Neurocomputing in Complex Domain - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 60

Fig. 3.7 a Plane and b Surface plots for absolute error function

When it is applied to data prone to outliers, analysis obtains a better curve of fit
than quadratic EF. Absolute EF is a generalisation of the absolute function defined
to compute errors using the absolute function yet retaining the functional form. The
absolute error in real domain is given by (Fig. 3.7 )

E = | e i | (3.7)

n

The complex absolute EF ( E : C −→ R ) is defined to be

ʵ i ʵ i E = (3.8)

n

where n is the number of outputs. In the complex absolute EF, the definition is a
surface as both real and imaginary parts are involved in it. It can also be noted that
the function form in fact is the quadric cone. The complex EF is not differentiable
at the origin as the function inside the radical is always positive (Fig. 3.7 ).

3.3.2.3 Fourth Power Error Function

This EF will be useful when dealing with data known to be free from outliers, or in
cases where it is important to minimize the worst-case error, rather than the average
error (Hassoun 1995). The Fourth Power EF is:

e i

E = (3.9)

n