Complex-Valued Neural Networks

Advances and Applications

Akira Hirose

• Publisher: Wiley-IEEE Press
• Year: 2013
• Print ISBN: 9781118344606
• eBook ISBN: 9781118590065
• Edition: 1
• Topic: Computer Science
• Subtopic: Neural Networks
• Index: Computer Science

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.

CHAPTER 1

APPLICATION FIELDS AND FUNDAMENTAL MERITS OF COMPLEX-VALUED NEURAL NETWORKS

AKIRA HIROSE

The University of Tokyo, Tokyo, Japan

This chapter presents historical and latest advances in applications of complex-valued neural networks (CVNNs) first. Then it also shows one of the most important merits of CVNNs, namely, the suitability for adaptive processing of coherent signals.

1.1 INTRODUCTION

This chapter presents historical and latest advances in applications of complex-valued neural networks (CVNNs) first. Then it also shows one of the most important merits of CVNNs, namely, the suitability for adaptive processing of coherent signals.

CVNNs are effective and powerful in particular to deal with wave phenomena such as electromagnetic and sonic waves, as well as to process wave-related information. Regarding the history of CVNNs, we can trace back to the middle of the 20th century. The first introduction of phase information in computation was made by Eiichi Goto in 1954 in his invention of ”Parametron” [17, 18, 61]. He utilized the phase of a high-frequency carrier to represent binary or multivalued information. However, the computational principle employed there was ”logic” of Turing type, or von Neumann type, based on symbol processing, so that he could not make further extensive use of the phase. In the present CVNN researches, contrarily, the researchers extend the world of computation to pattern processing fields based on a novel use of the structure of complex-amplitude (phase and amplitude) information.

We notice that the above feature is significantly important when we give thought to the fact that various modern technologies centered on electronics orient toward coherent systems and devices rather than something incoherent. The feature will lead to future general probability statistics, stochastic methods, and statistical learning and self-organization framework in coherent signal processing and information analysis. The fundamental idea is applicable also to hypercomplex processing based on quaternion, octonion, and Clifford algebraic networks.

Some parts of the following contents of this chapter were published in detail in the Journal of Society of Instrument and Control Engineers [29], the Frontiers in Electrical and Electronic Engineering in China [28], and IEEE Transactions in Neural Networks and Learning Systems [35].

1.2 APPLICATIONS OF COMPLEX-VALUED NEURAL NETWORKS

Complex-valued neural networks (CVNNs) have become widely used in various fields. The basic ideas and fundamental principles have been published in several books in recent years [27, 22, 26, 41, 53, 2]. The following subsections present major application fields.

1.2.1 Antenna Design

The most notable feature of CVNNs is the compatibility with wave phenomena and wave information related to, for example, electromagnetic wave, lightwave, electron wave, and sonic wave [28]. Application fields include adaptive design of antennas such as patch antennas for microwave and millimeter wave. Many researches have been reported on how to determine patch-antenna shape and sub-element arrangement, as well as on the switching patterns of the sub-elements [46, 10, 47]. A designer assigns desired frequency-domain characteristics of complex amplitude, or simply amplitude, such as transmission characteristics, return loss, and radiation patterns. A CVNN mostly realizes a more suitable design than a real-valued network does even when he/she presents only simple amplitude. The reason lies in the elemental dynamics consisting of phase rotation (or time delay × carrier frequency) and amplitude increase or decrease, based on which dynamics the CVNN learning or self-organization works. As a result, the generalization characteristics (error magnitude at nonlearning points in supervised learning) and the classification manner often become quite different from those of real-valued neural networks [28, 35]. The feature plays the most important role also in other applications referred to below.

1.2.2 Estimation of Direction of Arrival and Beamforming

The estimation of direction of arrival (DoA) of electromagnetic wave using CVNNs has also been investigated for decades [67, 6]. A similar application field is the beamforming. When a signal has a narrow band, we can simply employ Huygens’ principle. However, in an ultra-wideband (UWB) system, where the wavelength is distributed over a wide range, we cannot assume a single wavelength, resulting in unavailability of Huygens’ principle. To overcome this difficulty, an adaptive method based on a CVNN has been proposed [60] where a unit module consists of a tapped-delay-line (TDL) network.

1.2.3 Radar Imaging

CVNNs are widely applied in coherent electromagnetic-wave signal processing. An area is adaptive processing of interferometric synthetic aperture radar (InSAR) images captured by satellite or airplane to observe land surface [59, 65]. There they aim at solving one of the most serious problems in InSAR imaging that there exist many rotational points (singular points) in the observed data so that the height cannot be determined in a straightforward way.

Ground penetrating radar (GPR) is another field [21, 66, 43, 44, 49, 34]. GPR systems usually suffer from serious clutter (scattering and reflection from non-target objects). Land surface as well as stones and clods generate such heavy clutter that we cannot observe what are underground if we pay attention only to the intensity. Complex-amplitude texture often provides us with highly informative features that can be processed adaptively in such a manner that we do in our early vision.

1.2.4 Acoustic Signal Processing and Ultrasonic Imaging

Another important application field is sonic and ultrasonic processing. Pioneering works were done into various directions [69, 58]. The problem of singular points exists also in ultrasonic imaging. They appear as speckles. A technique similar to that used in InSAR imaging was successfully applied to ultrasonic imaging [51].

1.2.5 Communications Signal Proce...

Table of contents

• Cover
• Half Title page
• Title page
• Copyright page
• Contributors
• Preface
• Chapter 1: Application Fields and Fundamental Merits of Complex-Valued Neural Networks
• Chapter 2: Neural System Learning on Complex-Valued Manifolds
• Chapter 3: N-Dimensional Vector Neuron and Its Application to the N-Bit Parity Problem
• Chapter 4: Learning Algorithms in Complex-Valued Neural Networks using Wirtinger Calculus
• Chapter 5: Quaternionic Neural Networks for Associative Memories
• Chapter 6: Models of Recurrent Clifford Neural Networks and Their Dynamics
• Chapter 7: Meta-Cognitive Complex-Valued Relaxation Network and its Sequential Learning Algorithm
• Chapter 8: Multilayer Feedforward Neural Network with Multi-Valued Neurons for Brain–Computer Interfacing
• Chapter 9: Complex-Valued B-Spline Neural Networks for Modeling and Inverse of Wiener Systems
• Chapter 10: Quaternionic Fuzzy Neural Network for View-Invariant Color Face Image Recognition
• Index