Information Technology Reference
In-Depth Information
The SRM principle takes both factors into account by choosing the subset Sn for
which minimizing the empirical risk yields the best bound on the actual risk.
Figure 8.3. The bound on the structural risk is the sum of the empirical
risk and the confidence interval. (Picture from Vapnik 1995).
8.4 Support Vector Machine
Support Vector Machine (SVM) is a new type of universal learning machine
proposedrecently. SVM has extra advantages for pattern classification.
8.4.1
Linearly separable case
Suppose the training data
x
1
,y
1
…
x
l
,y
l
x
∈
R
n
y
∈
{+1,-1}, where
l
is the sample size, n is the dimension of input data. We can construct a
hyperplane to absolutely separate two-class samples for the case where the
training data are linearly separable. The hyperplane be described as:
(
w
•
x
) + b = 0
(8.19)
