Complex-valued neural networks: advances and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ [u.a.]
Wiley-Blackwell
2013
|
| Schriftenreihe: | IEEE Press series on computational intelligence
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 281 S. graf. Darst. |
| ISBN: | 9781118344606 |
Internformat
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| 245 | 1 | 0 | |a Complex-valued neural networks |b advances and applications |c ed. by Akira Hirose |
| 264 | 1 | |a Hoboken, NJ [u.a.] |b Wiley-Blackwell |c 2013 | |
| 300 | |a XVII, 281 S. |b graf. Darst. | ||
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| 653 | |a Neural networks (Computer science)--Industrial applications. | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-026040827 | ||
Datensatz im Suchindex
| _version_ | 1804150429310779392 |
|---|---|
| adam_text | CONTENTS
Preface
xv
1 Application
Fields and Fundamental Merits
1
Akira Hirose
1.1
Introduction
1
1.2
Applications of Complex-Valued Neural Networks
2
1.2.1
Antenna Design
2
1.2.2
Estimation of Direction of Arrival and
Beamforming
3
1.2.3
Radar Imaging
3
1.2.4
Acoustic Signal Processing and Ultrasonic Imaging
3
1.2.5
Communications Signal Processing
3
1.2.6
Image Processing
4
1.2.7
Social Systems Such as Traffic and Power Systems
4
1.2.8
Quantum Devices Such as Superconductive
Devices
4
1.2.9
Optical/Lightwave Information Processing
Including Carrier-Frequency Multiplexing
4
VIII CONTENTS
1.2.10
Hypercomplex-
Valued
Neural Networks
5
1.3
What is a complex number?
5
1.3.1
Geometric and Intuitive Definition
5
1.3.2
Definition as Ordered Pair of Real Numbers
6
1.3.3
Real
2x2
Matrix Representation
7
1.4
Complex numbers in feedforward neural networks
8
1.4.1
Synapse and Network Function in Layered
Feedforward Neural Networks
9
1.4.2
Circularity
11
1.5
Metric in complex domain
12
1.5.1
Metric in Complex-Valued Self-Organizing Map
12
1.5.2
Euclidean Metric
12
1.5.3
Complex Inner-Product Metric
14
1.5.4
Comparison Between Complex Inner Product and
Euclidean Distance
14
1.5.5
Metric in Correlation Learning
15
1.6
Experiments to elucidate the generalization characteristics
16
1.6.1
Forward Processing and Learning Dynamics
17
1.6.2
Experimental Setup
21
1.6.3
Results
24
1.7
Conclusions
26
References
27
2
Neural System Learning on Complex-Valued Manifolds
33
Simone
Fiori
2.1
Introduction
34
2.2
Learning Averages over the Lie Group of Unitary Matrices
35
2.2.1
Differential-Geometric Setting
36
2.2.2
An Averaging Procedure over the Lie Group of
Unitary Matrices
37
2.3
Riemannian-Gradient-Based Learning on the Complex
Matrix-Hypersphere
41
2.3.1
Geometric Characterization of the Matrix
Hypersphere
43
2.3.2
Geodesic-Stepping Optimization Method
45
2.3.3
Application to Optimal Precoding in
MIMO
Broadcast Channels
46
2.4
Complex
ICA
Applied to Telecommunications
49
CONTENTS
IX
2.4.1
Complex-Weighted Rigid-Body Learning
Equations for
ICA
51
2.4.2
Application to the Blind Separation of QAM/PSK
Signals
53
2.5
Conclusion
53
References
55
iV-Dimensional Vector Neuron and Its Application to the iV-Bit
Parity Problem
59
Tohru Nitta
3.1
Introduction
59
3.2
Neuron Models with High-Dimensional Parameters
60
3.2.1
Complex-Valued Neuron
60
3.2.2
Hyperbolic Neuron
61
3.2.3
Three-Dimensional Vector Neuron
61
3.2.4
Three-Dimensional Vector Product Neuron
62
3.2.5
Quaternary Neuron
63
3.2.6
Clifford Neuron
63
3.3
./V-Dimensional Vector Neuron
65
3.3.1
TV-Dimensional Vector Neuron Model
65
3.3.2
Decision Boundary
65
3.3.3
iV-Bit Parity Problem
67
3.3.4
A Solution
67
3.4
Discussion
69
3.5
Conclusion
70
References
71
4
Learning Algorithms in Complex-Valued Neural Networks using
Wirtinger Calculus
75
Md. Faijul
Amin
and Kazuyuki
Murase
4.1
Introduction
76
4.2
Derivatives in Wirtinger Calculus
78
4.3
Complex Gradient
80
4.4
Learning Algorithms for Feedforward CVNNs
82
4.4.1
Complex Gradient Descent Algorithm
