Information Technology Reference
In-Depth Information
Machines [3], Kernel Fisher's Discriminant Analysis (KFDA) [11], Kernel Princi-
pal Component Analysis (KPCA) [12] and Kernel Partial Least Squares (KPLS)
[13] can use the RBF function to build interval data models in classification,
regression and novelty detection.
5.3
Interval Data Mining with Kernel-Based Methods
5.3.1
Support Vector Classification (SVC)
Let us consider a binary linear classification task depicted in figure 5.2 with
m
data points in a
n-dimensional
input space
x
1
,x
2
,...,x
m
having corresponding
labels
y
i
=
1. SVM classification algorithm aims to find the best separating
surface as being furthest from both classes. It is simultaneously to maximize the
margin between the support planes for each class and minimize the errors. This
can be accomplished through the quadratic program (4).
±
m
m
m
min (1
/
2)
y
i
y
j
α
i
α
j
K
x
i
,x
j
−
α
i
i
=1
j
=1
i
=1
m
s.t.
y
i
α
i
=0
(5.4)
i
=1
C
≥
α
i
≥
0(
i
=1
,...,m
)
where
C
is a positive constant used to tune the margin and the errors.
Fig. 5.2.
Linear support vector classification
