Neural Networks and Learning Machines

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ISBN: 9780131471399 | 0131471392
Cover: Hardcover
Copyright: 11/18/2008

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Fluid and authoritative, this well-organized book represents the first comprehensive treatment of neural networks from an engineering perspective, providing extensive, state-of-the-art coverage that will expose readers to the myriad facets of neural networks and help them appreciate the technology's origin, capabilities, and potential applications.Examines all the important aspects of this emerging technolgy, covering the learning process, back propogation, radial basis functions, recurrent networks, self-organizing systems, modular networks, temporal processing, neurodynamics, and VLSI implementation. Integrates computer experiments throughout to demonstrate how neural networks are designed and perform in practice. Chapter objectives, problems, worked examples, a bibliography, photographs, illustrations, and a thorough glossary all reinforce concepts throughout. New chapters delve into such areas as support vector machines, and reinforcement learning/neurodynamic programming, plus readers will find an entire chapter of case studies to illustrate the real-life, practical applications of neural networks. A highly detailed bibliography is included for easy reference.For professional engineers and research scientists.

Preface	p. x
Introduction	p. 1
What is a Neural Network?	p. 1
The Human Brain	p. 6
Models of a Neuron	p. 10
Neural Networks Viewed As Directed Graphs	p. 15
Feedback	p. 18
Network Architectures	p. 21
Knowledge Representation	p. 24
Learning Processes	p. 34
Learning Tasks	p. 38
Concluding Remarks	p. 45
Notes and References	p. 46
Rosenblatt's Perceptron	p. 47
Introduction	p. 47
Perceptron	p. 48
The Perceptron Convergence Theorem	p. 50
Relation Between the Perceptron and Bayes Classifier for a Gaussian Environment	p. 55
Computer Experiment: Pattern Classification	p. 60
The Batch Perceptron Algorithm	p. 62
Summary and Discussion	p. 65
Notes and References	p. 66
Problems	p. 66
Model Building through Regression	p. 68
Introduction	p. 68
Linear Regression Model: Preliminary Considerations	p. 69
Maximum a Posteriori Estimation of the Parameter Vector	p. 71
Relationship Between Regularized Least-Squares Estimation and MAP Estimation	p. 76
Computer Experiment: Pattern Classification	p. 77
The Minimum-Description-Length Principle	p. 79
Finite Sample-Size Considerations	p. 82
The Instrumental-Variables Method	p. 86
Summary and Discussion	p. 88
Notes and References	p. 89
Problems	p. 89
The Least-Mean-Square Algorithm	p. 91
Introduction	p. 91
Filtering Structure of the LMS Algorithm	p. 92
Unconstrained Optimization: a Review	p. 94
The Wiener Filter	p. 100
The Least-Mean-Square Algorithm	p. 102
Markov Model Portraying the Deviation of the LMS Algorithm from the Wiener Filter	p. 104
The Langevin Equation: Characterization of Brownian Motion	p. 106
Kushner's Direct-Averaging Method	p. 107
Statistical LMS Learning Theory for Small Learning-Rate Parameter	p. 108
Computer Experiment I: Linear Prediction	p. 110
Computer Experiment II: Pattern Classification	p. 112
Virtues and Limitations of the LMS Algorithm	p. 113
Learning-Rate Annealing Schedules	p. 115
Summary and Discussion	p. 117
Notes and References	p. 118
Problems	p. 119
Multilayer Perceptrons	p. 122
Introduction	p. 123
Some Preliminaries	p. 124
Batch Learning and On-Line Learning	p. 126
The Back-Propagation Algorithm	p. 129
XOR Problem	p. 141
Heuristics for Making the Back-Propagation Algorithm Perform Better	p. 144
Computer Experiment: Pattern Classification	p. 150
Back Propagation and Differentiation	p. 153
