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Semi-Supervised Learning$
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Olivier Chapelle, Bernhard Scholkopf, and Alexander Zien

Print publication date: 2006

Print ISBN-13: 9780262033589

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262033589.001.0001

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Semi-Supervised Learning Using Semi-Definite Programming

Semi-Supervised Learning Using Semi-Definite Programming

Chapter:
(p.118) (p.119) 7 Semi-Supervised Learning Using Semi-Definite Programming
Source:
Semi-Supervised Learning
Author(s):

De Bie Tijl

Cristianini Nello

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262033589.003.0007

This chapter discusses an alternative approach that is based on a convex relaxation of the optimization problem associated with support vector machine transduction. The result is a semi-definite programming (SDP) problem which can be optimized in polynomial time, the solution of which is an approximation of the optimal labeling as well as a bound on the true optimum of the original transduction objective function. To further decrease the computational complexity, this chapter proposes an approximation that allows solving transduction problems of up to 1,000 unlabeled samples. Finally, the formulation is extended to more general settings of semi-supervised learning, where equivalence and inequivalence constraints are given on labels of some of the samples.

Keywords:   convex relaxation, optimization problem, support vector machine transduction, semi-definite programming problem, SDP, transduction objective function

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