NEURAL AND ADAPTIVE SYSTEMS: Fundamentals through Simulations

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1 NEURAL AND ADAPTIVE SYSTEMS: Fundamentals through Simulations JOSE C. PRINCIPE NEIL R. EULIANO W. CURT LEFEBVRE JOHN WILEY & SONS, INC. New York / Chichester / Weinheim / Brisbane / Singapore / Toronto

2 CHAPTER 1, DATA FITTING WITH LINEAR MODELS i 1.1 Introduction Linear Models Least Squares Adaptive Linear Systems Estimation of the Gradient: the LMS Algorithm A Methodology for Stable Adaptation Regression for Multiple Variables Newton's Method Analytic versus Iterative Solutions The Linear Regression Model Conclusions Exercises NeuroSolutions Examples Concept Map for Chapter 1 66 References 67 CHAPTER 2 PATTERN RECOGNITION The Pattern-Recognition Problem Statistical Formulation of Classifiers Linear and Nonlinear Classifier Machines Methods of Training Parametric Classifiers Conclusions 97 / 2.6 Exercises NeuroSolutions Example Concept Map for Chapter 2 98 References 99 CHAPTER 3 MULTILAYER PERCEPTRONS Artificial Neural Networks (ANNs) Pattern-Recognition Ability of the McCulloch-Pitts PE The Perceptron One-Hidden-Layer Multilayer Perceptrons MLPs With Two Hidden Layers Training Static Networks with the Backpropagation Procedure Training Embedded Adaptive Systems 160 ix

3 3.8 MLPs as Optimal Classifiers Conclusions NeuroSolutions Examples Exercises Concept Map for Chapter References 172 CHAPTER 4 DESIGNING AND TRAINING MLPS Introduction Controlling Learning in Practice Other Search Procedures Stop Criteria How Good Are MLPs as Learning Machines? Error Criterion Network Size and Generalization Project: Application of the MLP to Real-World Data Conclusion List of NeuroSolutions Examples Exercises Concept Map for Chapter ; References 222 CHAPTER 5 FUNCTION APPROXIMATION WITH MLPS, RADIAL BASIS FUNCTIONS, AND SUPPORT VECTOR MACHINES Introduction Function Approximation Choices for the Elementary Functions Probablistic Interpretation of,the Mappings: Nonlinear Regression Training Neural Networks for Function Approximation How to Select the Number of Bases Applications of Radial Basis Functions Support Vector Machines Project: Applications of Neural Networks as Function Approximators Conclusion Exercises NeuroSolutions Examples Concept Map for Chapter References 278 CHAPTER 6 HEBBIAN LEARNING AND PRINCIPAL COMPONENT ANALYSIS Introduction Effect of the Hebbian Update 281

4 XI 6.3 Oja's Rule Principal Component Analysis Anti-Hebbian Learning Estimating Cross-Correlation with Hebbian Networks Novelty Filters and Lateral Inhibition > Linear Associative Memories (LAMs) LMS Learning as a Combination of Hebbian Rules Autoassociation Nonlinear Associative Memories Project: Use of Hebbian Networks for Data Compression and Associative Memories Conclusions Exercises NeuroSolutions Examples Concept Map for Chapter References 332 CHAPTER 7 COMPETITIVE AND KOHONEN NETWORKS Introduction Competition and Winner-Take-All Networks Competitive Learning Clustering 341 7:5 Improving Competitive Learning Soft Competition Kohonen Self-Organizing Map Creating Classifiers from Competitive Networks Adaptive Resonance Theory (ART) Modular Networks Conclusions 360, 7.12 Exercises NeuroSolutions Examples Concept Map for Chapter References 363 CHAPTER 8 PRINCIPLES OF DIGITAL SIGNAL PROCESSING Time Series and Computers Vectors and Discrete Signals The Concept of Filtering Time Domain Analysis of Linear Systems / Recurrent Systems and Stability Frequency Domain Analysis The Z Transform and the System Transfer Function 8.8 The Frequency Response

5 XII CONTENTS 8.9 Frequency Response and Poles and Zeros 8.10 Types of Linear Filters Project: Design of Digital Filters Conclusions Exercises NeuroSolutions Examples Concept Map for Chapter References CHAPTER 9 ADAPTIVE FILTERS Introduction The Adaptive Linear Combiner and Linear Regression 9.3 Optimal Filter Weights Properties of the Iterative Solution Hebbian Networks for Time Processing Applications of the Adaptive Linear Combiner Applications of Temporal PCA Networks Conclusions Exercises NeuroSolutions Examples Concept Map for Chapter References CHAPTER 10 TEMPORAL PROCESSING WITH NEURAL NETWORKS Static versus Dynamic Systems Extracting Information in Time The Focused Time-Delay Neural Network (TDNN) The Memory PE 485, 10.5 The Memory Filter 491 '' 10.6 Design of the Memory Space The Gamma Memory PE Time-Lagged Feedforward Networks Focused TLFNs Built From RBFs Project: Iterative Prediction of Chaotic Time Series Conclusions Exercises NeuroSolutions Examples Concept Map for Chapter References 524 CHAPTER 11 TRAINING AND USING RECURRENT NETWORKS Introduction Simple Recurrent Topologies 527

6 XIII 11.3 Adapting the Feedback Parameter Unfolding Recurrent Networks in Time The Distributed TLFN Topology Dynamic Systems Recurrent Neural Networks Learning Paradigms for Recurrent Systems Applications of Dynamic Networks to System Identification and Control Hopfield Networks Grossberg's Additive Model Beyond First-Order Dynamics: Freeman's Model Conclusions Exercises NeuroSolutions Examples Concept Map for Chapter References 587 APPENDIX A ELEMENTS OF LINEAR ALGEBRA AND PATTERN RECOGNITION 589 A.I Introduction 589 A.2 Vectors: Concepts and Definitions 590 A.3 Matrices: Concepts and Definitions 596 A.4 Random Vectors 602 A.5 Conclusions 611 APPENDIX B NEUROSOLUTIONS TUTORIAL 613 B.I Introduction to Neurosolutions 613 B.2 Introduction to the Interactive Examples 614 B.3 Basic Operation of Neurosolutions 616 B.4 Probing the System 623 B.5 The Input Family 627 B.6 Training a Network 632 B.7 Summary 635 APPENDIX C DATADIRECTORY 637 GLOSSARY 639 INDEX 647

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