He / Xu Process Neural Networks

Theory and Applications
1. Auflage 2010
ISBN: 978-3-540-73762-9
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 240 Seiten

Reihe: Advanced Topics in Science and Technology in China

For the first time, this book sets forth the concept and model for a process neural network. You'll discover how a process neural network expands the mapping relationship between the input and output of traditional neural networks and greatly enhances the expression capability of artificial neural networks. Detailed illustrations help you visualize information processing flow and the mapping relationship between inputs and outputs.

Autoren/Hrsg.

He, Xingui

Xu, Shaohua

Inhaltsverzeichnis

1;Preface;6
2;Table of Contents;8
3;1 Introduction;14
3.1;1.1 Development of Artificial Intelligence;14
3.2;1.2 Characteristics of Artificial Intelligent System;18
3.3;1.3 Computational Intelligence;22
3.3.1;1.3.1 Fuzzy Computing;22
3.3.2;1.3.2 Neural Computing;25
3.3.3;1.3.3 Evolutionary Computing;25
3.3.4;1.3.4 Combination of the Three Branches;28
3.4;1.4 Process Neural Networks;29
3.5;References;30
4;2 Artificial Neural Networks;33
4.1;2.1 Biological Neuron;34
4.2;2.2 Mathematical Model of a Neuron;35
4.3;2.3 Feedforward/Feedback Neural Networks;36
4.3.1;2.3.1 Feedforward/Feedback Neural Network Model;36
4.3.2;2.3.2 Function Approximation Capability of Feedforward Neural Networks;38
4.3.3;2.3.3 Computing Capability of Feedforward Neural Networks;40
4.3.4;2.3.4 Learning Algorithm for Feedforward Neural Networks;41
4.3.5;2.3.5 Generalization Problem for Feedforward Neural Networks;41
4.3.6;2.3.6 Applications of Feedforward Neural Networks;43
4.4;2.4 Fuzzy Neural Networks;45
4.4.1;2.4.1 Fuzzy Neurons;45
4.4.2;2.4.2 Fuzzy Neural Networks;46
4.5;2.5 Nonlinear Aggregation Artificial Neural Networks;48
4.5.1;2.5.1 Structural Formula Aggregation Artificial Neural Networks;48
4.5.2;2.5.2 Maximum (or Minimum) Aggregation Artificial Neural Networks;48
4.5.3;2.5.3 Other Nonlinear Aggregation Artificial Neural Networks;49
4.6;2.6 Spatio-temporal Aggregation and Process Neural Networks;50
4.7;2.7 Classification of Artificial Neural Networks;52
4.8;References;53
5;3 Process Neurons;56
5.1;3.1 Revelation of Biological Neurons;56
5.2;3.2 Definition of Process Neurons;57
5.3;3.3 Process Neurons and Functionals;60
5.4;3.4 Fuzzy Process Neurons;61
5.4.1;3.4.1 Process Neuron Fuzziness;62
5.4.2;3.4.2 Fuzzy Process Neurons Constructed using Fuzzy Weighted Reasoning Rule;63
5.5;3.5 Process Neurons and Compound Functions;64
5.6;References;65
6;4 Feedforward Process Neural Networks;66
6.1;4.1 Simple Model of a Feedforward Process Neural Network;66
6.2;4.2 A General Model of a Feedforward Process Neural Network;68
6.3;4.3 A Process Neural Network Model Based on Weight Function Basis Expansion;69
6.4;4.4 Basic Theorems of Feedforward Process Neural Networks;71
6.4.1;4.4.1 Existence of Solutions;72
6.4.2;4.4.2 Continuity;75
6.4.3;4.4.3 Functional Approximation Property;77
6.4.4;4.4.4 Computing Capability;80
6.5;4.5 Structural Formula Feedforward Process Neural Networks;80
6.5.1;4.5.1 Structural Formula Process Neurons;81
6.5.2;4.5.2 Structural Formula Process Neural Network Model;82
6.6;4.6 Process Neural Networks with Time-varying Functions as Inputs and Outputs;84
6.6.1;4.6.1 Network Structure;84
6.6.2;4.6.2 Continuity and Approximation Capability of the Model;86
6.7;4.7 Continuous Process Neural Networks;88
6.7.1;4.7.1 Continuous Process Neurons;89
6.7.2;4.7.2 Continuous Process Neural NetworkModel;90
6.7.3;4.7.3 Continuity, Approximation Capability, and Computing Capability of the Model;91
6.8;4.8 Functional Neural Network;96
6.8.1;4.8.1 Functional Neuron;97
6.8.2;4.8.2 Feedforward Functional Neural Network Model;98
6.9;4.9 Epilogue;99
6.10;References;100
7;5 Learning Algorithms for Process Neural Networks;101
7.1;5.1 Learning Algorithms Based on the Gradient Descent Method and Newton Descent Method;102
7.1.1;5.1.1 A General Learning Algorithm Based on Gradient Descent;102
7.1.2;5.1.2 Learning Algorithm Based on Gradient-Newton Combination;104
7.1.3;5.1.3 Learning Algorithm Based on the Newton Descent Method;106
7.2;5.2 Learning Algorithm Based on Orthogonal Basis Expansion;106
7.2.1;5.2.1 Orthogonal Basis Expansion of Input Functions;107
7.2.2;5.2.2 Learning Algorithm Derivation;108
