Neural Networks for Applied Sciences and Engineering

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In response to the exponentially increasing need to analyze vast amounts of data, Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition provides scientists with a simple but systematic introduction to neural networks. Beginning with an introductory discussion on the role of neural networks in scientific data analysis, this book provides a solid foundation of basic neural network concepts. It contains an overview of neural network architectures for practical data analysis followed by extensive step-by-step coverage on linear networks, as well as, multi-layer perceptron for nonlinear prediction and classification explaining all stages of processing and model development illustrated through practical examples and case studies. Later chapters present an extensive coverage on Self Organizing Maps for nonlinear data clustering, recurrent networks for linear nonlinear time series forecasting, and other network types suitable for scientific data analysis. With an easy to understand format using extensive graphical illustrations and multidisciplinary scientific context, this book fills the gap in the market for neural networks for multi-dimensional scientific data, and relates neural networks to statistics. Features x Explains neural networks in a multi-disciplinary context x Uses extensive graphical illustrations to explain complex mathematical concepts for quick and easy understanding ? Examines in-depth neural networks for linear and nonlinear prediction, classification, clustering and forecasting x Illustrates all stages of model development and interpretation of results, including data preprocessing, data dimensionality reduction, input selection, model development and validation, model uncertainty assessment, sensitivity analyses on inputs, errors and model parameters Sandhya Samarasinghe obtained her MSc in Mechanical Engineering from Lumumba University in Russia and an MS and PhD in Engineering from Virginia Tech, USA.
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LL( Neural Networks for Applied Sciences and Engineering From fundamentals to Complex Pattern Recognition Sandhya samarasinghe △ Auerbach Publications Taylor francis g Boca raton New york Auerbach Publications is an imprint of the Taylor francis group an informa business O 2006 by Taylor Francis Group, LL.( MATLAB is a trademark of The Math Works, Inc. and is used with permission. The Math Works does not warrant the accuracy of the text or exercises in this book. this book's use or discussion of MaTLAB software or related products does not constitute endorsement or sponsorship by Th MathWorks of a particular pedagogical approach or particular use of the MATLAB"software Auerbach publications Taylor Francis Group 6000 Broken Sound Parkway nw, Suite 300 Boca raton Fl 33487-2742 o 2007 by Taylor Francis Group, LLC Auerbach is an imprint of Taylor Francis Group, an Informa business No claim to original U.s. govcrnment works Printed in the United States of America on acid-free paper 10987654321 International Standard Book Number-10: 0-84193-3375-X (Hardcover) International Standard book Number-13: 978-0-8493-3375-0(Hardcover) 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 author and the publisher cannot assume responsibility for the validity of all materials or for the conse- quences of their use No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this worl ease access www copyrightcom(http://www.copyright.com/)orcontacttheCopyrightClearanceCenter,Inc.(ccc) 222 Rosewood Drive, Danvers, MA,978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users, For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data Samarasinghe, Sandhya. Neural networks for applied sciences and engineering: from fundamentals to omplex pattern recognition/Sandhya Samarasinghe. p Includes bibliographical references and index SBN-13:978-0-8493-3375-0ak. Paper) ISBN-10: 0-8493-3375-X(alk. paper) 1. Neural networks(Computer science)2. Pattern recognition systems. I Title QA7687S2552006 006.32-dc22 2006007265 Visit the Taylor francis Web site at http://www.taylorandfrancis.com d the auerbach web site at http://www.auerbach-publications.com C 200 hy taylor I Giroup. LLC Dedication TO Do My husban For your constant love, support, and encouragement To do the best i can do in all My endeavors as a Woman and a Scholar O 2006 by Taylor Francis Group, LL.( C 2006 by Taylor Francis Giroup LLc Contents Preface.×ii Acknowledgments About the author ····:·4··;···:····+··*·:····.····:·············.