The Hessian and Its Role in On-Line Learning	p. 155
Optimal Annealing and Adaptive Control of the Learning Rate	p. 157
Generalization	p. 164
Approximations of Functions	p. 166
Cross-Validation	p. 171
Complexity Regularization and Network Pruning	p. 175
Virtues and Limitations of Back-Propagation Learning	p. 180
Supervised Learning Viewed as an Optimization Problem	p. 186
Convolutional Networks	p. 201
Nonlinear Filtering	p. 203
Small-Scale Versus Large-Scale Learning Problems	p. 209
Summary and Discussion	p. 217
Notes and References	p. 219
Problems	p. 221
Kernel Methods and Radial-Basis Function Networks	p. 230
Introduction	p. 230
Cover's Theorem on the Separability of Patterns	p. 231
The Interpolation Problem	p. 236
Radial-Basis-Function Networks	p. 239
K-Means Clustering	p. 242
Recursive Least-Squares Estimation of the Weight Vector	p. 245
Hybrid Learning Procedure for RBF Networks	p. 249
Computer Experiment: Pattern Classification	p. 250
Interpretations of the Gaussian Hidden Units	p. 252
Kernel Regression and Its Relation to RBF Networks	p. 255
Summary and Discussion	p. 259
Notes and References	p. 261
Problems	p. 263
Support Vector Machines	p. 268
Introduction	p. 268
Optimal Hyperplane for Linearly Separable Patterns	p. 269
Optimal Hyperplane for Nonseparable Patterns	p. 276
The Support Vector Machine Viewed as a Kernel Machine	p. 281
Design of Support Vector Machines	p. 284
XOR Problem	p. 286
Computer Experiment: Pattern Classification	p. 289
Regression: Robustness Considerations	p. 289
Optimal Solution of the Linear Regression Problem	p. 293
The Representer Theorem and Related Issues	p. 296
Summary and Discussion	p. 302
Notes and References	p. 304
Problems	p. 307
Regularization Theory	p. 313
Introduction	p. 313
Hadamard's Conditions for Well-Posedness	p. 314
Tikhonov's Regularization Theory	p. 315
Regularization Networks	p. 326
Generalized Radial-Basis-Function Networks	p. 327
The Regularized Least-Squares Estimator: Revisited	p. 331
Additional Notes of Interest on Regularization	p. 335
Estimation of the Regularization Parameter	p. 336
Semisupervised Learning	p. 342
Manifold Regularization: Preliminary Considerations	p. 343
Differentiable Manifolds	p. 345
Generalized Regularization Theory	p. 348
Spectral Graph Theory	p. 350
Generalized Representer Theorem	p. 352
Laplacian Regularized Least-Squares Algorithm	p. 354
Experiments on Pattern Classification Using Semisupervised Learning	p. 356
Summary and Discussion	p. 359
Notes and References	p. 361
Problems	p. 363
Principal-Components Analysis	p. 367
Introduction	p. 367
Principles of Self-Organization	p. 368
Self-Organized Feature Analysis	p. 372
Principal-Components Analysis: Perturbation Theory	p. 373
Hebbian-Based Maximum Eigenfilter	p. 383
Hebbian-Based Principal-Components Analysis	p. 392
Case Study: Image Coding	p. 398
Kernel Principal-Components Analysis	p. 401
Basic Issues Involved in the Coding of Natural Images	p. 406
Kernel Hebbian Algorithm	p. 407
Summary and Discussion	p. 412
Notes and References	p. 415
Problems	p. 418
Self-Organizing Maps	p. 425
Introduction	p. 425
Two Basic Feature-Mapping Models	p. 426
Self-Organizing Map	p. 428
Properties of the Feature Map	p. 437
Computer Experiments I: Disentangling Lattice Dynamics Using SOM	p. 445
Contextual Maps	p. 447
Hierarchical Vector Quantization	p. 450
Kernel Self-Organizing Map	p. 454
Computer Experiment II: Disentangling Lattice Dynamics Using Kernel SOM	p. 462
Relationship Between Kernel SOM and Kullback-Leibler Divergence	p. 464
Summary and Discussion	p. 466
Notes and References	p. 468
Problems	p. 470
Information-Theoretic Learning Models	p. 475
Introduction	p. 476
Entropy	p. 477
Maximum-Entropy Principle	p. 481
Mutual Information	p. 484
Kullback-Leibler Divergence	p. 486
Copulas	p. 489
