Computational Intelligence - May 2013 - 77

Gouhei Tanaka
The University of Tokyo, JAPAN

Complex-Valued Neural Networks: Advances and Applications,
by Akira Hirose (Wiley-IEEE
Press, 2013, 320 pp.) ISBN: 9781-1183-4460-6.

omplex-valued neural networks
(CVNNs) are artificial neural
networks that are based on complex numbers and complex number
arithmetic. They are particularly suited
for signal and information with complex amplitude, i.e., amplitude and
phase, as typically found in wave phenomena including electromagnetic
wave, light wave, sonic wave, electron
wave, and electroencephalogram (EEG).
In this decade, the application fields of
CVNNs have been considerably
expanded together with the development of their theories and algorithms.
This book covers the recent advances of
CVNNs and their variants, demonstrating their applicability to optimization of
telecommunication systems, blind
source separation of complex-valued
signals, N-bit parity problems, wind
prediction, classification problems
in complex domain, brain computer
interface, digital predistorter design for
high power amplifiers, and color face
image recognition.
The contents of the book include not
only conventional CVNNs but also quaternion neural networks and CliffordDigital Object Identifier 10.1109/MCI.2013.2247895
Date of publication: 11 April 2013

Book
Review

developed in the individual chapters, by
algebraic neural networks, which are the
extending or generalizing the counterextended neural networks utilizing
parts of the conventional artificial neuhypercomplex number systems. The new
ral networks.
methods and challenges for establishThe book begins with an introducment of these hypercomplex-valued
tion to the theories and applications of
neural networks are more highlighted,
conventional CVNNs. In the former half,
compared with the first-ever book on
the representative application fields of
CVNNs published ten years ago [1]. The
CVNNs are compactly
book reviewed here
presented. The engiprovides an excellent
neer ing applications
overview of the current
include antenna design,
trends in the research of
beam-forming, radar
CVNNs for students
image processing, sonic
and researchers interComplexand ultrasonic processested in computational
Valued
ing, communication sigintelligence as well as
Neural
nal processing, image
offers up-to-date theories and applications of
Networks processing, traffic signal
control, quantum comCVNNs for experts and
Advances and Applications
putation, and optical
practitioners. The readinformation processing.
ers can refer to the
Akira Hirose
In the latter half, the
introductory textbook
emphasis is placed on
[2] on CVNNs for
the difference between
m o re f u n d a m e n t a l
the CVNNs and the
aspects and refer also to
ordinary real-valued
the book [3] for other
neural networks. It is shown in numerical
research topics related to CVNNs.
experiments that a feedforward layered
The entire book is organized into
CVNN yields a better generalization
ten chapters. The first chapter is an
ability for coherent signals compared to
overview of the methods and applicaother methods.
tions of conventional CVNNs. The
Chapter 2 deals with CVNNs
nine consecutive chapters focus on difwhose adaptable parameters lay on
ferent kinds of CVNNs and hypercomcomplex manifolds. Based on differenplex-valued neural networks. Various
tial geometrical methods, efficient
methods relying on CVNNs and
optimization algorithms to adapt the
hypercomplex-valued neural networks,
parameters of such CVNNs are preincluding learning algorithms, optimisented and successfully applied to
zation methods, classification algosignal processing problems. The probrithms, system estimation methods, and
lems include the purely algorithmic
system prediction methods, are

MAY 2013 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

Table of Contents for the Digital Edition of Computational Intelligence - May 2013