82
4.4.2
Complex Levenberg-Marquardt Algorithm
86
4.4.3
Computer Simulations
89
4.5
Learning Algorithms for Recurrent CVNNs
91
X
CONTENTS
4.5.1
Complex
Real-Time Recurrent Learning
Algorithm
92
4.5.2
Complex Extended
Kalman
Filter Algorithm
95
4.5.3
Computer Simulations
96
4.6
Conclusion
99
References
100
5
Quaternionic Neural Networks for Associative Memories
103
Teijiro Isokawa, Haruhiko Nishimura, and Nobuyuki Matsui
5.1
Introduction
104
5.2
Quaternionic Algebra
105
5.2.1
Definition of Quaternion
105
5.2.2
Phase Representation of Quaternion
106
5.2.3
Quaternionic Analyticity
106
5.3
Stability of Quaternionic Neural Networks
108
5.3.1
Network with Bipolar State Neurons
108
5.3.2
Network with Continuous State Neurons 111
5.3.3
Network with Continuous State Neurons Having
Local Analytic Activation Function
115
5.3.4
Network with Multistate Neurons
118
5.4
Learning Schemes for Embedding Patterns
124
5.4.1
Hebbian Rule
124
5.4.2
Projection Rule
125
5.4.3
Iterative Learning for Quaternionic Multistate
Neural Network
126
5.5
Conclusion
128
References
129
6
Models of Recurrent Clifford Neural Networks and Their Dynamicsl33
Yasuaki Kuroe
6.1
Introduction
134
6.2
Clifford Algebra
134
6.2.1
Definition
134
6.2.2
Basic Properties and Algebraic Basis
136
6.3
Hopfield-Type Neural Networks and Their Energy
Functions
137
6.4
Models of Hopfield-Type Clifford Neural Networks
139
6.5
Definition of Energy Functions
140
CONTENTS
ХІ
6.6
Existence Conditions of Energy Functions
142
6.6.1
Assumptions on Clifford Activation Functions
142
6.6.2
Existence Conditions for Clifford Neural Networks
of Class G0,2,o
143
6.6.3
Existence Conditions for Clifford Neural Networks
of Class Go,i,o
146
6.7
Conclusion
149
References
150
7
Meta-cognitive
Complex-valued Relaxation Network and its Sequential
Learning Algorithm
153
Ramasamy Savitha,
Sundaram Suresh,
and Narasimhan Sundararajan
7.1
Meta-cognition in Machine Learning
154
7.1.1
Models of Meta-cognition
154
7.1.2
Meta-cognitive
Neural Networks
155
7.2
Meta-cognition in Complex-valued Neural Networks
156
7.2.1
Problem Definition
157
7.2.2
Meta-cognitive
Fully Complex-valued Radial Basis
Function Network
157
7.2.3
Complex-Valued Self-Regulatory Resource
Allocation Network
160
7.2.4
Issues in Mc-FCRBF and CSRAN
164
7.3
Meta-cognitive
Fully Complex-valued Relaxation Network
164
7.3.1
Cognitive Component: A Fully Complex-valued
Relaxation Network (FCRN)
164
7.3.2
Meta-cognitive
Component: A Self-regulatory
Learning Mechanism
168
7.4
Performance Evaluation of McFCRN: Synthetic Complex-
valued Function Approximation Problem
171
7.5
Performance Evaluation of McFCRN: Real-valued
Classification Problems
172
7.5.1
Real-valued Classification Problem in the Complex
Domain
173
7.5.2
Data Sets
174
7.5.3
Modifications in McFCRN Learning Algorithm to
Solve Real-Valued Classification Problems
175
7.5.4
Performance Measures
176
7.5.5
Multi-category Benchmark Classification Problems
177
XII CONTENTS
7.5.6
Binary Classification Problems
178
7.6
Conclusion
178
References
181
8
Multilayer Feedforward Neural Network with Multi-Valued Neurons
for Brain-Computer Interfacing
185
Nikolay V. Manyakov, Igor Aizenberg, Nikolay Chuinerin, and
Marc M. Van Hullo
8.1
Brain Computer Interface
(ВСІ)
185
8.1.1
Invasive
ВСІ
187
8.1.2
Noninvasive
ВСІ
188
8.2
ВСІ
Based on Steady-State Visual Evoked Potentials
188
8.2.1
Frequency-Coded SSVEP
ВСІ
190
8.2.2
Phase-Coded SSVEP
ВСІ
191
8.3
EEG
Signal Preprocessing
192
8.3.1
EEG
Data Acquisition
192
8.3.2
Experiment Description
192
8.3.3
Feature Selection
194
8.4
Decoding Based on MLMVN for Phase-Coded SSVEP
ВСІ
196
8.4.1
Multi-
Valued Neuron
196
8.4.2
Multilayer Feedforward Neural Network with
Multi-
Valued Neurons (MLMVN)
198
8.4.3
MLMVN for Phase-Coded SSVEP
ВСІ
200
8.5
System Validation
201
8.6
Discussion
203
Appendix: Decoding Methods
204
A.I Method of Jia and Co-workers
204
A.
