Complex-valued neural networks : advances and applications /

Complex-valued neural networks : advances and applications /

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-organ...

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Bibliographic Details
Other Authors: Hirose, Akira, 1963-
Format: eBook
Language:English
Published: Hoboken : IEEE Press : Wiley, ©2013.
Series:IEEE series on computational intelligence.
Subjects:
Neural networks (Computer science)
Neural Networks, Computer
Online Access:Connect to the full text of this electronic book
Table of 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
  • 1.3 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.