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Combining Inductive and Analytical Learning
TangentProp Example
X
are images of single handwritten characters.
Task is to correctly classify these characters.
B is "the target function is invariant to small rotations of the character in the image". How do we express this mathematically?
Define a transformation
s
(
α
,
x
)
which rotates
x
by
α
degrees. Then say
∂
f
(
s
(
α
,
x
i
)
)
∂
α
=
0
Then incorporate these into the error function. How?
Add an additional term to the error function
E
=
∑
i
[
(
f
(
x
i
)
-
f
^
(
x
i
)
)
2
+
μ
i
∑
j
(
∂
f
(
s
j
(
α
,
x
i
)
)
∂
α
-
∂
f
^
(
s
j
(
α
,
x
i
)
)
∂
α
)
(
α
=
0
)
2
]
then modify the gradient descent rule to use this. How?
José M. Vidal
.
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