This preview shows page 1. Sign up to view the full content.
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 twoway classiﬁcation is
f (x) = 1 if aT x + b > 0
2 if aT x + b < 0. In the simplest form, ﬁnding f is equivalent to solving a feasibility problem: ﬁnd a and b such
that
aT x + b > 0 if x ∈ C1
aT x + b < 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...
View
Full
Document
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.
 Fall '13
 F.Borrelli
 The Aeneid

Click to edit the document details