bv_cvxbook_extra_exercises

# Since f is invariant with respect to a scaling of p

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Unformatted text preview: he problem given in (8.23), p424, §8.6.1; see also exercise 8.23.) In this problem we seek (a, b) that separate the two classes with a thick slab, and also has a sparse, i.e., there are many j with aj = 0. Note that if aj = 0, the aﬃne function aT z − b does not depend on zj , i.e., the j th feature is not used to carry out classiﬁcation. So a sparse a corresponds to a classiﬁcation function that is parsimonious; it depends on just a few features. So our goal is to ﬁnd an aﬃne classiﬁcation function that gives a thick separating slab, and also uses as few features as possible to carry out the classiﬁcation. This is in general a hard combinatorial (bi-criterion) optimization problem, so we use the standard heuristic of solving minimize a 2+λ a 1 subject to aT x(i) − b ≥ 1, i = 1, . . . , N aT y (i) − b ≤ −1, i = 1, . . . , M, where λ ≥ 0 is a weight vector that controls the trade-oﬀ between separating slab thickness and (indirectly, through the ℓ1 norm) sparsity of a. Get the data in sp_ln_sp_data.m, which gives x(i) and y (i) as the co...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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