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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 > 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.

Ask a homework question - tutors are online