An Introduction to Support Vector Machines and Other Kernel-based Learning Methods,9780521780193

An Introduction to Support Vector Machines and Other Kernel-based Learning Methods

by
ISBN13: 9780521780193
ISBN10: 0521780195
Format: Hardcover
Pub. Date: 2000-03-28
Publisher(s): Cambridge University Press
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Summary

This is the first comprehensive introduction to Support Vector Machines (SVMs), a new generation learning system based on recent advances in statistical learning theory. Students will find the book both stimulating and accessible, while practitioners will be guided smoothly through the material required for a good grasp of the theory and its applications. The concepts are introduced gradually in accessible and self-contained stages, while the presentation is rigorous and thorough. Pointers to relevant literature and web sites containing software make it an ideal starting point for further study.

Table of Contents

Preface ix
Notation xiii
The Learning Methodology
1(8)
Supervised Learning
1(2)
Learning and Generalisation
3(1)
Improving Generalisation
4(2)
Attractions and Drawbacks of Learning
6(1)
Support Vector Machines for Learning
7(1)
Exercises
7(1)
Further Reading and Advanced Topics
8(1)
Linear Learning Machines
9(17)
Linear Classification
9(11)
Rosenblatt's Perceptron
11(8)
Other Linear Classifiers
19(1)
Multi-class Discrimination
20(1)
Linear Regression
20(4)
Least Squares
21(1)
Ridge Regression
22(2)
Dual Representation of Linear Machines
24(1)
Exercises
25(1)
Further Reading and Advanced Topics
25(1)
Kernel-Induced Feature Spaces
26(26)
Learning in Feature Space
27(3)
The Implicit Mapping into Feature Space
30(2)
Making Kernels
32(14)
Characterisation of Kernels
33(9)
Making Kernels from Kernels
42(2)
Making Kernels from Features
44(2)
Working in Feature Space
46(2)
Kernels and Gaussian Processes
48(1)
Exercises
49(1)
Further Reading and Advanced Topics
50(2)
Generalisation Theory
52(27)
Probably Approximately Correct Learning
52(2)
Vapnik Chervonenkis (VC) Theory
54(5)
Margin-Based Bounds on Generalisation
59(10)
Maximal Margin Bounds
59(5)
Margin Percentile Bounds
64(1)
Soft Margin Bounds
65(4)
Other Bounds on Generalisation and Luckiness
69(1)
Generalisation for Regression
70(4)
Bayesian Analysis of Learning
74(2)
Exercises
76(1)
Further Reading and Advanced Topics
76(3)
Optimisation Theory
79(14)
Problem Formulation
79(2)
Lagrangian Theory
81(6)
Duality
87(2)
Exercises
89(1)
Further Reading and Advanced Topics
90(3)
Support Vector Machines
93(32)
Support Vector Classification
93(19)
The Maximal Margin Classifier
94(9)
Soft Margin Optimisation
103(9)
Linear Programming Support Vector Machines
112(1)
Support Vector Regression
112(9)
ε-Insensitive Loss Regression
114(4)
Kernel Ridge Regression
118(2)
Gaussian Processes
120(1)
Discussion
121(1)
Exercises
121(1)
Further Reading and Advanced Topics
122(3)
Implementation Techniques
125(24)
General Issues
125(4)
The Native Solution: Gradient Ascent
129(6)
General Techniques and Packages
135(1)
Chunking and Decomposition
136(1)
Sequential Minimal Optimisation (SMO)
137(7)
Analytical Solution for Two Points
138(2)
Selection Heuristics
140(4)
Techniques for Gaussian Processes
144(1)
Exercises
145(1)
Further Reading and Advanced Topics
146(3)
Applications of Support Vector Machines
149(13)
Text Categorisation
150(2)
A Kernel from IR Applied to Information Filtering
150(2)
Image Recognition
152(4)
Aspect Independent Classification
153(1)
Colour-Based Classification
154(2)
Hand-written Digit Recognition
156(1)
Bioinformatics
157(3)
Protein Homology Detection
157(2)
Gene Expression
159(1)
Further Reading and Advanced Topics
160(2)
A Pseudocode for the SMO Algorithm 162(3)
B Background Mathematics 165(8)
Vector Spaces
165(2)
Inner Product Spaces
167(2)
Hilbert Spaces
169(2)
Operators, Eigenvalues and Eigenvectors
171(2)
References 173(14)
Index 187

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