Optimization Techniques
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Table of contents
- Cover
- Contentsv
- Contributorsxv
- Prefacexvii
- Chapter 1. Optimal Learning in Artificial Neural Networks: A Theoretical View1
- I. Introduction1
- II. Formulation of Learning as an Optimization Problem4
- III. Learning with No Local Minima10
- IV. Learning with Suboptimal Solutions33
- V. Advanced Techniques for Optimal Learning44
- VI. Conclusions45
- References47
- Chapter 2. Orthogonal Transformation Techniques in the Optimization of Feedforward Neural Network Sy53
- I. Introduction53
- II. Mathematical Background for the Transformations Used55
- III. Network-Size Optimization through Subset Selection58
- IV. Introduction to Illustrative Examples61
- V. Example 1: Modeling of the Mackey–Glass Series62
- VI. Example 2: Modeling of the Sunspot Series65
- VII. Example 3: Modeling of the Rocket Engine Testing Problem71
- VIII. Assessment of Convergence in Training Using Singular Value Decomposition74
- IX. Conclusions76
- Appendix A: Configuration of a Series with Nearly Repeating Periodicity for Singular Value Decomposi76
- Appendix B: Singular Value Ratio Spectrum77
- References77
- Chapter 3. Sequential Constructive Techniques81
- I. Introduction81
- II. Problems in Training with Back Propagation82
- III. Constructive Training Methods85
- IV. Sequential Constructive Methods: General Structure88
- V. Sequential Constructive Methods: Specific Approaches105
- VI. Hamming Clustering Procedure123
- VII. Experimental Results125
- VIII. Conclusions139
- References140
- Chapter 4. Fast Backpropagation Training Using Optimal Learning Rate and Momentum145
- I. Introduction145
- II. Computation of Derivatives of Learning Parameters148
- III. Optimization of Dynamic Learning Rate154
- IV. Simultaneous Optimization of μ and α158
- V. Selection of the Descent Direction160
- VI. Simulation Results161
- VII. Conclusion168
- References172
- Chapter 5. Learning of Nonstationary Processes175
- I. Introduction175
- II. A Priori Limitations177
- III. Formalization of the Problem178
- IV. Transformation into an Unconstrained Minimization Problem179
- V. One-to-One Mapping D182
- VI. Learning with Minimal Degradation Algorithm183
- VII. Adaptation of Learning with Minimal Degradation for Radial Basis Function Units186
- VIII. Choosing the Coefficients of the Cost Function188
- IX. Implementation Details190
- X. Performance Measures191
- XI. Experimental Results194
- XII. Discussion200
- XIII. Conclusion204
- References206
- Chapter 6. Constraint Satisfaction Problems209
- I. Constraint Satisfaction Problems209
- II. Assessment Criteria for Constraint Satisfaction Techniques213
- III. Constraint Satisfaction Techniques221
- IV. Neural Networks for Constraint Satisfaction227
- V. Assessment240
- References244
- Chapter 7. Dominant Neuron Techniques249
- I. Introduction249
- II. Continuous Winner-Take-All Neural Networks252
- III. Iterative Winner-Take-All Neural Networks256
- IV. K-Winners-Take-All Neural Networks268
- V. Conclusions273
- References274
- Chapter 8. CMAC-Based Techniques for Adaptive Learning Control277
- I. Introduction277
- II. Neural Networks for Learning Control278
- III. Conventional Cerebellar Model Articulation Controller284
- IV. Advanced Cerebellar Model Articulation Controller-Based Techniques290
- V. Structure Composed of Small Cerebellar Model Articulation Controllers298
- VI. Conclusions302
- References303
- Chapter 9. Information Dynamics and Neural Techniques for Data Analysis305
- I. Introduction305
- II. Statistical Structure Extraction: Parametric Formulation by Unsupervised Neural Learning307
- III. Statistical Structure Extraction: Nonparametric Formulation326
- IV. Nonparametric Characterization of Dynamics: The Information Flow Concept337
- V. Conclusions345
- References349
- Chapter 10. Radial Basis Function Network Approximation and Learning in Task-Dependent Feedforward C353
- I. Introduction353
- II. Problem Statement357
- III. Radial Basis Function Approximation366
- IV. Learning Feedforward for a Given Task373
- V. On-Line Learning Update in Task-Dependent Feedforward378
- VI. Adaptive Learning of Task-Dependent Feedforward382
- VII. Conclusions391
- References391
- Index395
- Erratum399
Optimization Techniques is a unique reference source to a diverse array of methods for achieving optimization, and includes both systems structures and computational methods. The text devotes broad coverage toa unified view of optimal learning, orthogonal transformation techniques, sequential constructive techniques, fast back propagation algorithms, techniques for neural networks with nonstationary or dynamic outputs, applications to constraint satisfaction,optimization issues and techniques for unsupervised learning neural networks, optimum Cerebellar Model of Articulation Controller systems, a new statistical theory of optimum neural learning, and the role of the Radial Basis Function in nonlinear dynamical systems.This volume is useful for practitioners, researchers, and students in industrial, manufacturing, mechanical, electrical, and computer engineering.
Key Features
* Provides in-depth treatment of theoretical contributions to optimal learning for neural network systems
* Offers a comprehensive treatment of orthogonal transformation techniques for the optimization of neural network systems
* Includes illustrative examples and comprehensive treatment of sequential constructive techniques for optimization of neural network systems
* Presents a uniquely comprehensive treatment of the highly effective fast back propagation algorithms for the optimization of neural network systems
* Treats, in detail, optimization techniques for neural network systems with nonstationary or dynamic inputs
* Covers optimization techniques and applications of neural network systems in constraint satisfaction
Key Features
* Provides in-depth treatment of theoretical contributions to optimal learning for neural network systems
* Offers a comprehensive treatment of orthogonal transformation techniques for the optimization of neural network systems
* Includes illustrative examples and comprehensive treatment of sequential constructive techniques for optimization of neural network systems
* Presents a uniquely comprehensive treatment of the highly effective fast back propagation algorithms for the optimization of neural network systems
* Treats, in detail, optimization techniques for neural network systems with nonstationary or dynamic inputs
* Covers optimization techniques and applications of neural network systems in constraint satisfaction