Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Executive Summary
- 1 Rudiments of Statistical Learning Theory
- 2 Vapnik–Chervonenkis Dimension
- 3 Learnability for Binary Classification
- 4 Support Vector Machines
- 5 Reproducing Kernel Hilbert Spaces
- 6 Regression and Regularization
- 7 Clustering
- 8 Dimension Reduction
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Part Four Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
4 - Support Vector Machines
from Part One - Machine Learning
Published online by Cambridge University Press: 21 April 2022
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Executive Summary
- 1 Rudiments of Statistical Learning Theory
- 2 Vapnik–Chervonenkis Dimension
- 3 Learnability for Binary Classification
- 4 Support Vector Machines
- 5 Reproducing Kernel Hilbert Spaces
- 6 Regression and Regularization
- 7 Clustering
- 8 Dimension Reduction
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Part Four Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
Summary
This chapter studies binary classification from a non-statistical viewpoint. For data that are linearly separable, the perceptron algorithm is presented first. It is followed by an optimization program, known as the hard support vector machine (SVM), consisting in maximizing the margin. For data that are not exactly linearly separable, this optimization program is relaxed into soft SVM. Finally, for data that are linearly separable only after applying a feature map, the representer theorem is used to validate the so-called kernel trick.
- Type
- Chapter
- Information
- Mathematical Pictures at a Data Science Exhibition , pp. 23 - 30Publisher: Cambridge University PressPrint publication year: 2022