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Fig. 3.9
a Plane and b Surface graphs for Minkowski EF for typical value of r = 4
3.3.2.5 Mean-Median Error Function
This EF takes the advantage of both the mean error function and the median EF.
Hence, reduces the influence of large errors but at the same time retains its convexity.
The mean-median EF is given by
1
e i
2
=
×
+
(3.13)
E
2
1
n
The complex mean-median EF is defined to be
1
1
+ ʵ i ʵ i
2
E
=
2
×
(3.14)
n
where n is the number of outputs (Fig. 3.10 ).
3.3.2.6 Sine-Hyperbolic Error Function
This EF is steeper than the quadratic EF. Moreover the function is symmetric about
the origin and hence the update involves two parts, the first is the gradient in the
first quadrant while the second is gradient in the third quadrant. In both cases, the
gradient is directed toward the origin. The sine-hyperbolic error function is given by
 
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