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Unformatted text preview: ave you the trouble of plotting data points and separation boundaries, we have
included the plotting code in sep3way_data.m. (Note that a1, a2, a3, b1 and b2 contain arbitrary
numbers; you should compute the correct values using CVX.)
7.6 Feature selection and sparse linear separation. Suppose x(1) , . . . , x(N ) and y (1) , . . . , y (M ) are two
given nonempty collections or classes of vectors in Rn that can be (strictly) separated by a hyperplane, i.e., there exists a ∈ Rn and b ∈ R such that
aT x(i) − b ≥ 1, aT y (i) − b ≤ −1, i = 1, . . . , N, i = 1, . . . , M. This means the two classes are (weakly) separated by the slab
S = {z  aT z − b ≤ 1},
which has thickness 2/ a 2 . You can think of the components of x(i) and y (i) as features ; a and b
deﬁne an aﬃne function that combines the features and allows us to distinguish the two classes.
To ﬁnd the thickest slab that separates the two classes, we can solve the QP
minimize
a2
subject to aT x(i) − b ≥ 1, i = 1, . . . , N
aT y (i) − b ≤ −1, i = 1, . . . , M,
with variables a ∈ Rn and b ∈ R. (This is equivalent to t...
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 Fall '13
 F.Borrelli
 The Aeneid

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