In the field of machine learning, semi-supervised learning (SSL) occupies the middle ground, between supervised learning (in which all training examples are labeled) and unsupervised learning (in which no label data are given). Interest in SSL has increased in recent years, particularly because of application domains in which unlabeled data are plentiful, such as images, text, and bioinformatics. This first comprehensive overview of SSL presents state-of-the-art algorithms, a taxonomy of the field, selected applications, benchmark experiments, and perspectives on ongoing and future research. Semi-Supervised Learningfirst presents the key assumptions and ideas underlying the field: smoothness, cluster or low-density separation, manifold structure, and transduction. The core of the book is the presentation of SSL methods, organized according to algorithmic strategies. After an examination of generative models, the book describes algorithms that implement the low-density separation assumption, graph-based methods, and algorithms that perform two-step learning. The book then discusses SSL applications and offers guidelines for SSL practitioners by analyzing the results of extensive benchmark experiments. Finally, the book looks at interesting directions for SSL research. The book closes with a discussion of the relationship between semi-supervised learning and transduction. Olivier Chapelle and Alexander Zien are Research Scientists and Bernhard Schölkopf is Professor and Director at the Max Planck Institute for Biological Cybernetics in Tübingen. Schölkopf is coauthor of Learning with Kernels(MIT Press, 2002) and is a coeditor of Advances in Kernel Methods: Support Vector Learning(1998), Advances in Large-Margin Classifiers(2000), and Kernel Methods in Computational Biology(2004), all published by The MIT Press.

Olivier Chapelle is Senior Research Scientist in Machine Learning at Yahoo.

Bernhard Schölkopf is Director at the Max Planck Institute for Intelligent Systems in Tübingen, Germany. He is coauthor of Learning with Kernels (2002) and is a coeditor of Advances in Kernel Methods: Support Vector Learning (1998), Advances in Large-Margin Classifiers (2000), and Kernel Methods in Computational Biology (2004), all published by the MIT Press.

Alexander Zien is Senior Analyst in Bioinformatics at LIFE Biosystems GmbH, Heidelberg.

