最近正在看这本书，CVNN算是现在计算智能的前沿，希望大家多多交流
书主要分两部分：
Part 1 Basic Ideas and Fundamentals: Why Are Complex-Valued
和
Part 2 Applications: How Wide Are the Application Fields?

目录：
Part I Basic Ideas and Fundamentals: Why Are Complex-Valued
Neural Networks Inevitable?
1 Complex-Valued Neural Networks Fertilize Electronics . . . 3
1.1 Imitate the Brain, and Surpass the Brain . . . . . . . . . . . . . . . . . . 3
1.2 Create a “Superbrain” by Enrichment of the Information
Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Application Fields Expand Rapidly and Steadily . . . . . . . . . . . 6
1.4 Book Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Neural Networks: The Characteristic Viewpoints . . . . . . . . . 9
2.1 Brain, Artificial Brain, Artificial Intelligence (AI), and
Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Physicality of Brain Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Neural Networks: General Features . . . . . . . . . . . . . . . . . . . . . . . 13
3 Complex-Valued Neural Networks: Distinctive Features . . 17
3.1 What Is a Complex Number? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 Geometric and Intuitive Definition. . . . . . . . . . . . . . . . . . 17
3.1.2 Definition as Ordered Pair of Real Numbers . . . . . . . . . 18
3.1.3 Real 2×2 Matrix Representation . . . . . . . . . . . . . . . . . . . 19
3.2 Comparison of Complex- and Real-Valued Feedforward
Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Function of Complex-Valued Synapse and Network
Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Circularity and Widely-Linear Systems . . . . . . . . . . . . . . 23
3.2.3 Nonlinearity That Enhances the Features of
Complex-Valued Networks . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Activation Functions in Neurons. . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Nonlinear Activation Functions in Real-Valued
Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3.2 Problem Concerning Activation Functions in
Complex-Valued Neural Networks . . . . . . . . . . . . . . . . . . 28
3.3.3 Construction of CVNNs with Partial Derivatives in
Complex Domain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.4 Real-Imaginary-Type Activation Function . . . . . . . . . . . 31
3.3.5 Amplitude-Phase-Type Activation Function . . . . . . . . . 32
3.4 Metric in Complex Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.1 Importance of Metric: An Example in
Complex-Valued Self-organizing Map . . . . . . . . . . . . . . . 34
3.4.2 Euclidean Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.3 Complex-Valued Inner-Product Metric . . . . . . . . . . . . . . 36
3.4.4 Comparison between Complex-Valued Inner Product
and Euclidean Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.5 Metric in Correlation Learning . . . . . . . . . . . . . . . . . . . . . 37
3.5 What Is the Sense of Complex-Valued Information and Its
Processing? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.6 In What Fields Are CVNNs Effective? . . . . . . . . . . . . . . . . . . . . 40
3.6.1 Electromagnetic and Optical Waves, Electrical
Signals in Analog and Digital Circuits. . . . . . . . . . . . . . . 40
3.6.2 Electron Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.6.3 Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6.4 Quantum Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6.5 Sonic and Ultrasonic Waves. . . . . . . . . . . . . . . . . . . . . . . . 45
3.6.6 Compatibility of Controllability and Adaptability. . . . . 46
3.6.7 Periodic Topology and Metric . . . . . . . . . . . . . . . . . . . . . . 46
3.6.8 Direct Use of Polar Coordinates . . . . . . . . . . . . . . . . . . . . 48
3.6.9 High Stability in Recurrent Dynamics . . . . . . . . . . . . . . . 48
3.6.10 Preservation of Relative Directions and Segmentation
Boundaries in Two-Dimensional Information
Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6.11 Chaos and Fractals in Complex Domain . . . . . . . . . . . . . 49
3.6.12 Quaternion and Other Higher-Order Complex
Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7 Investigations in Complex-Valued Neural Networks . . . . . . . . . 50
3.7.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7.2 Recent Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4 Constructions and Dynamics of Neural Networks . . . . . . . . . 57
4.1 Processing, Learning, and Self-organization . . . . . . . . . . . . . . . . 57
4.1.1 Pulse-Density Signal Representation . . . . . . . . . . . . . . . . 57
4.1.2 Neural Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.3 Task Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.4 Learning and Self-organization . . . . . . . . . . . . . . . . . . . . . 60
4.1.5 Changes in Connection Weights . . . . . . . . . . . . . . . . . . . . 60
4.2 Hebbian Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3 Associative Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.1 Function: Memory and Recall of Pattern
Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.2 Network Construction and Processing Dynamics . . . . . . 63
4.3.3 Energy Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.4 Use of Generalized Inverse Matrix . . . . . . . . . . . . . . . . . . 69
4.3.5 Weight Learning by Sequential Correlation Learning . . 69
4.3.6 Complex-Valued Associative Memory . . . . . . . . . . . . . . . 70
4.3.7 Amplitude–Phase Expression of Hebbian Rule . . . . . . . 72
4.3.8 Lightwave Neural Networks and
Carrier-Frequency-Dependent Learning. . . . . . . . . . . . . . 73
4.4 Function Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.1 Function: Generation of Desirable Outputs for Given
Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.2 Network Construction and Processing Dynamics . . . . . . 76
4.4.3 Learning by Steepest Descent Method. . . . . . . . . . . . . . . 78
4.4.4 Backpropagation Learning . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.5 Learning by Complex-Valued Steepest Descent
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4.6 Function Approximation by Use of Complex-Valued
Hebbian Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4.7 Backpropagation Learning by Backward Propagation
of Teacher Signals instead of Errors . . . . . . . . . . . . . . . . . 87
4.5 Adaptive Clustering and Visualization of Multidimensional
Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.5.1 Function: Vector Quantization and Visualization . . . . . 90
4.5.2 Network Construction, Processing, and
Self-organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5.3 Complex-Valued Self-organizing Map: CSOM . . . . . . . . 94

