Digital Signal Processing Reference
In-Depth Information
Fig. 5.
Covering two neighbor points (2-Dim)
2
xx qxxx
−
,(, , ) 0
<
i
i
j
2
2
dxxx
(, , )
=−
xx qxxx
, (, , )
>−
x x
(4)
i
j
j
i
j
i
j
2
2
xx
−−
qxxx
(, , ),others
i
i
j
qxx x
is defined as below.
(, , )
i
Among this expression, where
j
x
−
x
j
i
q
(
x
,
x
,
x
)
=
x
−
x
,
i
j
i
x
−
x
j
i
(5)
The definition of covering S can be shown in formula 6.
S
(
x
;
x
,
x
,
r
)
=
{
x
|
d
2
(
x
,
x
,
x
)
<
r
2
}
i
j
i
j
(6)
As for a sample pair, classifier
c:X
→
Y
is defined as the probability according to
an unknown distribution
D
over
XY
×
.
3
Algorithm
Suppose that in constructive neural network, the whole mapping objects are con-
structed step by step. Samples covering objects can be generated with different proce-
dure number. The whole architecture is shown in Fig.6.
Let's consider the binary classification problem. The input space is
X
, an arbi-
trary subset of
, and the output is
Y={0,1}
which is a binary classification
problem. Therefore a pair of input and output can be symbolized as
z{x, }
≡
,
xX,yY
∈∈
. The output sequence of the Samples Mapping Objects can be written
