Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond

Bernhard Schölkopf, Alexander J. Smola

MIT Press, 2002 - Computers - 626 pages

A comprehensive introduction to Support Vector Machines and related kernel methods.

In the 1990s, a new type of learning algorithm was developed, based on results from statistical learning theory: the Support Vector Machine (SVM). This gave rise to a new class of theoretically elegant learning machines that use a central concept of SVMs---kernels--for a number of learning tasks. Kernel machines provide a modular framework that can be adapted to different tasks and domains by the choice of the kernel function and the base algorithm. They are replacing neural networks in a variety of fields, including engineering, information retrieval, and bioinformatics.

Learning with Kernels provides an introduction to SVMs and related kernel methods. Although the book begins with the basics, it also includes the latest research. It provides all of the concepts necessary to enable a reader equipped with some basic mathematical knowledge to enter the world of machine learning using theoretically well-founded yet easy-to-use kernel algorithms and to understand and apply the powerful algorithms that have been developed over the last few years.

Contents

• A Tutorial Introduction: 1
• CONCEPTS AND TOOLS: 23
• Risk and Loss Functions: 61
• Regularization 88888: 87
• Elements of Statistical Learning Theory: 128
• Optimization: 152
• Maximum Search Problems: 179
• SUPPORT VECTOR MACHINES: 204
• Quantile Estimation and Novelty Detection: 227
• Regression Estimation: 251
• Implementation: 279
• Incorporating Invariances: 333
• Learning Theory Revisited: 359
• KERNEL METHODS: 405
• Kernel Feature Extraction: 427
• Kernel Fisher Discriminant: 457
• Bayesian Kernel Methods: 469
• Regularized Principal Manifolds: 517
• PreImages and Reduced Set Methods: 543
• A Addenda: 569
• B Mathematical Prerequisites: 575
• References: 591
• 125: 596
• Index: 617
• Notation and Symbols: 625

Popular passages

Page 593 - PS Bradley and OL Mangasarian. Feature selection via concave minimization and support vector machines. In J. Shavlik, editor, Machine Learning Proceedings of the Fifteenth International Conference (ICML '98), pages 82-90, San Francisco, California, 1998.‎

Page 610 - A tutorial on support vector machines for pattern recognition," Data Mining and Knowledge Discovery 2, 1-47(1998). 5. B. Scholkopf, CJC Burges, and AJ Smola, eds., Advances in Kernel Methods, Support Vector Learning, MIT Press, Cambridge MA (1999). 6. Y. Lecun et al., "Comparison of learning algorithms for handwritten digit recognition,‎

About the author

Bernhard Schölkopf is Professor and Director at the Max Planck Institute for Biological Cybernetics 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 J. Smola is Senior Principal Researcher and Machine Learning Program Leader at National ICT Australia/Australian National University, Canberra.

Bibliographic information

• Title: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond; Adaptive computation and machine learning
• Authors: Bernhard Schölkopf, Alexander J. Smola
• Edition: illustrated
• Publisher: MIT Press, 2002
• ISBN: 0262194759, 9780262194754
• Length: 626 pages
• Subjects: Computers / Artificial Intelligence / General; Computers / Computer Science; Computers / Data Science / Machine Learning; Mathematics / General