For graduate-level neural network courses offered in the departments of Computer Engineering, Electrical Engineering, and Computer Science. Neural Networks and Learning Machines, Third Edition is renowned for its thoroughness and readability. This well-organized and completely up-to-date text remains the most comprehensive treatment of neural networks from an engineering perspective. This is ideal for professional engineers and research scientists. Matlab codes used for the computer experiments in the text are available for download at: http://www.pearsonhighered.com/haykin/ Refocused, revised and renamed to reflect the duality of neural networks and learning machines, this edition recognizes that the subject matter is richer when these topics are studied together. Ideas drawn from neural networks and machine learning are hybridized to perform improved learning tasks beyond the capability of either independently.
Preface x Introduction 1 1. What is a Neural Network? 1 2. The Human Brain 6 3. Models of a Neuron 10 4. Neural Networks Viewed As Directed Graphs 15 5. Feedback 18 6. Network Architectures 21 7. Knowledge Representation 24 8. Learning Processes 34 9. Learning Tasks 38 10. Concluding Remarks 45 Notes and References 46 Chapter 1 Rosenblatts Perceptron 47 1.1 Introduction 47 1.2. Perceptron 48 1.3. The Perceptron Convergence Theorem 50 1.4. Relation Between the Perceptron and Bayes Classifier for a Gaussian Environment 55 1.5. Computer Experiment: Pattern Classification 60 1.6. The Batch Perceptron Algorithm 62 1.7. Summary and Discussion 65 Notes and References 66 Problems 66 Chapter 2 Model Building through Regression 68 2.1 Introduction 68 2.2 Linear Regression Model: Preliminary Considerations 69 2.3 Maximum a Posteriori Estimation of the Parameter Vector 71 2.4 Relationship Between Regularized Least-Squares Estimation and MAP Estimation 76 2.5 Computer Experiment: Pattern Classification 77 2.6 The Minimum-Description-Length Principle 79 2.7 Finite Sample-Size Considerations 82 2.8 The Instrumental-Variables Method 86 2.9 Summary and Discussion 88 Notes and References 89 Problems 89 Chapter 3 The Least-Mean-Square Algorithm 91 3.1 Introduction 91 3.2 Filtering Structure of the LMS Algorithm 92 3.3 Unconstrained Optimization: a Review 94 3.4 The Wiener Filter 100 3.5 The Least-Mean-Square Algorithm 102 3.6 Markov Model Portraying the Deviation of the LMS Algorithm from the Wiener Filter 104 3.7 The Langevin Equation: Characterization of Brownian Motion 106 3.8 Kushners Direct-Averaging Method 107 3.9 Statistical LMS Learning Theory for Small Learning-Rate Parameter 108 3.10 Computer Experiment I: Linear Prediction 110 3.11 Computer Experiment II: Pattern Classification 112 3.12 Virtues and Limitations of the LMS Algorithm 113 3.13 Learning-Rate Annealing Schedules 115 3.14 Summary and Discussion 117 Notes and References 118 Problems 119 Chapter 4 Multilayer Perceptrons 122 4.1 Introduction 123 4.2 Some Preliminaries 124 4.3 Batch Learning and On-Line Learning 126 4.4 The Back-Propagation Algorithm 129 4.5 XOR Problem 141 4.6 Heuristics for Making the Back-Propagation Algorithm Perform Better 144 4.7 Computer Experiment: Pattern Classification 150 4.8 Back Propagation and Differentiation 153 4.9 The Hessian and Its Role in On-Line Learning 155 4.10 Optimal Annealing and Adaptive Control of the Learning Rate 157 4.11 Generalization 164 4.12 Approximations of Functions 166 4.13 Cross-Validation 171 4.14 Complexity Regularization and Network Pruning 175 4.15 Virtues and Limitations of Back-Propagation Learning 180 4.16 Supervised Learning Viewed as an Optimization Problem 186 