1st Edition

Foundations of Wavelet Networks and Applications

By S. Sitharama Iyengar, V.V. Phoha Copyright 2002
    284 Pages 66 B/W Illustrations
    by Chapman & Hall

    288 Pages 66 B/W Illustrations
    by Chapman & Hall

    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.

    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
    "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