Regularized Radial Basis Function Networks

Simon Haykin is a well-known author of books on neural networks. * An authoritative book dealing with cutting edge technology. * This book has no competition.

Paul V. Yee is the author of Regularized Radial Basis Function Networks: Theory and Applications, published by Wiley.

Simon Haykin is the author of Regularized Radial Basis Function Networks: Theory and Applications, published by Wiley.

Preface

xi

Notations

xv

Introduction

1

(1)

Problem Description

1

(5)

Review of Current Approaches

6

(21)

Traditional ANN Approaches

6

(3)

Limitations of the ANN Approaches

9

(6)

Kernel Regression Approach

15

(7)

Limitations of the Kernel Regression Approach

22

(1)

Guided Tour of Book

23

(4)

Basic Tools

27

(30)

Introduction

27

(1)

Asymptotic Equivalence of NWRE to Regularized Strict Interpolation RBFN via Constructive Approximation

28

(12)

Relationship between R2 and R2

40

(6)

Implications for Regularized Strict Interpolation RBFN Estimation

46

(7)

Asymptotic Optimality with Respect to Mean-Squared Error

46

(3)

Consistency with Respect to Mean-Squared Error over Compacta

49

(4)

Summary and Discussion

53

(4)

Probability Estimation and Pattern Classification

57

(18)

Introduction

57

(1)

Problem Description

58

(1)

Review of Current Approaches

59

(6)

Traditional ANN Approaches

59

(4)

Kernel-Based Approaches

63

(2)

Theoretical Results for Regularized Probability Estimates

65

(6)

Consistency of Probability Estimates in Mean-Square and Bayes Risk

65

(6)

Summary and Discussion

71

(4)

Nonlinear Time-Series Prediction

75

(40)

Introduction

75

(1)

Problem Description

76

(1)

Review of Current Approaches

77

(2)

Traditional ANN Approaches

77

(2)

Kernel Regression Approach

79

(3)

Consistency of Prediction

82

(4)

Recursive Updating for Regularized RBFN Predictors

86

(8)

Augmented (Infinite Memory) Case

88

(2)

Fixed-Size (Finite Memory) Case

90

(4)

Application to Speech Prediction

94

(19)

Experiment 1: Partial Update Algorithm for Fixed-Size Networks

94

(7)

Experiment 2: Full Update Algorithm for Fixed-Size Networks

101

(12)

Summary and Discussion

113

(2)

Nonlinear State Estimation

115

(22)

Introduction

115

(1)

Problem Description

115

(2)

ANN Approach

117

(2)

Review of Current Approaches

119

(5)

Proposed Approach

124

(1)

Experimental Results

125

(1)

Comparison to the SDE Approach

126

(4)

Comparison to the RMLP Approach

130

(4)

Summary and Discussion

134

(3)

Dynamic Reconstruction of Chaotic Processes

137

(18)

Introduction

137

(1)

Problem Description

138

(2)

Review of Current Approaches

140

(2)

Experiment: Reconstruction of the Lorenz System from Noisy Data

142

(11)

Results for Noise-Free Case

142

(6)

Results for 30-dB Signal-to-Noise Ratio (SNR) Case

148

(4)

Results for 20-dB SNR Case

152

(1)

Summary and Discussion

153

(2)

Discussion

155

(16)

Relationship Between Radial Basis Function Networks and Kernel Regression Estimates

156

(3)

Limitations of the Approach Taken in this Book

159

(1)

Design of RBF Networks Using Deterministic Annealing

160

(3)

Semi-Parametric Machine Learning

163

(2)

Continuous Learning in a Regularized Manner

165

(6)

Appendix of Notes to the Text

171

(6)

A.1 Notes for Introduction

171

(3)

A.2 Notes for Chapter 1

174

(1)

A.3 Notes for Chapter 2

175

(1)

A.4 Notes for Chapter 4

176

(1)

References

177

(12)

Additional Bibliography

185

(4)

Index

189

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Regularized Radial Basis Function Networks Theory and Applications

Summary

Author Biography

Table of Contents

Supplemental Materials