·.;··········· XX 1 From Data to Models: Complexity and Challenges in Understanding Biological, Ecological, and Natural Systems 1.1: Introduction 1 1.2: Layout of the Book 4 References 7 2 Fundamentals of Neural Networks and Models for Linear Data Analysis 中······ 2.1: Introduction and overview 1 1 2.2: Neural Networks and Their Capabilities 12 2.3: Inspirations from Biology 16 2.4: Modeling Information Processing in Neurons 18 2.5: Neuron Models and Learning Strategies 19 2.5.1: Threshold Neuron as a Simple classifier 20 2.5.2: Learning Models for Neurons and Neural Assemblies 23 2.5.2.1: Hebbian Learning 23 2.5.2.2: Unsupervised or Competitive Learning 26 2.5.2.3: Supervised Learning 26 2.5.3: Perceptron with Supervised Learning as a Classifier 27 2.5.3.1: Perceptron Learning Algorithm 28 2.5.3.2: A Practical Example of Perceptron on a larger Realistic Data Set: Identifying the Origin of Fish from the growth-Ring Diameter of Scales 35 2.5.3.3: Comparison of Perceptron with Linear Discriminant Function Analysis in Statistics 38 O 2006 by Taylor Francis Giroup, LL.( VIl 2.5.3.4: Multi-Output Perceptron for Multicategory Classification 40 2.5.3.5: Higher-Dimensional Classification Using Perceptron 45 2.5.3.6: Perceptron Summary 45 2.5.4: Linear Neuron for Linear Classification and Prediction 46 2.5.4.1: Learning with the Delta Rule 47 2.5.4.2: Linear Neuron as a Classifier 51 2.5.4.3: Classification Properties of a Linear Neuron as a Subset of Predictive Capabilities 53 2.5.4.4: Example: Linear Neuron as a Predictor 54 2.5.4.5: A Practical Example of Linear Prediction Predicting the Heat Influx in a Home 61 2.5.4.6: Comparison of Linear Neuron Model with Linear Regression 62 2.5.4.7: Example: Multiple Input Linear Neuron Model--Improving the Prediction Accurac of Heat Influx in a Home 63 2.5.4.8: Comparison of a Multiple-Input Linear Neuron with Multiple Linear Regression 63 2.5.4.9: Multiple Linear Neuron Models 64 2.5.4.10: Comparison of a Multiple Linear neuron Network with Canonical Correlation Analysis 65 2.5.4.11: Linear Neuron and Linear Network Summary 65 2.6: Summary 66 Problems 66 References 67 3 Neural Networks for Nonlinear Pattern Recognition.....69 3.1: Overview and Introduction 69 3.1.1: Multilayer Perceptron 71 3.2: Nonlinear Neurons 72 3.2.1: Neuron Activation Functions 73 3.2.1.1: Sigmoid Functions 74 3.2.1.2: Gaussian Functions 76 3.2.2: Example: Population Growth Modeling Using a Nonlinear Neuron 77 3.2.3: Comparison of Nonlinear Neuron with Nonlinear Regression Analysis 80 3.3: One-Input Multilayer Nonlinear Networks 80 3.3.1: Processing with a Single nonlinear Hidden Neuron 80 3.3.2: Examples: Modeling Cyclical Phenomena with Multiple Nonlinear Neurons 86 3.3.2.1: Example 1: Approximating a Square Wave 86 3.3.2.2: Example 2: Modeling Seasonal Species Migration 94 3.4: Two-Input Multilayer Perceptron Network 98 3.4.1: Processing of Two-Dimensional Inputs by Nonlinear neurons 98 3.4.2: Network Output 102 C 2006 by Taylor Francis Giroup. LLc IX 3.4.3: Examples: Two-Dimensional Prediction and Classification 103 3.4.3.1: Example 1: Two-Dimensional Nonlinear Function Approximation 103 3.4.3.2: Example 2: Two-Dimensional Nonlinear Classification Model 105 3.5: Multidimensional Data Modeling with Nonlinear Multilayer Perceptron Networks 109 3.6: Summary 110 Problems 110 References 112 4 Learning of Nonlinear Patterns by Neural Networks 4.1: Introduction and Overview 113 4.2: Supervised Training of Networks for Nonlinear Pattern Recognition 114 4.3 Gradient Descent and Error Minimization 115 4.4: Backpropagation Learning 116 4.4.1: Example: Backpropagation Training-A Hand Computation 117 4.4.1.1: Error Gradient with Respect to Output Neuron Weights 120 4.4.1.2: The Error Gradient with Respect to the Hidden-Neuron Weights 123 4.4.1.3: Application of Gradient Descent. in Backpropagation Learning 127 4.4.1.4 Batch Learning 128 4. 4.1.5: Learning Rate and Weight Update 130 4.4.1.6: Example-by-Example(Online)Learning 134 4.4.1.7: Momentum 134 1.4.2: Example: Backpropagation Learning Computer Experiment 138 4.4.3: Single-Input Single-Output Network with Multiple hidden Neurons 141 4.4.4: Multiple-Input, Multiple-Hidden Neuron, and Single-Output Network 1412 4.4.5: Multiple-Input, Multiple-Hidden Neuron Multiple-Output Network 143 4.4.6: Example: Backpropagation Learning Case Study--Solving a Complex Classification Problen 115 4.5: Delta-Bar-Delta Learning(Adaptive Learning Rate) Method 152 4.5.1: Example: Network Training with Delta-Bar-Delta- A Hand computation 154 4.5.2: Example: Delta-Bar-Delta with Monentum- A Hand computation 157 4.5.3: Network Training with Delta-Bar Delta A Computer Experiment 158 4.5.4: Comparison of Delta-Bar-Delta Method with Backpropagation 159 O 2006 by Taylor Francis Giroup, LL.(

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