bv_cvxbook_extra_exercises

# 23 in this problem we seek a b that separate the two

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Unformatted text preview: ectors in class i. The learning problem is to ﬁnd a decision function f : Rn → {1, 2, . . . , m} that maps each training example to its class, and also generalizes reliably to feature vectors that are not included in the training sets Ci . 60 (a) A common type of decision function for two-way classiﬁcation is f (x) = 1 if aT x + b &gt; 0 2 if aT x + b &lt; 0. In the simplest form, ﬁnding f is equivalent to solving a feasibility problem: ﬁnd a and b such that aT x + b &gt; 0 if x ∈ C1 aT x + b &lt; 0 if x ∈ C2 . Since these strict inequalities are homogeneous in a and b, they are feasible if and only if the nonstrict inequalities aT x + b ≥ 1 if x ∈ C1 aT x + b ≤ −1 if x ∈ C2 are feasible. This is a feasibility problem with N1 + N2 linear inequalities in n + 1 variables a, b. As an extension that improves the robustness (i.e., generalization capability) of the classiﬁer, we can impose the condition that the decision function f classiﬁes all points in a neighborhood of C...
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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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