Mutual Information as an Objective Function to be Optimized	p. 493
Maximum Mutual Information Principle	p. 494
Infomax and Redundancy Reduction	p. 499
Spatially Coherent Features	p. 501
Spatially Incoherent Features	p. 504
Independent-Components Analysis	p. 508
Sparse Coding of Natural Images and Comparison with ICA Coding	p. 514
Natural-Gradient Learning for Independent-Components Analysis	p. 516
Maximum-Likelihood Estimation for Independent-Components Analysis	p. 526
Maximum-Entropy Learning for Blind Source Separation	p. 529
Maximization of Negentropy for Independent-Components Analysis	p. 534
Coherent Independent-Components Analysis	p. 541
Rate Distortion Theory and Information Bottleneck	p. 549
Optimal Manifold Representation of Data	p. 553
Computer Experiment: Pattern Classification	p. 560
Summary and Discussion	p. 561
Notes and References	p. 564
Problems	p. 572
Stochastic Methods Rooted in Statistical Mechanics	p. 579
Introduction	p. 580
Statistical Mechanics	p. 580
Markov Chains	p. 582
Metropolis Algorithm	p. 591
Simulated Annealing	p. 594
Gibbs Sampling	p. 596
Boltzmann Machine	p. 598
Logistic Belief Nets	p. 604
Deep Belief Nets	p. 606
Deterministic Annealing	p. 610
Analogy of Deterministic Annealing with Expectation-Maximization Algorithm	p. 616
Summary and Discussion	p. 617
Notes and References	p. 619
Problems	p. 621
Dynamic Programming	p. 627
Introduction	p. 627
Markov Decision Process	p. 629
Bellman's Optimality Criterion	p. 631
Policy Iteration	p. 635
Value Iteration	p. 637
Approximate Dynamic Programming: Direct Methods	p. 642
Temporal-Difference Learning	p. 643
Q-Learning	p. 648
Approximate Dynamic Programming: Indirect Methods	p. 652
Least-Squares Policy Evaluation	p. 655
Approximate Policy Iteration	p. 660
Summary and Discussion	p. 663
Notes and References	p. 665
Problems	p. 668
Neurodynamics	p. 672
Introduction	p. 672
Dynamic Systems	p. 674
Stability of Equilibrium States	p. 678
Attractors	p. 684
Neurodynamic Models	p. 686
Manipulation of Attractors as a Recurrent Network Paradigm	p. 689
Hopfield Model	p. 690
The Cohen-Grossberg Theorem	p. 703
Brain-State-In-A-Box Model	p. 705
Strange Attractors and Chaos	p. 711
Dynamic Reconstruction of a Chaotic Process	p. 716
Summary and Discussion	p. 722
Notes and References	p. 724
Problems	p. 727
Bayseian Filtering for State Estimation of Dynamic Systems	p. 731
Introduction	p. 731
State-Space Models	p. 732
Kalman Filters	p. 736
The Divergence-Phenomenon and Square-Root Filtering	p. 744
The Extended Kalman Filter	p. 750
The Bayesian Filter	p. 755
Cubature Kalman Filter: Building on the Kalman Filter	p. 759
Particle Filters	p. 765
Computer Experiment: Comparative Evaluation of Extended Kalman and Particle Filters	p. 775
Kalman Filtering in Modeling of Brain Functions	p. 777
Summary and Discussion	p. 780
Notes and References	p. 782
Problems	p. 784
Dynamically Driven Recurrent Networks	p. 790
Introduction	p. 790
Recurrent Network Architectures	p. 791
Universal Approximation Theorem	p. 797
Controllability and Observability	p. 799
Computational Power of Recurrent Networks	p. 804
Learning Algorithms	p. 806
Back Propagation Through Time	p. 808
Real-Time Recurrent Learning	p. 812
Vanishing Gradients in Recurrent Networks	p. 818
Supervised Training Framework for Recurrent Networks Using Nonlinear Sequential State Estimators	p. 822
Computer Experiment: Dynamic Reconstruction of Mackay-Glass Attractor	p. 829
Adaptivity Considerations	p. 831
Case Study: Model Reference Applied to Neurocontrol	p. 833
Summary and Discussion	p. 835
Notes and References	p. 839
Problems	p. 842
Bibliography	p. 845
Index	p. 889
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Neural Networks and Learning Machines

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