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Process Neural Networks Theory and Applications

:	Xingui He, Shaohua Xu
:	Process Neural Networks Theory and Applications
:	Springer-Verlag
:	9783540737629
:	Advanced Topics in Science and Technology in China
:	1
:	CHF 123.50
:

:	Anwendungs-Software
:	English

:	240
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

	Preface	6
	Table of Contents	8
	1 Introduction	14
	1.1 Development of Artificial Intelligence	14
	1.2 Characteristics of Artificial Intelligent System	18
	1.3 Computational Intelligence	22
	1.3.1 Fuzzy Computing	22
	1.3.2 Neural Computing	25
	1.3.3 Evolutionary Computing	25
	1.3.4 Combination of the Three Branches	28
	1.4 Process Neural Networks	29
	References	30
	2 Artificial Neural Networks	33
	2.1 Biological Neuron	34
	2.2 Mathematical Model of a Neuron	35
	2.3 Feedforward/Feedback Neural Networks	36
	2.3.1 Feedforward/Feedback Neural Network Model	36
	2.3.2 Function Approximation Capability of Feedforward Neural Networks	38
	2.3.3 Computing Capability of Feedforward Neural Networks	40
	2.3.4 Learning Algorithm for Feedforward Neural Networks	41
	2.3.5 Generalization Problem for Feedforward Neural Networks	41
	2.3.6 Applications of Feedforward Neural Networks	43
	2.4 Fuzzy Neural Networks	45
	2.4.1 Fuzzy Neurons	45
	2.4.2 Fuzzy Neural Networks	46
	2.5 Nonlinear Aggregation Artificial Neural Networks	48
	2.5.1 Structural Formula Aggregation Artificial Neural Networks	48
	2.5.2 Maximum (or Minimum) Aggregation Artificial Neural Networks	48
	2.5.3 Other Nonlinear Aggregation Artificial Neural Networks	49
	2.6 Spatio-temporal Aggregation and Process Neural Networks	50
	2.7 Classification of Artificial Neural Networks	52
	References	53
	3 Process Neurons	56
	3.1 Revelation of Biological Neurons	56
	3.2 Definition of Process Neurons	57
	3.3 Process Neurons and Functionals	60
	3.4 Fuzzy Process Neurons	61
	3.4.1 Process Neuron Fuzziness	62
	3.4.2 Fuzzy Process Neurons Constructed using Fuzzy Weighted Reasoning Rule	63
	3.5 Process Neurons and Compound Functions	64
	References	65
	4 Feedforward Process Neural Networks	66
	4.1 Simple Model of a Feedforward Process Neural Network	66
	4.2 A General Model of a Feedforward Process Neural Network	68
	4.3 A Process Neural Network Model Based on Weight Function Basis Expansion	69
	4.4 Basic Theorems of Feedforward Process Neural Networks	71
	4.4.1 Existence of Solutions	72
	4.4.2 Continuity	75
	4.4.3 Functional Approximation Property	77
	4.4.4 Computing Capability	80
	4.5 Structural Formula Feedforward Process Neural Networks	80
	4.5.1 Structural Formula Process Neurons	81
	4.5.2 Structural Formula Process Neural Network Model	82
	4.6 Process Neural Networks with Time-varying Functions as Inputs and Outputs	84
	4.6.1 Network Structure	84
	4.6.2 Continuity and Approximation Capability of the Model	86
	4.7 Continuous Process Neural Networks	88
	4.7.1 Continuous Process Neurons	89
	4.7.2 Continuous Process Neural NetworkModel	90
	4.7.3 Continuity, Approximation Capability, and Computing Capability of the Model	91
	4.8 Functional Neural Network	96
	4.8.1 Functional Neuron	97
	4.8.2 Feedforward Functional Neural Network Model	98
	4.9 Epilogue	99
	References	100
	5 Learning Algorithms for Process Neural Networks	101
	5.1 Learning Algorithms Based on the Gradient Descent Method and Newton Descent Method	102
	5.1.1 A General Learning Algorithm Based on Gradient Descent	102
	5.1.2 Learning Algorithm Based on Gradient-Newton Combination	104
	5.1.3 Learning Algorithm Based on the Newton Descent Method	106
	5.2 Learning Algorithm Based on Orthogonal Basis Expansion	106
	5.2.1 Orthogonal Basis Expansion of Input Functions	107
	5.2.2 Learning Algorithm Derivation	108
	5.2.3 Algorithm Description and Complexity Analysis	109
	5.3 Learning Algorithm Based on the Fourier Function Transformation	110
	5.3.1 FourierOrthogonal Basis Expansion of the Function in L2[0, 2rr]	110
	5.3.2 Learning Algorithm Derivation	112
	5.4 Learning Algorithm Based on the Walsh Function Transformation	114
	5.4.1 Learning Algorithm Based on Discrete Walsh Function Transformation	114
	5.4.2 Learning Algorithm Based on Continuous Walsh Function Transformation	118
	5.5 Learning Algorithm Based on Spline Function Fitting	121
	5.5.1 Spline Function	121
	5.5.2 Learning Algorithm Derivation	122
	5.5.3 Analysis of the Adaptability and Complexity of a Learning Algorithm	124
	5.6 Learning Algorithm Based on Rational Square Approximation and Optimal Piecewise Approximation	125
	5.6.1 Learning Algorithm Based on Rational Square Approximation	125
	5.6.2 Learning Algorithm Based on Optimal Piecewise Approximation	132
	5.7 Epilogue	139
	References	139
	6 Feedback Process Neural Networks	141
	6.1 A Three-Layer Feedback Process Neural Network	142
	6.1.1 Network Structure	142
	6.1.2 Learning Algorithm	143
	6.1.3 Stability Analysis	145
	6.2 Other Feedback Process Neural Networks	148
	6.2.1 Feedback Process Neural Network with Time-varying Functions as Inputs and Outputs	148
	6.2.2 Feedback Process Neural Network for Pattern Classification	149
	6.2.3 Feedback Process Neural Network for Associative Memory Storage	150
	6.3 Application Examples	151
	References	155
	7 Multi-aggregation Process Neural Networks	156
	7.1 Multi-aggregation Process Neuron	156
	7.2 Multi-aggregation Process Neural Network Model	158
	7.2.1 A General Model of Multi-aggregation