4.6 Markov Random Field Estimation . . . . . . . . . . . . . . . . . . . . . . . . 94
4.6.1 Function: Signal Estimation from Neighbors . . . . . . . . . 94
4.6.2 Network Construction and Processing Dynamics . . . . . . 95
4.6.3 Learning Correlations between Signals at a Pixel and
Its Neighbors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.7 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.7.1 Function: Extraction of Principal Information in
Statistical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.7.2 Network Construction and Dynamics of Task
Processing and Self-organization. . . . . . . . . . . . . . . . . . . . 97
4.8 Independent Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . 99

Part II Applications: How Wide Are the Application Fields?
5 Land-Surface Classification with Unevenness and
Reflectance Taken into Consideration . . . . . . . . . . . . . . . . . . . . . 103
5.1 Interferometric Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 CMRF Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3 CMRF Model and Complex-Valued Hebbian learning Rule . . . 107
5.4 Construction of CSOM Image Classification System. . . . . . . . . 108
5.5 Generation of Land-Surface Classification Map . . . . . . . . . . . . . 110
5.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6 Adaptive Radar System to Visualize Antipersonnel
Plastic Landmines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.1 Ground Penetrating Radars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2 Construction of CSOM Plastic Landmine Visualization
System Dealing with Frequency- and Space-Domain
Texture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.3 Adaptive Signal Processing in CSOM . . . . . . . . . . . . . . . . . . . . . 115
6.3.1 Feature Vector Extraction by Paying Attention to
Frequency Domain Information . . . . . . . . . . . . . . . . . . . . 115
6.3.2 Dynamics of CSOM Classification . . . . . . . . . . . . . . . . . . 117
6.4 Visualization of Antipersonnel Plastic Landmines . . . . . . . . . . . 118
6.4.1 Measurement Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.2 Results of Observation and Classification . . . . . . . . . . . . 120
6.4.3 Performance Evaluation by Visualization Rate . . . . . . . 121
6.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7 Removal of Phase Singular Points to Create Digital
Elevation Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.1 Phase Unwrapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.2 Noise Reduction with a Complex-Valued Cellular Neural
Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.3 System Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.4 Dynamics of Singular-Point Reduction . . . . . . . . . . . . . . . . . . . . 128
7.5 DEM Quality and Calculation Cost . . . . . . . . . . . . . . . . . . . . . . . 129
7.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
8 Lightwave Associative Memory That Memorizes and
Recalls Information Depending on Optical-Carrier
Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.1 Utilization of Wide Frequency Bandwidth in Optical Neural
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.2 Optical-Carrier-Frequency Dependent Associative Memory:
The Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

8.2.1 Recalling Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
8.2.2 Memorizing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
8.3 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.4 Frequency-Dependent Learning. . . . . . . . . . . . . . . . . . . . . . . . . . . 138
8.5 Frequency-Dependent Recall Experiment . . . . . . . . . . . . . . . . . . 141
8.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
9 Adaptive Optical-Phase Equalizer . . . . . . . . . . . . . . . . . . . . . . . . 143
9.1 System Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
9.2 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
9.3 Dynamics of Output Phase-Value Learning . . . . . . . . . . . . . . . . 146
9.4 Performance of Phase Equalization . . . . . . . . . . . . . . . . . . . . . . . 147
9.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
10 Developmental Learning with Behavioral-Mode Tuning
by Carrier-Frequency Modulation . . . . . . . . . . . . . . . . . . . . . . . . 151
10.1 Development, Context Dependence, Volition, and
Developmental Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
10.2 Neural Construction and Human-Bicycle Model . . . . . . . . . . . . 153
10.3 Developmental Learning in Bicycle Riding . . . . . . . . . . . . . . . . . 156
10.3.1 Task 1: Ride as Long as Possible . . . . . . . . . . . . . . . . . . . 157
10.3.2 Task 2: Ride as Far as Possible . . . . . . . . . . . . . . . . . . . . . 160
10.3.3 Comparative Experiment: Direct FML in Task 2 . . . . . . 161
10.3.4 Comparison between the Results . . . . . . . . . . . . . . . . . . . 161
10.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193