Foundations of Wavelet Networks 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