1st Edition

Foundations of Wavelet Networks and Applications




ISBN 9781584882749
Published June 27, 2002 by Chapman and Hall/CRC
288 Pages 66 B/W Illustrations

USD $150.00

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Book Description

Traditionally, neural networks and wavelet theory have been two separate disciplines, taught separately and practiced separately. In recent years the offspring of wavelet theory and neural networks-wavelet networks-have emerged and grown vigorously both in research and applications. Yet the material needed to learn or teach wavelet networks has remained scattered in various research monographs.

Foundations of Wavelet Networks and Applications unites these two fields in a comprehensive, integrated presentation of wavelets and neural networks. It begins by building a foundation, including the necessary mathematics. A transitional chapter on recurrent learning then leads to an in-depth look at wavelet networks in practice, examining important applications that include using wavelets as stock market trading advisors, as classifiers in electroencephalographic drug detection, and as predictors of chaotic time series. The final chapter explores concept learning and approximation by wavelet networks.

The potential of wavelet networks in engineering, economics, and social science applications is rich and still growing. Foundations of Wavelet Networks and Applications prepares and inspires its readers not only to help ensure that potential is achieved, but also to open new frontiers in research and applications.

Table of Contents

PART A
MATHEMATICAL PRELIMINARIES
Sets
Functions
Sequences and Series
Complex Numbers
Linear Spaces
Matrices
Hilbert Spaces
Topology
Measure and Integral
Fourier Series
Exercises
WAVELETS
Introduction
Dilation and Translation
Inner Product
Haar Wavelet
Multiresolution Analysis
Continuous Wavelet Transform
Discrete Wavelet Transform
Fourier Transform
Discrete Fourier Transform
Discrete Fourier Transform of Finite Sequences
Convolution
Exercises
NEURAL NETWORKS
Introduction
Multilayer Perceptrons
Hebbian Learning
Competitive and Kohonen Networks
Recurrent Neural Networks
WAVELET NETWORKS
Introduction
What Are Wavelet Networks
Dyadic Wavelet Network
Theory of Wavelet Networks
Wavelet Network Structure
Multidimensional Wavelets
Learning in Wavelet Networks
Initialization of Wavelet Networks
Properties of Wavelet Networks
Scaling at Higher Dimensions
Exercises

PART B
RECURRENT LEARNING
Introduction
Recurrent Neural Networks
Recurrent Wavenets
Numerical Experiments
Concluding Remarks
Exercises
SEPARATING ORDER FROM DISORDER
Order Within Disorder
Wavelet Networks: Trading Advisors
Comparison Results
Conclusions
Exercises
RADIAL WAVELET NEURAL NETWORKS
Introduction
Data Description and Preparation
Classification Systems
Results
Conclusions
Exercises
PREDICTING CHAOTIC TIME SERIES
Introduction
Nonlinear Prediction
Wavelet Networks
Short-Term Prediction
Parameter-Varying Systems
Long-Term Prediction
Conclusions
Acknowledgements
Appendix
Exercises
CONCEPT LEARNING
An Overview
An Illustrative Example of Learning
Introduction
Preliminaries
Learning Algorithms
Summary
Exercises
BIBLIOGRAPHY
INDEX

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Reviews

"This book reviews both the theory of some kinds of wavelet networks and a number of applications … . The book is self-contained, as it contains both some mathematical preliminaries and a review of fundamentals about wavelets as well as neural networks. Moreover, at the end of each chapter it contains a number of exercises useful to help the reader to verify the degree of his/her understanding … . The book is highly recommended to all those looking for new methods in neural networks devoted to signal analysis."
- Mathematical Reviews, Issue 2005d