4.17 Convolutional Networks 201 4.18 Nonlinear Filtering 203 4.19 Small-Scale Versus Large-Scale Learning Problems 209 4.20 Summary and Discussion 217 Notes and References 219 Problems 221 Chapter 5 Kernel Methods and Radial-Basis Function Networks 230 5.1 Introduction 230 5.2 Covers Theorem on the Separability of Patterns 231 5.3 The Interpolation Problem 236 5.4 Radial-Basis-Function Networks 239 5.5 K-Means Clustering 242 5.6 Recursive Least-Squares Estimation of the Weight Vector 245 5.7 Hybrid Learning Procedure for RBF Networks 249 5.8 Computer Experiment: Pattern Classification 250 5.9 Interpretations of the Gaussian Hidden Units 252 5.10 Kernel Regression and Its Relation to RBF Networks 255 5.11 Summary and Discussion 259 Notes and References 261 Problems 263 Chapter 6 Support Vector Machines 268 6.1 Introduction 268 6.2 Optimal Hyperplane for Linearly Separable Patterns 269 6.3 Optimal Hyperplane for Nonseparable Patterns 276 6.4 The Support Vector Machine Viewed as a Kernel Machine 281 6.5 Design of Support Vector Machines 284 6.6 XOR Problem 286 6.7 Computer Experiment: Pattern Classification 289 6.8 Regression: Robustness Considerations 289 6.9 Optimal Solution of the Linear Regression Problem 293 6.10 The Representer Theorem and Related Issues 296 6.11 Summary and Discussion 302 Notes and References 304 Problems 307 Chapter 7 Regularization Theory 313 7.1 Introduction 313 7.2 Hadamards Conditions for Well-Posedness 314 7.3 Tikhonovs Regularization Theory 315 7.4 Regularization Networks 326 7.5 Generalized Radial-Basis-Function Networks 327 7.6 The Regularized Least-Squares Estimator: Revisited 331 7.7 Additional Notes of Interest on Regularization 335 7.8 Estimation of the Regularization Parameter 336 7.9 Semisupervised Learning 342 7.10 Manifold Regularization: Preliminary Considerations 343 7.11 Differentiable Manifolds 345 7.12 Generalized Regularization Theory 348 7.13 Spectral Graph Theory 350 7.14 Generalized Representer Theorem 352 7.15 Laplacian Regularized Least-Squares Algorithm 354 7.16 Experiments on Pattern Classification Using Semisupervised Learning 356 7.17 Summary and Discussion 359 Notes and References 361 Problems 363 Chapter 8 Principal-Components Analysis 367 8.1 Introduction 367 8.2 Principles of Self-Organization 368 8.3 Self-Organized Feature Analysis 372 8.4 Principal-Components Analysis: Perturbation Theory 373 8.5 Hebbian-Based Maximum Eigenfilter 383 8.6 Hebbian-Based Principal-Components Analysis 392 8.7 Case Study: Image Coding 398 8.8 Kernel Principal-Components Analysis 401 8.9 Basic Issues Involved in the Coding of Natural Images 406 8.10 Kernel Hebbian Algorithm 407 8.11 Summary and Discussion 412 Notes and References 415 Problems 418 Chapter 9 Self-Organizing Maps 425 9.1 Introduction 425 9.2 Two Basic Feature-Mapping Models 426 9.3 Self-Organizing Map 428 9.4 Properties of the Feature Map 437 9.5 Computer Experiments I: Disentangling Lattice Dynamics Using SOM 445 9.6 Contextual Maps 447 9.7 Hierarchical Vector Quantization 450 9.8 Kernel Self-Organizing Map 454 9.9 Computer Experiment II: Disentangling Lattice Dynamics Using Kernel SOM 462 9.10 Relationship Between Kernel SOM and Kullback-Leibler Divergence 464 9.11 Summary and Discussion 466 Notes and References 468 Problems 470 Chapter 10 Information-Theoretic Learning Models 475 10.1 Introduction 476 10.2 Entropy 477 10.3 Maximum-Entropy Principle 481 10.4 Mutual Information 484 10.5 Kullback-Leibler Divergence 486 10.6 Copulas 489 10.7 Mutual Information as an Objective Function to be Optimized 493 10.8 Maximum Mutual Information Principle 494 10.9 Infomax and Redundancy