Foundations of Wavelet Networks and Applications PDF
Preview Foundations of Wavelet Networks and Applications
FOUNDATIONS of WAVELET NETWORKS and APPLICATIONS FOUNDATIONS of WAVELET NETWORKS and APPLICATIONS S. Sitharama Iyengar E. C. Cho Vir V. Phoha CHAPMAN & HALL/CRC A CRC Press Company Boca Raton London New York Washington, D.C. Library of Congress Cataloging-in-Publication Data Iyengar, S. S. (Sundararaja S.) Foundations of wavelet network and applications / S.S. Iyengar, E.C. Cho, V.V. Phoha. p. cm. Includes bibliographical references and index. ISBN 1-58488-274-3 1. Neural networks (Computer science) 2. Wavelets (Mathematics) I. Cho, E. C. II. Phoha, Vir V. III. Title. QA76.87 .I94 2002 006.3'2 —dc21 200205919 CIP Catalog record is available from the Library of Congress This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. All rights reserved. Authorization to photocopy items for internal or personal use, or the personal or internal use of specific clients, may be granted by CRC Press LLC, provided that $1.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA. The fee code for users of the Transactional Reporting Service is ISBN 1-58488-274- 3/02/$0.00+$1.50. The fee is subject to change without notice. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. Visit the CRC Press Web site at www.crcpress.com © 2002 by Chapman & Hall/CRC CRC Press LLC No claim to original U.S. Government works International Standard Book Number 1-58488-274-3 Library of Congress Card Number 2002025919 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper Dedication S.S. Iyengar would like to dedicate this book to Professor Hart- manis, a Turing Award winner, of Cornell for his pioneering contribution to complexity theory and to Puneeth, Veneeth, and Vijeth for their patience for my lectures, E.C. Cho would like to dedicate this book to his parents and his family, V. V. Phoha would like to dedicate this work to Professor William J.B, Oldham of Texas Tech University for his teachings and for his contributions to neural networks. Acknowledgments This book was made possible and thanks to generous support from the office of Naval Research Division of Electronics, DARPA- Sense IT, DOE-ORNL programs, Board of Regents-LEQSF etc. Special acknowledgments to the following individuals for their contributions to this book. Chapter 5 was contributed by Ri cardo Riaza, Raquel Gomez Sanchez, and Pedro J, Zuhria, Chap ters 6 and 7 were contributed by Javier Eehauz and George Vaehtsevanos, Chapter 8, contributed by Liangyue Cao, Yiguang Hong, Harping Fang, and Guowei He, is reproduced with their permission. Chapter 9 was contributed by Rao and Iyengar, Thanks for Professor Rao’s technical expertise in fusion learn ing. We are grateful to the following individuals in the LSU Robotics Research and LSU Networking Laboratories who have helped in the publication of this book: Sridhar Karra, Kanthi Adapa, and Sumanth Yenduri, Professor Seiden’s help in using LaTex was very useful. This book is an extension to our earlier (Prof Iyengar’s) book, Wavelet Analysis with Applications to Image Processing, CRC Press (1997), Boca Raton, Florida, which continues to be used in many universities across the world. Preface This text grew out of our lecture notes at Louisiana State Uni versity, Louisiana Tech University, and Kentucky State Univer sity and from many questions from our students that indicated the need for a comprehensive treatment of wavelet networks. Our two main purposes in writing this text are (1) to present a systematic treatment of wavelet networks based whenever possible on fundamental principles, and (2) to present a self contained treatment of wavelet networks in a clear and concise manner. Readers who sample the literature will note a recent vigor ous growth in this area. Wavelet networks are relatively new; however, their applications and growth have come from many areas including wavelet theory, neural networks, statistics, com puter science, pattern recognition, and communication, to name a few. In this text, neural networks and wavelet theory, tradi tionally taught in two different disciplines, are integrated under the common theme of wavelet networks. In our teaching and in research, we found that the material required to teach wavelet networks in an organized and compre hensive manner was scattered in many research monographs; there is no book that presents a comprehensive treatment of material in one place. This book is an attempt to fill that void. Approach We have followed a pedagogical approach in this text. The book presents a rigorous treatment of both wavelets and neu ral networks, because the foundations of wavelet networks can be found in neural networks, and wavelets-wavelet networks combine the decomposition powers of wavelets with universal approximation properties of neural networks, so a good under standing of wavelets and networks is essential to appreciate the universal approximation properties of wavelet networks. Theory and techniques of wavelet networks are mostly math ematical in nature, but we have focused on providing insight and understanding rather than establishing rigorous mathematical foundations, so we have avoided detailed proofs of theorems. A deliberate attempt is made to provide a balance between theory and applications of wavelet networks. We present the mate rial at a level that can be understood by senior undergraduate students in engineering and science. To follow this text no specific mathematical background is expected, with the exception of basic calculus. All the other requisite mathematical preliminaries are given in the hrst part. Topics The book has two parts. Part I deals with the foundational aspects of wavelet networks, and Part II presents applications of wavelet networks, A brief description of each part of the book follows. Part I is divided into four chapters. Chapter 1 deals with mathematical preliminaries. Wavelet transforms have come to be an important tool for approximation analysis of non-linear equations, with a wide and ever increasing range of applica tions, in recent years. The versatility of wavelet analytic tech niques has forged new interdisciplinary bonds by offering com mon solutions to diverse problems and providing a platform to wavelet networks. Chapter 2 describes in detail wavelet anal ysis and construction of wavelets. Chapter 3 addresses neural networks, where the stress is on pereeptron type networks and the back propagation learning algorithm with its various adap tations, Starting with a single MeCulloeh-Pitts neuron model to build intuition, we present pereeptrons and gradient-deseent learning, Hebb type learning is the basis of most artificial neural network models, and competition is a major learning principle, so we develop these concepts at some length. We also present other neural architectures, because it is our belief that the future lies in adapting and integrating wavelets to other neural archi tectures, Our presentation of other neural architecture gives the reader a firm foundation in the concepts, which we hope will generate new ideas. Chapter 4 is the capstone finale that deals with wavelet networks. In these final segments, we outline the theory underlying wavelet networks and present some basic applications. Part II, contributed by many distinguished researchers in this area, is divided into five chapters. There is a great amount of work available that uses wavelet networks, much of which de serves inclusion here. Although we provide a review of current work, we have selected that material which, in our view best represents important applications of wavelet networks. Chap ter 5 (contributed by Ricardo Riaza, Raquel Gomez Sanchez, and Pedro J, Zufiria) presents recurrent learning in dynamical wavelet networks. This chapter is a bridge between Part I and Part II of the book. It could easily have been included in Part I, but we chose to include it in Part II because of the advanced na ture of the concepts presented therein. Chapter 6 (contributed by Javier Eehauz and George Vaehtsevanos) presents the use of wavelet networks as trading advisors in the stock market; Chapter 7 (contributed by Javier Eehauz, and George Vaeht sevanos) presents radial wavelet networks as classifiers in elee- troeneephalographie drug detection; Chapter 8 (contributed by Liangvue Cao, Yiguang Hong, Haiping Fang, and Guowei He) presents the use and application of wavelet networks for pre diction of chaotic time series including the short term and long term predictions, where a number of times series generated from chaotic systems such as the Maekev-Glass equation are tested. Chapter 9 (contributed by Nageswara S.V, Rao and S.S. Iyengar) presents concept learning and deals with approxima tion by wavelet networks. The book includes a detailed bibliography arranged under chapter headings to help the reader easily locate references of interest. The bibliography contains additional references not explicitly cited in text, and will provide the reader with a rich resource for further exploration.
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