# Discussion on Support Vector Machines

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Homework # 11: Support Vector Machines (Chap. 9)
Due May 3.
1. (Chap. 9, # 3, p. 368) Here we explore the maximal margin classifier on a toy data set.
(a) We are given n = 7 observations in p = 2 dimensions. For each observation, there is an associated
class label.
Obs. X1 X2 Y
1 3 4 Red
2 2 2 Red
3 4 4 Red
4 1 4 Red
5 2 1 Blue
6 4 3 Blue
7 4 1 Blue
Sketch the observations.
(b) Sketch the optimal separating hyperplane, and provide the equation for this hyperplane such as in
exercise #1.
(c) Describe the classification rule for the maximal margin classifier. It should be something along the
lines of “Classify to Red if β0 + β1X1 + β2X2 > 0, and classify to Blue otherwise”. Provide the
values for β0, β1, and β2.
(d) On your sketch, indicate the margin for the maximal margin hyperplane.
(e) Indicate the support vectors for the maximal margin classifier.
(f) Argue that a slight movement of the seventh observation would not affect the maximal margin
hyperplane.
(g) Sketch a hyperplane that is not the optimal separating hyper- plane, and provide the equation for
this hyperplane.
(h) Draw an additional observation on the plot so that the two classes are no longer separable by a
hyperplane.

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