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(1) Train SVM with a primary kernel
(Gaussian kernel), then modify training
result according to equalities (8.42), (8.43) and (8.44), we attain
k
! .
k
! .
k
(2) Train SVM with the modified kernel
When SVM use the new training method, the performance of the classifier is
improved remarkably, and the number of support vectors decreases such that it
improves the velocity of pattern recognition.
Exercises
1. Compare Empirical Risk Minimization (ERM) Inductive Principle and
Structural Risk Minimization (SRM) Inductive Principle.
2. What is VC dimension's meaning? Why does VC dimension reflect function
set's learning capacity?
3. What are three milestones of statistics learning theory's? What problem was
resolved in each milestone?
4. Describe support vector machine's primitive idea and mathematical model.
5. Why does statistical learning theory be support vector machine's theory
foundation, and in which area it represent?
6. Under linearly separable case, given a hyperplane defined as follows:
0
T
w
x
+ b
=
where, w denotes weight vector,
b
denotes bias, x denotes input vector. If a
N
i
{
x
}
set of input pattern
satisfy the following conditions
1
i
=
1
T
min ,
|
w
x
+
b
|
=
i
i
=
1
2
,
?
N
(
) is called canonical pair of hyperplane. Prove it that conditions of
canonical pair conduce distance between bounds of two classification is
2/||
w,b
||.
7. Briefly narrate the primitive concept that support vector machine solve
nonlinearity separable problem.
8. Two layer perceptron's inner product kernel is defined as
)
w
T
K
(
x
,
x
)
=
tanh(
β
x
x
+
β
i
0
i
1
β
β
under which values of
and
, the kernel function does not satisfy
Mercer's condition.
9. What is the advantage and limitations for support vector machine and radial
basis function (RBF) network while they respectively solve the following
assignments?
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