3.6 a and b, respectively.
3.3.2.2 Absolute Error Function
Absolute error is one of several robust functions that displays less skewing of error
due to outliers. A small number of outliers are less likely to affect the total error
and so they do not affect the learning algorithm as severely as the quadratic error.
Fig. 3.6
a Plane and b Surface plots for quadratic EF
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