Reduction 499 10.10 Spatially Coherent Features 501 10.11 Spatially Incoherent Features 504 10.12 Independent-Components Analysis 508 10.13 Sparse Coding of Natural Images and Comparison with ICA Coding 514 10.14 Natural-Gradient Learning for Independent-Components Analysis 516 10.15 Maximum-Likelihood Estimation for Independent-Components Analysis 526 10.16 Maximum-Entropy Learning for Blind Source Separation 529 10.17 Maximization of Negentropy for Independent-Components Analysis 534 10.18 Coherent Independent-Components Analysis 541 10.19 Rate Distortion Theory and Information Bottleneck 549 10.20 Optimal Manifold Representation of Data 553 10.21 Computer Experiment: Pattern Classification 560 10.22 Summary and Discussion 561 Notes and References 564 Problems 572 Chapter 11 Stochastic Methods Rooted in Statistical Mechanics 579 11.1 Introduction 580 11.2 Statistical Mechanics 580 11.3 Markov Chains 582 11.4 Metropolis Algorithm 591 11.5 Simulated Annealing 594 11.6 Gibbs Sampling 596 11.7 Boltzmann Machine 598 11.8 Logistic Belief Nets 604 11.9 Deep Belief Nets 606 11.10 Deterministic Annealing 610 11.11 Analogy of Deterministic Annealing with Expectation-Maximization Algorithm 616 11.12 Summary and Discussion 617 Notes and References 619 Problems 621 Chapter 12 Dynamic Programming 627 12.1 Introduction 627 12.2 Markov Decision Process 629 12.3 Bellmans Optimality Criterion 631 12.4 Policy Iteration 635 12.5 Value Iteration 637 12.6 Approximate Dynamic Programming: Direct Methods 642 12.7 Temporal-Difference Learning 643 12.8 Q-Learning 648 12.9 Approximate Dynamic Programming: Indirect Methods 652 12.10 Least-Squares Policy Evaluation 655 12.11 Approximate Policy Iteration 660 12.12 Summary and Discussion 663 Notes and References 665 Problems 668 Chapter 13 Neurodynamics 672 13.1 Introduction 672 13.2 Dynamic Systems 674 13.3 Stability of Equilibrium States 678 13.4 Attractors 684 13.5 Neurodynamic Models 686 13.6 Manipulation of Attractors as a Recurrent Network Paradigm 689 13.7 Hopfield Model 690 13.8 The Cohen-Grossberg Theorem 703 13.9 Brain-State-In-A-Box Model 705 13.10 Strange Attractors and Chaos 711 13.11 Dynamic Reconstruction of a Chaotic Process 716 13.12 Summary and Discussion 722 Notes and References 724 Problems 727 Chapter 14 Bayseian Filtering for State Estimation of Dynamic Systems 731 14.1 Introduction 731 14.2 State-Space Models 732 14.3 Kalman Filters 736 14.4 The Divergence-Phenomenon and Square-Root Filtering 744 14.5 The Extended Kalman Filter 750 14.6 The Bayesian Filter 755 14.7 Cubature Kalman Filter: Building on the Kalman Filter 759 14.8 Particle Filters 765 14.9 Computer Experiment: Comparative Evaluation of Extended Kalman and Particle Filters 775 14.10 Kalman Filtering in Modeling of Brain Functions 777 14.11 Summary and Discussion 780 Notes and References 782 Problems 784 Chapter 15 Dynamically Driven Recurrent Networks 790 15.1 Introduction 790 15.2 Recurrent Network Architectures 791 15.3 Universal Approximation Theorem 797 15.4 Controllability and Observability 799 15.5 Computational Power of Recurrent Networks 804 15.6 Learning Algorithms 806 15.7 Back Propagation Through Time 808 15.8 Real-Time Recurrent Learning 812 15.9 Vanishing Gradients in Recurrent Networks 818 15.10 Supervised Training Framework for Recurrent Networks Using Nonlinear Sequential State Estimators 822 15.11 Computer Experiment: Dynamic Reconstruction of Mackay-Glass Attractor 829 15.12 Adaptivity Considerations 831 15.13 Case Study: Model Reference Applied to Neurocontrol 833 15.14 Summary and Discussion 835 Notes and References 839 Problems 842 Bibliography 845 Index 889