{"product_id":"complexvalued-neural-networks-9781118344606","title":"ComplexValued Neural Networks","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePresents the latest advances in complex-valued neural networks by demonstrating the theory in a wide range of applications\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eComplex-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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eComplex-Valued Neural Networks: Advances and Applications\u003c\/i\u003e covers cutting-edge topics and applications surrounding this timely subject. Demonstrating advanced theories with\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“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.”  (\u003ci\u003eIEEE Computational intelligence magazine\u003c\/i\u003e, 1 May 2013)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Application Fields and Fundamental Merits 1\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAkira Hirose\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Applications of Complex-Valued Neural Networks 2\u003c\/p\u003e \u003cp\u003e1.3 What is a complex number? 5\u003c\/p\u003e \u003cp\u003e1.4 Complex numbers in feedforward neural networks 8\u003c\/p\u003e \u003cp\u003e1.5 Metric in complex domain 12\u003c\/p\u003e \u003cp\u003e1.6 Experiments to elucidate the generalization characteristics 16\u003c\/p\u003e \u003cp\u003e1.7 Conclusions 26\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Neural System Learning on Complex-Valued Manifolds 33\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eSimone Fiori\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 34\u003c\/p\u003e \u003cp\u003e2.2 Learning Averages over the Lie Group of Unitary Matrices 35\u003c\/p\u003e \u003cp\u003e2.3 Riemannian-Gradient-Based Learning on the Complex Matrix-Hypersphere 41\u003c\/p\u003e \u003cp\u003e2.4 Complex ICA Applied to Telecommunications 49\u003c\/p\u003e \u003cp\u003e2.5 Conclusion 53\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 \u003ci\u003eN\u003c\/i\u003e-Dimensional Vector Neuron and Its Application to the \u003ci\u003eN\u003c\/i\u003e-Bit Parity Problem 59\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eTohru Nitta\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 59\u003c\/p\u003e \u003cp\u003e3.2 Neuron Models with High-Dimensional Parameters 60\u003c\/p\u003e \u003cp\u003e3.3 N-Dimensional Vector Neuron 65\u003c\/p\u003e \u003cp\u003e3.4 Discussion 69\u003c\/p\u003e \u003cp\u003e3.5 Conclusion 70\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Learning Algorithms in Complex-Valued Neural Networks using Wirtinger Calculus 75\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eMd. Faijul Amin and Kazuyuki Murase\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 76\u003c\/p\u003e \u003cp\u003e4.2 Derivatives in Wirtinger Calculus 78\u003c\/p\u003e \u003cp\u003e4.3 Complex Gradient 80\u003c\/p\u003e \u003cp\u003e4.4 Learning Algorithms for Feedforward CVNNs 82\u003c\/p\u003e \u003cp\u003e4.5 Learning Algorithms for Recurrent CVNNs 91\u003c\/p\u003e \u003cp\u003e4.6 Conclusion 99\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Quaternionic Neural Networks for Associative Memories 103\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eTeijiro Isokawa, Haruhiko Nishimura, and Nobuyuki Matsui\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 104\u003c\/p\u003e \u003cp\u003e5.2 Quaternionic Algebra 105\u003c\/p\u003e \u003cp\u003e5.3 Stability of Quaternionic Neural Networks 108\u003c\/p\u003e \u003cp\u003e5.4 Learning Schemes for Embedding Patterns 124\u003c\/p\u003e \u003cp\u003e5.5 Conclusion 128\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Models of Recurrent Clifford Neural Networks and Their Dynamics 133\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eYasuaki Kuroe\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 134\u003c\/p\u003e \u003cp\u003e6.2 Clifford Algebra 134\u003c\/p\u003e \u003cp\u003e6.3 Hopfield-Type Neural Networks and Their Energy Functions 137\u003c\/p\u003e \u003cp\u003e6.4 Models of Hopfield-Type Clifford Neural Networks 139\u003c\/p\u003e \u003cp\u003e6.5 Definition of Energy Functions 140\u003c\/p\u003e \u003cp\u003e6.6 Existence Conditions of Energy Functions 142\u003c\/p\u003e \u003cp\u003e6.7 Conclusion 149\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Meta-cognitive Complex-valued Relaxation Network and its Sequential Learning Algorithm 153\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eRamasamy Savitha, Sundaram Suresh, and Narasimhan Sundararajan\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Meta-cognition in Machine Learning 154\u003c\/p\u003e \u003cp\u003e7.2 Meta-cognition in Complex-valued Neural Networks 156\u003c\/p\u003e \u003cp\u003e7.3 Meta-cognitive Fully Complex-valued Relaxation Network 164\u003c\/p\u003e \u003cp\u003e7.4 Performance Evaluation of McFCRN: Synthetic Complexvalued Function Approximation Problem 171\u003c\/p\u003e \u003cp\u003e7.5 Performance Evaluation of McFCRN: Real-valued Classification Problems 172\u003c\/p\u003e \u003cp\u003e7.6 Conclusion 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Multilayer Feedforward Neural Network with Multi-Valued Neurons for Brain-Computer Interfacing 185\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eNikolay V. Manyakov, Igor Aizenberg, Nikolay Chumerin, and Marc M. Van Hulle\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Brain-Computer Interface (BCI) 185\u003c\/p\u003e \u003cp\u003e8.2 BCI Based on Steady-State Visual Evoked Potentials 188\u003c\/p\u003e \u003cp\u003e8.3 EEG Signal Preprocessing 192\u003c\/p\u003e \u003cp\u003e8.4 Decoding Based on MLMVN for Phase-Coded SSVEP BCI 196\u003c\/p\u003e \u003cp\u003e8.5 System Validation 201\u003c\/p\u003e \u003cp\u003e8.6 Discussion 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Complex-Valued B-Spline Neural Networks for Modeling and Inverse of Wiener Systems 209\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eXia Hong, Sheng Chen and Chris J. Harris\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 210\u003c\/p\u003e \u003cp\u003e9.2 Identification and Inverse of Complex-Valued Wiener Systems 211\u003c\/p\u003e \u003cp\u003e9.3 Application to Digital Predistorter Design 222\u003c\/p\u003e \u003cp\u003e9.4 Conclusions 229\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Quaternionic Fuzzy Neural Network for View-invariant Color Face Image Recognition 235\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eWai Kit Wong, Gin Chong Lee, Chu Kiong Loo, Way Soong Lim, and Raymond Lock\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 236\u003c\/p\u003e \u003cp\u003e10.2 Face Recognition System 238\u003c\/p\u003e \u003cp\u003e10.3 Quaternion-Based View-invariant Color Face Image Recognition 244\u003c\/p\u003e \u003cp\u003e10.4 Enrollment Stage and Recognition Stage for Quaternion- Based Color Face Image Correlator 255\u003c\/p\u003e \u003cp\u003e10.5 Max-Product Fuzzy Neural Network Classifier 260\u003c\/p\u003e \u003cp\u003e10.6 Experimental Results 266\u003c\/p\u003e \u003cp\u003e10.7 Conclusion and Future Research Directions 274\u003c\/p\u003e \u003cp\u003eReferences 274\u003c\/p\u003e \u003cp\u003eIndex 279\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406854037847,"sku":"9781118344606","price":104.36,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118344606.jpg?v=1730497349","url":"https:\/\/bookcurl.com\/products\/complexvalued-neural-networks-9781118344606","provider":"Book Curl","version":"1.0","type":"link"}