Akira Hirose

Complex-Valued Neural Networks

• Gebundenes Buch

Produktbeschreibung

This book is the second enlarged and revised edition of the first successful monograph on complex-valued neural networks (CVNNs) published in 2006, which lends itself to graduate and undergraduate courses in electrical engineering, informatics, control engineering, mechanics, robotics, bioengineering, and other relevant fields.

In the second edition the recent trends in CVNNs research are included, resulting in e.g. almost a doubled number of references. The parametron invented in 1954 is also referred to with discussion on analogy and disparity. Also various additional arguments on the advantages of the complex-valued neural networks enhancing the difference to real-valued neural networks are given in various sections.

The book is useful for those beginning their studies, for instance, in adaptive signal processing for highly functional sensing and imaging, control in unknown and changing environment, robotics inspired by human neural systems, and brain-like information processing, as well as interdisciplinary studies to realize comfortable society. It is also helpful to those who carry out research and development regarding new products and services at companies. The author wrote this book hoping in particular that it provides the readers with meaningful hints to make good use of neural networks in fully practical applications. The book emphasizes basic ideas and ways of thinking. Why do we need to consider neural networks that deal with complex numbers? What advantages do the complex-valued neural networks have? What is the origin of the advantages? In what areas do they develop principal applications? This book answers these questions by describing details and examples, which will inspire the readers with new ideas.

The book is useful for those beginning their studies, for instance, in adaptive signal processing for highly functional sensing and imaging, control in unknown and changing environment, roboticsinspired by human neural systems, and brain-like information processing, as well as interdisciplinary studies to realize comfortable society. It is also helpful to those who carry out research and development regarding new products and services at companies. The author wrote this book hoping in particular that it provides the readers with meaningful hints to make good use of neural networks in fully practical applications. The book emphasizes basic ideas and ways of thinking. Why do we need to consider neural networks that deal with complex numbers? What advantages do the complex-valued neural networks have? What is the origin of the advantages? In what areas do they develop principal applications? This book answers these questions by describing details and examples, which will inspire the readers with new ideas.

Produktdetails

• Studies in Computational Intelligence 400
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 86039206, 978-3-642-27631-6
• 2. Aufl.
• Seitenzahl: 216
• Erscheinungstermin: 23. März 2012
• Englisch
• Abmessung: 241mm x 160mm x 15mm
• Gewicht: 462g
• ISBN-13: 9783642276316
• ISBN-10: 3642276318
• Artikelnr.: 34572572

Inhaltsangabe

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.

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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

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)