Foundations of Wavelet Networks and Applications

Foundations of Wavelet Networks and Applications

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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 more

Product details

  • Hardback | 288 pages
  • 162.1 x 241.3 x 21.6mm | 530.71g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 2002.
  • 66 black & white illustrations, 1 black & white tables
  • 1584882743
  • 9781584882749
  • 2,451,285

Review quote

"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 2005dshow more

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 INDEXshow more