7.2.3;5.2.3 Algorithm Description and Complexity Analysis;109
7.3;5.3 Learning Algorithm Based on the Fourier Function Transformation;110
7.3.1;5.3.1 FourierOrthogonal Basis Expansion of the Function in L2[0, 2rr];110
7.3.2;5.3.2 Learning Algorithm Derivation;112
7.4;5.4 Learning Algorithm Based on the Walsh Function Transformation;114
7.4.1;5.4.1 Learning Algorithm Based on Discrete Walsh Function Transformation;114
7.4.2;5.4.2 Learning Algorithm Based on Continuous Walsh Function Transformation;118
7.5;5.5 Learning Algorithm Based on Spline Function Fitting;121
7.5.1;5.5.1 Spline Function;121
7.5.2;5.5.2 Learning Algorithm Derivation;122
7.5.3;5.5.3 Analysis of the Adaptability and Complexity of a Learning Algorithm;124
7.6;5.6 Learning Algorithm Based on Rational Square Approximation and Optimal Piecewise Approximation;125
7.6.1;5.6.1 Learning Algorithm Based on Rational Square Approximation;125
7.6.2;5.6.2 Learning Algorithm Based on Optimal Piecewise Approximation;132
7.7;5.7 Epilogue;139
7.8;References;139
8;6 Feedback Process Neural Networks;141
8.1;6.1 A Three-Layer Feedback Process Neural Network;142
8.1.1;6.1.1 Network Structure;142
8.1.2;6.1.2 Learning Algorithm;143
8.1.3;6.1.3 Stability Analysis;145
8.2;6.2 Other Feedback Process Neural Networks;148
8.2.1;6.2.1 Feedback Process Neural Network with Time-varying Functions as Inputs and Outputs;148
8.2.2;6.2.2 Feedback Process Neural Network for Pattern Classification;149
8.2.3;6.2.3 Feedback Process Neural Network for Associative Memory Storage;150
8.3;6.3 Application Examples;151
8.4;References;155
9;7 Multi-aggregation Process Neural Networks;156
9.1;7.1 Multi-aggregation Process Neuron;156
9.2;7.2 Multi-aggregation Process Neural Network Model;158
9.2.1;7.2.1 A General Model of Multi-aggregation Process Neural Network;158
9.2.2;7.2.2 Multi-aggregation Process Neural Network Model with Multivariate Process Functions as Inputs and Outputs;160
9.3;7.3 Learning Algorithm;161
9.3.1;7.3.1 Learning Algorithm of General Models of Multi-aggregation Process Neural Networks;161
9.3.2;7.3.2 Learning Algorithm of Multi-aggregation Process Neural Networks with Multivariate Functions as Inputs and Outputs;165
9.4;7.4 Application Examples;168
9.5;7.5 Epilogue;172
9.6;References;173
10;8 Design and Construction of Process Neural Networks;174
10.1;8.1 Process Neural Networks with Double Hidden Layers;174
10.1.1;8.1.1 Network Structure;175
10.1.2;8.1.2 Learning Algorithm;176
10.1.3;8.1.3 Application Examples;178
10.2;8.2 Discrete Process Neural Network;179
10.2.1;8.2.1 Discrete Process Neuron;180
10.2.2;8.2.2 Discrete Process Neural Network;181
10.2.3;8.2.3 Learning Algorithm;182
10.2.4;8.2.4 Application Examples;183
10.3;8.3 Cascade Process Neural Network;185
10.3.1;8.3.1 Network Structure;186
10.3.2;8.3.2 Learning Algorithm;188
10.3.3;8.3.3 Application Examples;189
10.4;8.4 Self-organizing Process Neural Network;191
10.4.1;8.4.1 NetworkStructure;191
10.4.2;8.4.2 Learning Algorithm;192
10.4.3;8.4.3 Application Examples;195
10.5;8.5 Counter Propagation Process Neural Network;197
10.5.1;8.5.1 Network Structure;198
10.5.2;8.5.2 Learning Algorithm;198
10.5.3;8.5.3 Determination of the Number of Pattern Classifications;199
10.5.4;8.5.4 Application Examples;200
10.6;8.6 Radial-Basis Function Process Neural Network;201
10.6.1;8.6.1 Radial-Basis Process Neuron;201
10.6.2;8.6.2 Network Structure;202
10.6.3;8.6.3 Learning Algorithm;203
10.6.4;8.6.4 Application Examples;205
10.7;8.7 Epilogue;206
10.8;References;206
11;9 Application of Process Neural Networks;208
11.1;9.1 Application in Process Modeling;208
11.2;9.2 Application in Nonlinear System Identification;211
11.2.1;9.2.1 Principle of Nonlinear System Identification;212
11.2.2;9.2.2 Process Neural Network for System Identification;213
11.2.3;9.2.3 Nonlinear System Identification Process;214
11.3;9.3 Application in Process Control;216
11.3.1;9.3.1 Process Control of Nonlinear System;217
11.3.2;9.3.2 Designing and Solving of the Process Controller;217
11.3.3;9.3.3 Simulation Experiment;221
11.4;9.4 Application in Clustering and Classification;223
11.5;9.5 Application in Process Optimization;228
11.6;9.6 Applications in Forecast and Prediction;229
11.7;9.7 Application in Evaluation and Decision;237
11.8;9.8 Application in Macro Control;239
11.9;9.9 Other Applications;240
11.10;References;244
12;Postscript;246
13;Index;251