Akira Hirose

Complex-Valued Neural Networks

Herausgeber: Hirose, Akira

• Gebundenes Buch

Produktbeschreibung

Presents the latest advances in complex-valued neural networks by demonstrating the theory in a wide range of applications

Complex-valued neural networks is a rapidly developing neural network framework that utilizes complex arithmetic, exhibiting specific characteristics in its learning, self-organizing, and processing dynamics. They are highly suitable for processing complex amplitude, composed of amplitude and phase, which is one of the core concepts in physical systems to deal with electromagnetic, light, sonic/ultrasonic waves as well as quantum waves, namely, electron and superconducting waves. This fact is a critical advantage in practical applications in diverse fields of engineering, where signals are routinely analyzed and processed in time/space, frequency, and phase domains.

Complex-Valued Neural Networks: Advances and Applications covers cutting-edge topics and applications surrounding this timely subject. Demonstrating advanced theories with a wide range of applications, including communication systems, image processing systems, and brain-computer interfaces, this text offers comprehensive coverage of:
Conventional complex-valued neural networks
Quaternionic neural networks
Clifford-algebraic neural networks

Presented by international experts in the field, Complex-Valued Neural Networks: Advances and Applications is ideal for advanced-level computational intelligence theorists, electromagnetic theorists, and mathematicians interested in computational intelligence, artificial intelligence, machine learning theories, and algorithms.

Produktdetails

• IEEE Press Series on Computational Intelligence .
• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 304
• Erscheinungstermin: 29. April 2013
• Englisch
• Abmessung: 240mm x 161mm x 21mm
• Gewicht: 679g
• ISBN-13: 9781118344606
• ISBN-10: 111834460X
• Artikelnr.: 36697729

Autorenporträt

AKIRA HIROSE, PhD, is a Professor in the Department of Electrical Engineering and Information Systems, the University of Tokyo, Japan. His main fields of interest are wireless electronics and neural networks on which he has published several books. Dr. Hirose is a Fellow of the IEEE, a senior member of the IEICE, and Vice President of the Japanese Neural Network Society. All contributors are members of the Task Force on Complex-Valued Neural Networks, IEEE Computational Intelligence Society Neural Network Technical Committee.

Inhaltsangabe

Preface xv 1 Application Fields and Fundamental Merits 1 Akira Hirose 1.1
Introduction 1 1.2 Applications of Complex-Valued Neural Networks 2 1.3
What is a complex number? 5 1.4 Complex numbers in feedforward neural
networks 8 1.5 Metric in complex domain 12 1.6 Experiments to elucidate the
generalization characteristics 16 1.7 Conclusions 26 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 2.3
Riemannian-Gradient-Based Learning on the Complex Matrix-Hypersphere 41 2.4
Complex ICA Applied to Telecommunications 49 2.5 Conclusion 53 3
N-Dimensional Vector Neuron and Its Application to the N-Bit Parity Problem
59 Tohru Nitta 3.1 Introduction 59 3.2 Neuron Models with High-Dimensional
Parameters 60 3.3 N-Dimensional Vector Neuron 65 3.4 Discussion 69 3.5
Conclusion 70 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 4.5 Learning Algorithms for
Recurrent CVNNs 91 4.6 Conclusion 99 5 Quaternionic Neural Networks for
Associative Memories 103 Teijiro Isokawa, Haruhiko Nishimura, and Nobuyuki
Matsui 5.1 Introduction 104 5.2 Quaternionic Algebra 105 5.3 Stability of
Quaternionic Neural Networks 108 5.4 Learning Schemes for Embedding
Patterns 124 5.5 Conclusion 128 6 Models of Recurrent Clifford Neural
Networks and Their Dynamics 133 Yasuaki Kuroe 6.1 Introduction 134 6.2
Clifford Algebra 134 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 6.6 Existence Conditions of Energy
Functions 142 6.7 Conclusion 149 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 7.2 Meta-cognition in Complex-valued Neural Networks 156 7.3
Meta-cognitive Fully Complex-valued Relaxation Network 164 7.4 Performance
Evaluation of McFCRN: Synthetic Complexvalued Function Approximation
Problem 171 7.5 Performance Evaluation of McFCRN: Real-valued
Classification Problems 172 7.6 Conclusion 178 8 Multilayer Feedforward
Neural Network with Multi-Valued Neurons for Brain-Computer Interfacing 185
Nikolay V. Manyakov, Igor Aizenberg, Nikolay Chumerin, and Marc M. Van
Hulle 8.1 Brain-Computer Interface (BCI) 185 8.2 BCI Based on Steady-State
Visual Evoked Potentials 188 8.3 EEG Signal Preprocessing 192 8.4 Decoding
Based on MLMVN for Phase-Coded SSVEP BCI 196 8.5 System Validation 201 8.6
Discussion 203 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 9.3 Application to Digital Predistorter Design 222 9.4
Conclusions 229 10 Quaternionic Fuzzy Neural Network for View-invariant
Color Face Image Recognition 235 Wai Kit Wong, Gin Chong Lee, Chu Kiong
Loo, Way Soong Lim, and Raymond Lock 10.1 Introduction 236 10.2 Face
Recognition System 238 10.3 Quaternion-Based View-invariant Color Face
Image Recognition 244 10.4 Enrollment Stage and Recognition Stage for
Quaternion- Based Color Face Image Correlator 255 10.5 Max-Product Fuzzy
Neural Network Classifier 260 10.6 Experimental Results 266 10.7 Conclusion
and Future Research Directions 274 References 274 Index 279

---

Complex-valued neural networks fertilize electronics.- Neural networks: The characteristic viewpoints.- Complex-valued neural networks: Distinctive features.- Constructions and dynamics of neural networks.- Land-surface classification with unevenness and reflectance taken into consideration.- Adaptive radar system to visualize antipersonnel plastic landmines.- Removal of phase singular points to create digital elevation map.- Lightwave associative memory that memorizes and recalls information depending on optical-carrier frequency.- Adaptive optical-phase equalizer.- Developmental learning with behavioral-mode tuning by carrier-frequency modulation.- Pitch-asynchronous overlap-add waveform-concatenation speech synthesis by optimizing phase spectrum in frequency domain.

Rezensionen

"In summary, this book contains a wide variety of hot topics on advanced computational intelligence methods which incorporate the concept of complex and hypercomplex number systems into the framework of artificial neural networks . . . Nevertheless, it seems that the applications of CVNNs and hypercomplex-valued neural networks are very promising." (IEEE Computational intelligence magazine, 1 May 2013)