Information Technology Reference
In-Depth Information
as shown in Figure 10.1. From all the possible hyperplanes separating the two
classes,
op
H
is at equal distance between the data points that are nearest to the
boundary between the two classes.
Such data points, satisfying one of the
following conditions
T
wx
b
,
1
for
y
1
0
i
0
T
wx
b
,
1
for
y
,
1
0
i
0
are called
support vectors
(see Figure 10.1).
w
11
w
12
k
1
Summation
x
1
y
Minimizer
x
2
Summation
k
2
:
:
:
:
:
:
x
N
k
N
Summation
w
NN
Figure 10.2.
Structure of a kernel-based machine
to the higher
dimensional feature space is carried out using the
kernel function family
x
[
xx
,
,...,
x
]
Nonlinear mapping from the input space
12
N
kx
() [ (), (), ,
k x k x
k x
()]
1
2
N
which helps in defining the linear discriminant function
N
¦
wk x
()
b
0
(10.5)
ii
i
1
w
,
i
= 1, 2, …,
N
, are parameters of the discrimination
in the feature space, where
function. Assuming that
bwkx
00
() 1
, then Equation (10.5) can be rewritten in
the more compact form
N
¦
wk x
() 0
(10.6)
ii
i
i
0
which is equivalent to the vector form
Search WWH ::
Custom Search