Series Foreword	p. xi
Preface	p. xiii
Introduction to Semi-Supervised Learning	p. 1
Supervised, Unsupervised, and Semi-Supervised Learning	p. 1
When Can Semi-Supervised Learning Work?	p. 4
Classes of Algorithms and Organization of This Book	p. 8
Generative Models
A Taxonomy for Semi-Supervised Learning Methods	p. 15
The Semi-Supervised Learning Problem	p. 15
Paradigms for Semi-Supervised Learning	p. 17
Examples	p. 22
Conclusions	p. 31
Semi-Supervised Text Classification Using EM	p. 33
Introduction	p. 33
A Generative Model for Text	p. 35
Experminental Results with Basic EM	p. 41
Using a More Expressive Generative Model	p. 43
Overcoming the Challenges of Local Maxima	p. 49
Conclusions and Summary	p. 54
Risks of Semi-Supervised Learning	p. 57
Do Unlabled Data Improve or Degrade Classification Performance?	p. 57
Understanding Unlabeled Data: Asymptotic Bias	p. 59
The Asymptotic Analysis of Generative Smei-Supervised Learning	p. 63
The Value of Labeled and Unlabeled Data	p. 67
Finite Sample Effects	p. 69
Model Search and Robustness	p. 70
Conclusion	p. 71
Probabilistic Semi-Supervised Cluster with Constraints	p. 73
Introduction	p. 74
HMRF Model for Semi-Supervised Clustering	p. 75
HMRF-KMeans Algorithm	p. 81
Active Learning for Constraint Acquistion	p. 93
Experimental Results	p. 96
Related Work	p. 100
Conclusions	p. 101
Low-Density Separation
Transductive Support Vector Machines	p. 105
Introduction	p. 105
Transductive Support Vector Machines	p. 108
Why Use Margin on the Test Set?	p. 111
Experiments and Applications of the TSVMs	p. 112
Solving the TSVM Optimization Problem	p. 114
Connection to Related Approaches	p. 116
Summary and Conclusions	p. 116
Semi-Supervised Learning Using Semi-Definite Programming	p. 119
Relaxing SVM transduction	p. 119
An Approximation for Speedup	p. 126
General Semi-Supervised Learning Settings	p. 128
Empirical Results	p. 129
Summary and Outlook	p. 133
Appendix: The Extended Schur Complement Lemma	p. 134
Gaussian Processes and the Null-Category Noise Model	p. 137
Introduction	p. 137
The Noise Model	p. 141
Process Model and the Effect of the Null-Category	p. 143
Posterior Inference and Prediction	p. 145
Results	p. 147
Discussion	p. 149
Entropy Regularization	p. 151
Introduction	p. 151
Derivation of the Criterion	p. 152
Optimization Algorithms	p. 155
Related Methods	p. 158
Experiments	p. 160
Conclusion	p. 166
Appendix: Proof of Theorem 9.1	p. 166
Data-Dependent Regularization	p. 169
Introduction	p. 169
Information Regularization on Metric Spaces	p. 174
Information Regularization and Relational Data	p. 182
Discussion	p. 189
Graph-Based Models
Label Propogation and Quadratic Criterion	p. 193
Introduction	p. 193
Label Propogation on a Similarity Graph	p. 194
Quadratic Cost Criterion	p. 198
From Transduction to Induction	p. 205
Incorporating Class Prior Knowledge	p. 205
Curse of Dimensionality for Semi-Supervised Learning	p. 206
Discussion	p. 215
The Geometric Basis of Semi-Supervised Learning	p. 217
Introduction	p. 217
Incorporating Geometry in Regularization	p. 220
Algorithms	p. 224
Data-Dependent Kernels for Semi-Supervised Learning	p. 229
Linear Methods for Large-Scale Semi-Supervised Learning	p. 231
Connections to Other Algorithms and Related Work	p. 232
Future Directions	p. 234
Discrete Regularization	p. 237
Introduction	p. 237
Discrete Analysis	p. 239
Discrete Regularization	p. 245
Conclusion	p. 249
Semi-Supervised Learning with Conditional Harmonic Mixing	p. 251
Introduction	p. 251
Conditional Harmonic Mixing	p. 255
Learning in CHM Models	p. 256
Incorporating Prior Knowledge	p. 261
Learning the Conditionals	p. 261
Model Averaging	p. 262
Experiments	p. 263
Conclusions	p. 273
Change of Representation
Graph Kernels by Spectral Transforms	p. 277
The Graph Laplacian	p. 278
Kernels by Spectral Transforms	p. 280
Kernel Alignment	p. 281
Optimizing Alignment Using QCQP for Semi-Supervised Learning	p. 282
Semi-Supervised Kernels with Order Restraints	p. 283
Experimental Results	p. 285
Conclusion	p. 289
Spectral Methods for Dimensionality Reduction	p. 293
Introduction	p. 293
Linear Methods	p. 295
Graph-Based Methods	p. 297
Kernel Methods	p. 303
Discussion	p. 306
Modifying Distances	p. 309
Introduction	p. 309
Estimating DBD Metrics	p. 312
Computing DBD Metrics	p. 321
Semi-Supervised Learning Using Density-Based Metrics	p. 327
Conclusions and Future Work	p. 329
Semi-Supervised Learning in Practice
Large-Scale Algorithms	p. 333
Introduction	p. 333
Cost Approximations	p. 334
Subset Selection	p. 337
Discussion	p. 340
Semi-Supervised Protein Classification Using Cluster Kernels	p. 343
Introduction	p. 343
Representation and Kernels for Protein Sequences	p. 345
Semi-Supervised Kernels for Protein Sequences	p. 348
Experiments	p. 352
Discussion	p. 358
Prediction of Protein Function from Networks	p. 361
Introduction	p. 361
Graph-Based Semi-Supervised Learning	p. 364
Combining Multiple Graphs	p. 366
Experiments on Function Prediction of Proteins	p. 369
Conclusion and Outlook	p. 374
Analysis of Benchmarks	p. 377
The Benchmark	p. 377
Application of SSL Methods	p. 383
Results and Discussion	p. 390
Perspectives
An Augmented PAC Model for Semi-Supervised Learning	p. 397
Introduction	p. 398
A Formal Framework	p. 400
Sample Complexity Results	p. 403
Algorithmic Results	p. 412
Related Models and Discussion	p. 416
Metric-Based Approaches for Semi-Supervised Regression and Classification	p. 421
Introduction	p. 421
Metric Structure of Supervised Learning	p. 423
Model Selection	p. 426
Regularization	p. 436
Classification	p. 445
Conclusion	p. 449
Transductive Inference and Semi-Supervised Learning	p. 453
Problem Settings	p. 453
Problem of Generalization in Inductive and Transductive Inference	p. 455
Structure of the VC Bounds and Transductive Inference	p. 457
The Symmetrization Lemma and Transductive Inference	p. 458
Bounds for Transductive Inference	p. 459
The Structural Risk Minimization Principle for Induction and Transduction	p. 460
Combinatorics in Transductive Inference	p. 462
Measures of Size of Equivalence Classes	p. 463
Algorithms for Inductive and Transductive SVMs	p. 465
Semi-Supervised Learning	p. 470
Conclusion: Transductive Inference and the New Problems of Inference	p. 470
Beyond Transduction: Selective Inference	p. 471
A Discussion of Semi-Supervised Learning and Transduction	p. 473
References	p. 479
Notation and Symbols	p. 499
Contributors	p. 503
Index	p. 509
Online Index
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