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# Neural Networks and Learning Machines: A Comprehensive Foundation

## bySimon O. Haykin

### Hardcover | July 22, 2008

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**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.

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The following ISBNs are associated with this title:

ISBN - 10:0131471392

ISBN - 13:9780131471399

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Table of Contents

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 Rosenblatt’s 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 Kushner’s 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 Cover’s 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 Hadamard’s Conditions for Well-Posedness 314

7.3 Tikhonov’s 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 Bellman’s 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