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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)