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Part Ⅰ Traces of History and A Neuroscience Briefer3

1．Brain Style Computing：Origins and Issues3

1.1 From the Greeks to the Renaissance3

1.2 The Advent of Modern Neuroscience6

1.3 On the Road to Artificial Intelligence9

1.4 Classical AI and Neural Networks12

1.5 Hybrid Intelligent Systems14

Chapter Summary15

Bibliographic Remarks16

2．Lessons from Neuroscience17

2.1 The Human Brain17

2.2 Biological Neurons23

Chapter Summary37

Bibliographic Remarks38

Part Ⅱ Feedforward Neural Networks and Supervised Learning38

3．Artificial Neurons,Neural Networks and Architectures41

3.1 Neuron Abstraction41

3.2 Neuron Signal Functions44

3.3 Mathematical Preliminaries53

3.4 Neural Networks Defined61

3.5 Architectures：Feedforward and Feedback62

3.6 Salient Properties and Application Domains of Neural Networks65

Chapter Summary68

Bibliographic Remarks69

Review Questions69

4．Geometry of Binary Threshold Neurons and Their Networks72

4.1 Pattern Recognition and Data Classification72

4.2 Convex Sets.Convex Hulls and Linear Separability76

4.3 Space of Boolean Functions78

4.4 Binary Neurons are Pattern Dichotomizers80

4.5 Non-linearly Separable Problems83

4.6 Capacity of a Simple Threshold Logic Neuron87

4.7 Revisiting thie XOR Problem92

4.8 Multilayer Networks95

4.9 How Many Hidden Nodes are Enough?97

Chapter Summary99

Bibliographic Remarks100

Review Questions100

5．Supervised Learning Ⅰ：Perceptrons and LMS104

5.1 Learning and Memory104

5.2 From Synapses to Behaviour：The Case of Aplysia106

5.3 Learning Algorithms110

5.4 Error Correction and Gradient Descent Rules114

5.5 The Learning Objective for TLNs115

5.6 Pattern Space and Weight Space117

5.7 Perceptron Learning Algorithm119

5.8 Perceptron Convergence Theorem122

5.9 A Handworked Example and MATLAB Simulation125

5.10 Perceptron Learning and Non-separable Sets128

5.11 Handling Linearly Non-separable Sets130

5.12 α-Least Mear Square Learning132

5.13 MSE Error Surface and its Geometry137

5.14 Steepest Descent Search with Exact Gradient Information143

5.15 μ-LMS：Approximate Gradient Descent147

5.16 Application of LMS to Noise Cancellation152

Chapter Summary156

Bibliographic Remarks157

Review Questions158

6．Supervised Learning Ⅱ：Backpropagation and Beyond164

6.1 Multilayered Network Architectures164

6.2 Backpropagation Learning Algorithm167

6.3 Handworked Example177

6.4 MATLAB Simulation Examples181

6.5 Practical Considerations in Implementing the BP Algorithm187

6.6 Structure Growing Algorithms196

6.7 Fast Relatives of Backpropagation198

6.8 Universal Function Approximation and Neural Networks199

6.9 Applications of Feedforward Neural Networks201

6.10 Reinforcement Learning:A Brief Review205

Chapter Summary212

Bibliographic Remarks213

Review Questions214

7．Neural Networks:A Statistical Pattern Recognition Perspective218

7.1 Introduction218

7.2 Bayes'Theorem219

7.3 Two Instructive MATLAB Simulations222

7.4 Implementing Classification Decisions with Bayes'Theorem227

7.5 Probabilistic Interpretation of a Neuron Discriminant Function230

7.6 MATLAB Simulation:Plotting Bayesian Decision Boundaries232

7.7 Interpreting Neuron Signals as Probabilities236

7.8 Multilayered Networks,Error Functions and Posterior Probabilities239

7.9 Error Functions for Classification Problems245

Chapter Summary254

Bibliographic Remarks255

Review Questions255

8．Focussing on Generalization:Support Vector Machines and Radial Basis Function Networks259

