 Title Pages
 Series Foreword
 Preface

1 Introduction to SemiSupervised Learning 
1 A Taxonomy for SemiSupervised Learning Methods 
3 SemiSupervised Text Classification Using EM 
4 Risks of SemiSupervised Learning: How Unlabeled Data Can Degrade Performance of Generative Classifiers 
5 Probabilistic SemiSupervised Clustering with Constraints 
6 Transductive Support Vector Machines 
7 SemiSupervised Learning Using SemiDefinite Programming 
8 Gaussian Processes and the NullCategory Noise Model 
9 Entropy Regularization 
10 DataDependent Regularization 
11 Label Propagation and Quadratic Criterion 
12 The Geometric Basis of SemiSupervised Learning 
13 Discrete Regularization 
14 SemiSupervised Learning with Conditional Harmonic Mixing 
15 Graph Kernels by Spectral Transforms 
16 Spectral Methods for Dimensionality Reduction 
17 Modifying Distances 
18 LargeScale Algorithms 
19 SemiSupervised Protein Classification Using Cluster Kernels 
20 Prediction of Protein Function from Networks 
25 Analysis of Benchmarks 
22 An Augmented PAC Model for SemiSupervised Learning 
23 MetricBased Approaches for SemiSupervised Regression and Classification 
24 Transductive Inference and SemiSupervised Learning 
25 A Discussion of SemiSupervised Learning and Transduction  References
 Notation and Symbols
 Contributors
 Index
SemiSupervised Learning Using SemiDefinite Programming
SemiSupervised Learning Using SemiDefinite Programming
 Chapter:
 (p.118) (p.119) 7 SemiSupervised Learning Using SemiDefinite Programming
 Source:
 SemiSupervised Learning
 Author(s):
De Bie Tijl
Cristianini Nello
 Publisher:
 The MIT Press
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 semidefinite 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 semisupervised learning, where equivalence and inequivalence constraints are given on labels of some of the samples.
Keywords: convex relaxation, optimization problem, support vector machine transduction, semidefinite programming problem, SDP, transduction objective function
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 Title Pages
 Series Foreword
 Preface

1 Introduction to SemiSupervised Learning 
1 A Taxonomy for SemiSupervised Learning Methods 
3 SemiSupervised Text Classification Using EM 
4 Risks of SemiSupervised Learning: How Unlabeled Data Can Degrade Performance of Generative Classifiers 
5 Probabilistic SemiSupervised Clustering with Constraints 
6 Transductive Support Vector Machines 
7 SemiSupervised Learning Using SemiDefinite Programming 
8 Gaussian Processes and the NullCategory Noise Model 
9 Entropy Regularization 
10 DataDependent Regularization 
11 Label Propagation and Quadratic Criterion 
12 The Geometric Basis of SemiSupervised Learning 
13 Discrete Regularization 
14 SemiSupervised Learning with Conditional Harmonic Mixing 
15 Graph Kernels by Spectral Transforms 
16 Spectral Methods for Dimensionality Reduction 
17 Modifying Distances 
18 LargeScale Algorithms 
19 SemiSupervised Protein Classification Using Cluster Kernels 
20 Prediction of Protein Function from Networks 
25 Analysis of Benchmarks 
22 An Augmented PAC Model for SemiSupervised Learning 
23 MetricBased Approaches for SemiSupervised Regression and Classification 
24 Transductive Inference and SemiSupervised Learning 
25 A Discussion of SemiSupervised Learning and Transduction  References
 Notation and Symbols
 Contributors
 Index