Exercise 14.1 - Fitting an SVM classifier by hand

Answers

The mapped samples are [ 1 , 0 , 0 ] T and [ 1 , 2 , 2 ] T .

For question (a), the best decision plane is the one with normal [ 0 , 1 , 1 ] T and passes the point [ 1 , 1 , 1 ] T . Hence 𝐰 can be chosen as [ 0 , 1 , 1 ] T .

For question (b), the marginal is the distance between [ 1 , 1 , 1 ] T and [ 1 , 2 , 2 ] T , hence is 2 .

For question (c), we have:

𝐰 = [ 0 , 1 2 , 1 2 ] T .

For question (d), we have:

1 2 ⋅ 0 + 1 2 ⋅ 0 + w 0 = − 1 ,

1 2 ⋅ 2 + 1 2 ⋅ 2 + w 0 = 1 ,

hence w 0 = − 1 .

For question (e), the discriminant function is:

f ( x ) = − 1 + 1 2 x 2 + 1 2 x 3 .

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2021-03-24 13:42
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