DM825 - Introduction to Machine Learning
Sheet 8, Spring 2013 [pdf format]

Exercise 1 – Support vector machines

Suppose that the following are a set of points in two classes:

class 1:

⎡
⎢
⎣

1

1

⎤
⎥
⎦

⎡
⎢
⎣

1

2

⎤
⎥
⎦

⎡
⎢
⎣

2

1

⎤
⎥
⎦

class 2:

⎡
⎢
⎣

0

0

⎤
⎥
⎦

⎡
⎢
⎣

1

0

⎤
⎥
⎦

⎡
⎢
⎣

0

1

⎤
⎥
⎦

Plot them and find the optimal separating line. What are the support vectors, and what is the margin.

Exercise 2

Consider the four input points of an XOR function. Find a way to separate out the true cases from the false ones by using a linear separator.

Exercise 3

Show that, irrespective of the dimensionality of the data space, a data set consisting of just two data points, one from each class, is sufficient to determine the location of the maximum-margin hyperplane.