2
Method of Lee and Co-workers
204
References
205
9
Complex-Valued B-Spline Neural Networks for Modeling and Inverse
of Wiener Systems
209
Xia Hong, Sheng Chen and Chris J. Harris
9.1
Introduction
210
9.2
Identification and Inverse of Complex-Valued Wiener
Systems
211
9.2.1
The Complex-Valued Wiener System
212
CONTENTS XIII
9.2.2
Complex-
Valued B-Spline
Neural
Network
212
9.2.3
Wiener System Identification
215
9.2.4
Wiener System Inverse
219
9.3
Application
to
Digital Predistorter
Design
222
9.3.1
High-Power Amplifier
Model
222
9.3.2
A Novel Digital Predistorter Design
224
9.3.3
A Simulation Example
224
9.4
Conclusions
229
References
229
10
Quaternionic Fuzzy Neural Network for View-invariant Color Face
Image Recognition
235
Wai Kit Wong, Gin Cliong Lee,
Chu
Kiong Loo, Way Soong
Lim,
and
Raymond Lock
10.1
Introduction
236
10.2
Face Recognition System
238
10.2.1
Principal Component Analysis (PCA) Method
239
10.2.2
Non-negative Matrix Factorization (NMF) Method
240
10.2.3
Block Diagonal Non-negative Matrix Factorization
(BDNMF) Method
242
10.3
Quaternion-Based View-invariant Color Face Image
Recognition
244
10.3.1
Quaternion
244
10.3.2
Quaternion Fourier Transform
247
10.3.3
Quaternion-Based View-Invariant Color Face
Image Recognition System Model
253
10.4
Enrollment Stage and Recognition Stage for Quaternion-
Based Color Face Image Correlator
255
10.4.1
Enrollment Stage
255
10.4.2
Recognition Stage
259
10.5
Max-Product Fuzzy Neural Network Classifier
260
10.5.1
Fuzzy Neural Network System
261
10.5.2
Max-Product Fuzzy Neural Network Classification
264
10.6
Experimental Results
266
10.6.1
Database of Reference Face Images for
200
Persons
266
10.6.2
Quaternion-Based Face Image Correlation Using
Unconstrained Optimal Tradeoff Synthetic
Discriminant Filter (UOTSDF)
267
XIV CONTENTS
10.6.3
Efficiency of the View-invariant Color Face Image
Recognition System
269
10.6.4
Comparative Study with the Parallel Method
271
10.7
Conclusion and Future Research Directions
274
References
274
Index
279
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| indexdate | 2024-07-10T00:38:47Z |
| institution | BVB |
| isbn | 9781118344606 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026040827 |
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| spelling | Hirose, Akira 1963- Verfasser (DE-588)132071541 aut Complex-valued neural networks advances and applications ed. by Akira Hirose Hoboken, NJ [u.a.] Wiley-Blackwell 2013 XVII, 281 S. graf. Darst. txt rdacontent n rdamedia nc rdacarrier IEEE Press series on computational intelligence Neuronales Netz (DE-588)4226127-2 gnd rswk-swf Neural networks (Computer science) Neural networks (Computer science)--Industrial applications. (DE-588)4143413-4 Aufsatzsammlung gnd-content Neuronales Netz (DE-588)4226127-2 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026040827&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hirose, Akira 1963- Complex-valued neural networks advances and applications Neuronales Netz (DE-588)4226127-2 gnd |
| subject_GND | (DE-588)4226127-2 (DE-588)4143413-4 |
| title | Complex-valued neural networks advances and applications |
| title_auth | Complex-valued neural networks advances and applications |
| title_exact_search | Complex-valued neural networks advances and applications |
| title_full | Complex-valued neural networks advances and applications ed. by Akira Hirose |
| title_fullStr | Complex-valued neural networks advances and applications ed. by Akira Hirose |
| title_full_unstemmed | Complex-valued neural networks advances and applications ed. by Akira Hirose |
| title_short | Complex-valued neural networks |
| title_sort | complex valued neural networks advances and applications |
| title_sub | advances and applications |
| topic | Neuronales Netz (DE-588)4226127-2 gnd |
| topic_facet | Neuronales Netz Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026040827&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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