Support Vector Machines
Sample Exercises
1. Suppose you are considering the results of learning to classify some training set via
support vector machines using two different kernels. From the classification results
and the αvalues, how might you compare the two kernels in terms of overall classi-
fication performance on the training data and overfitting?
2. Recall that the key criterion relating a kernel function to a map is:
k(x, x0) := Φ(x),Φ(x0)
What is the purpose of the map, Φ? Why is this relationship so useful?
3. Given the following data set, provide a map function that would allow these points
to be linearly separable. Justify how the points can be so separated.
x1x2d
3
4
3
4⊕
3
2
1
4⊕
1−1
−1
4
1
2
−3
2
1
4
−3
4-1 ⊕
x1
x2
−3/2 −1 −1/2 0 1/2 1 3/2
−3/2 −1 −1/2 0 1/2 1 3/2