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0.16
x 2
^
E (e)
2
1
0.14
0
−1
0.12
−2
x 1
e
−3
0.1
−2
0
2
4
−2
−1
0
1
2
Error Rate (Test) = 0.060
0.134
0.8
^
Error Rate
ZED
0.132
0.6
0.13
0.4
0.128
0.2
epochs
epochs
0.126
0
0
20
40
60
80
0
20
40
60
80
Fig. 5.4
The final converged solution of Example 5.4 with h =3 .
5.1.2.2
Comparing MSE, CE, and ZED
Using formulas (2.5), (2.28) and (5.16) and noting that e i = t i
y i ,onemay
write, for some classifier parameter w that
n
∂ R MSE
∂w
1
n
e i ∂y i
=
∂w ,
(5.20)
i =1
n
∂ R CE
∂w
e i
y i (1
∂y i
∂w ,
=
(5.21)
y i )
i =1
e i G
∂y i
∂w
n
∂ R ZED
∂w
1
nh 3
e i
h
=
.
(5.22)
i =1
Define the following weight functions
ψ MSE ( e )= e,
(5.23)
e
t − y
y (1
ψ CE ( y )=
y ) =
y ) ,
t
∈{
0 , 1
}
,
(5.24)
y (1
ψ ZED ( e )= eG
.
e
h
(5.25)
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