8.1 Learning From Examples and Generalization259

8.2 Statistical Learning Theory Briefer264

8.3 Support Vector Machines273

8.4 Radial Basis Function Networks304

8.5 Regularization Theory Route to RBFNs314

8.6 Generalized Radial Basis Function Network323

8.7 Learning in RBFN's326

8.8 Image Classification Application329

8.9 Other Models For Valid Generalization334

Chapter Summary339

Bibliographic Remarks341

Review Questions341

Part Ⅲ Recurrent Neurodynamical Systems347

9．Dynamical Systems Review347

9.1 States,State Vectors and Dynamics347

9.2 State Equations350

9.3 Attractors and Stability352

9.4 Linear Dynamical Systems354

9.5 Non-linear Dynamical Systems358

9.6 Lyapunov Stability363

9.7 Neurodynamical Systems369

9.8 The Cohen-Grossberg Theorem373

Chapter Summary375

Bibliographic Remarks376

Review Questions376

10．Attractor Neural Networks378

10.1 Introduction378

10.2 Associative Learning379

10.3 Attractor Neural Network Associative Memory382

10.4 Linear Associative Memory386

10.5 Hopfield Network389

10.6 Content Addressable Memory397

10.7 Two Handworked Examples400

10.8 Example of Recall of Memories in Continuous Time404

10.9 Spurious Attractors405

10.10 Error Correction with Bipolar Encoding407

10.11 Error Performance of Hopfield Networks409

10.12 Applications of Hopfield Networks412

10.13 Brain-State-in-a-Box Neural Network419

10.14 Simulated Annealing426

10.15 Boltzmann Machine431

10.16 Bidirectional Associative Memory440

10.17 Handworked Example443

10.18 BAM Stability Analysis447

10.19 Error Correction in BAMs448

10.20 Memory Annihilation of Structured Maps in BAMs450

10.21 Continuous BAMs457

10.22 Adaptive BAMs458

10.23 Application：Pattern Association461

Chapter Summary462

Bibliographic Remarks464

Review Questions464

11．Adaptive Resonance Theory469

11.1 Noise-Saturation Dilemma469

11.2 Solving the Noise-Saturation Dilemma471

11.3 Recurrent On-center-Off-surround Networks477

11.4 Building Blocks of Adaptive Resonance482

11.5 Substrate of Resonance487

11.6 Structural Details of the Resonance Model489

11.7 Adaptive Resonance Theory Ⅰ（ART Ⅰ）491

11.8 Handworked Example502

11.9 MATLAB Code Description504

11.10 A Breezy Review of ART Operating Principles506

11.11 Neurophysiological Evidence for ART Mechanisms507

11.12 Applications511

Chapter Summary516

Bibliographic Remarks517

Review Questions518

12．Towards the Self-organizing Feature Map521

12.1 Self-organization521

12.2 Maximal Eigenvector Filtering522

12.3 Extracting Principal Components：Sanger's Rule530

12.4 Generalized Learning Laws532

12.5 Competitive Learning Revisited537

12.6 Vector Quantization540

12.7 Mexican Hat Networks546

12.8 Self-organizing Feature Maps552

12.9 Applications of the Self Organizing Map563

Chapter Summary569

Bibliographic Remarks570

Review Questions571

Part Ⅳ Contemporary Topics577

13．Pulsed Neuron Models：The New Generation577

13.1 Introduction577

13.2 Spiking Neuron Model578

13.3 Integrate-and-Fire Neurons586

13.4 Conductance Based Models594

13.5 Computing with Spiking Neurons608

13.6 Reflections...616

Chapter Summary617

Bibliographic Remarks618

14．Fuzzy Sets,Fuzzy Systems and Applications620

14.1 Need for Numeric and Linguistic Processing620

14.2 Fuzzy Uncertainty and the Linguistic Variable621

14.3 Fuzzy Set622

14.4 Membership Functions624

14.5 Geometry of Fuzzy Sets627

14.6 Simple Operations on Fuzzy Sets628

14.7 Fuzzy Rules for Approximate Reasoning632

14.8 Rule Composition and Deffuzification634

14.9 Fuzzy Engineering638

14.10 Applications644

Chapter Summary649

Bibliographic Remarks650

Review Questions650

15．Neural Networks and the Soft Computing Paradigm652

15.1 Soft Computing=Neural+Fuzzy+Evolutionary652

15.2 Neural Networks：A Summary654

15.3 Fuzzy Sets and Systems：A Summary656

15.4 Genetic Algorithms658

15.5 Neural Networks and Fuzzy Logic662

15.6 Neuro-Fuzzy-Genetic Integration671

15.7 Integration Example：Subsethood-Product Based Fuzzy-Neural Inference System675

15.8 A Concluding Note683

Chapter Summary684

Bibliographic Remarks685

Appendix A：Neural Network Hardware686

A.1 Motivation and Issues686

A.2 Analog Building Blocks for Neuromorphic Networks687

A.3 Digital Techniques691

A.4 Bibliographic Remarks692

Appendix B：Web Pointers694

Bibliography697

Index729