bv_cvxbook_extra_exercises

E nd the vectors l and u that is guaranteed to

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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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