独立成分分析详解：理论与应用

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独立成分分析(Independent Component Analysis, ICA)是一种强大的信号处理技术，它在许多领域，如信号处理、机器学习、通信、生物医学工程以及神经科学中扮演着关键角色。本资源由Aapo Hyvärinen、Juha Karhunen和Erkki Oja三位专家合作撰写，是关于ICA理论和应用的权威著作。《独立成分分析》一书于2001年由John Wiley & Sons, Inc. 出版，提供硬封面（ISBN 0-471-40540-X）和电子版（ISBN 0-471-22131-7）。 ICA的目标是将复杂混合信号分解成一组不可见的、相互独立的源信号，这些源信号彼此之间没有线性关系。这种分解有助于揭示隐藏在数据背后的潜在结构和特征，常用于噪声抑制、特征提取、信号分离和数据分析等任务。在实际应用中，ICA的优势在于其能够处理非高斯分布的数据，这是其他传统方法难以做到的。书中详细介绍了ICA的基本原理，包括算法的设计（如FastICA和JADE），以及如何通过统计独立性和非-Gaussian性这两个核心概念来识别和分离信号。此外，还包括了ICA在各种领域的具体应用案例，如图像处理中的颜色空间独立性分析，神经信号处理中的脑电图信号解耦，以及音频信号中的音乐合成等。版权方面，John Wiley & Sons, Inc. 保护本书的知识产权，强调读者在引用或复制内容时必须遵守1976年美国版权法第107节（关于合理使用）或108节（关于图书馆和教育机构的复制权）。对于商标问题，如果作者在书中提到的产品名称，通常会采用全大写或首字母大写的形式，但完整的商标信息应直接向相关公司查询以获得准确和完整的信息。《独立成分分析》是一本深入理解ICA理论和实践的宝贵参考资料，适合研究人员、工程师以及对信号处理感兴趣的专业人士阅读和学习。通过阅读这本书，读者不仅可以掌握ICA的核心算法，还能了解到如何将其应用于解决实际问题，提高数据处理和分析的效率和效果。

Preface

Independent component analysis (ICA) is a statistical and computational technique

for revealing hidden factors that underlie sets of random variables, measurements, or

signals. ICA deﬁnes a generative model for the observed multivariate data, which is

typically given as a large database of samples. In the model, the data variables are

assumed to be linear or nonlinear mixtures of some unknown latent variables, and

the mixing system is also unknown. The latent variables are assumed nongaussian

and mutually independent, and they are called the independent components of the

observed data. These independent components, also called sources or factors, can be

found by ICA.

ICA can be seen as an extension to principal component analysis and factor

analysis. ICA is a much more powerful technique, however, capable of ﬁnding the

underlying factors or sources when these classic methods fail completely.

The data analyzed by ICA could originate from many different kinds of applica-

tion ﬁelds, including digital images and document databases, as well as economic

indicators and psychometric measurements. In many cases, the measurements are

given as a set of parallel signals or time series; the term blind source separation is used

to characterize this problem. Typical examples are mixtures of simultaneous speech

signals that have been picked up by several microphones, brain waves recorded by

multiple sensors, interfering radio signals arriving at a mobile phone, or parallel time

series obtained from some industrial process.

The technique of ICA is a relatively new invention. It was for the ﬁrst time in-

troduced in early 1980s in the context of neural network modeling. In mid-1990s,

some highly successful new algorithms were introduced by several research groups,

xvii

xviii

PREFACE

together with impressive demonstrations on problems like the cocktail-party effect,

where the individual speech waveforms are found from their mixtures. ICA became

one of the exciting new topics, both in the ﬁeld of neural networks, especially unsu-

pervised learning, and more generally in advanced statistics and signal processing.

Reported real-world applications of ICA on biomedical signal processing, audio sig-

nal separation, telecommunications,fault diagnosis, feature extraction, ﬁnancial time

series analysis, and data mining began to appear.

Many articles on ICA were published during the past 20 years in a large number

of journals and conference proceedings in the ﬁelds of signal processing, artiﬁcial

neural networks, statistics, informationtheory, and variousapplication ﬁelds. Several

special sessions and workshops on ICA have been arranged recently [70, 348], and

some edited collections of articles [315, 173, 150] as well as some monographs on

ICA, blind source separation, and related subjects [105, 267, 149] have appeared.

However, while highly useful for their intended readership, these existing texts typ-

ically concentrate on some selected aspects of the ICA methods only. In the brief

scientiﬁc papers and book chapters, mathematical and statistical preliminaries are

usually not included, which makes it very hard for a wider audience to gain full

understanding of this fairly technical topic.

A comprehensive and detailed text book has been missing, which would cover

boththemathematicalbackgroundand principles,algorithmicsolutions,and practical

applications of the present state of the art of ICA. The present book is intended to ﬁll

that gap, serving as a fundamental introduction to ICA.

It is expected that the readership will be from a variety of disciplines, such

as statistics, signal processing, neural networks, applied mathematics, neural and

cognitive sciences, information theory, artiﬁcial intelligence, and engineering. Both

researchers, students, and practitioners will be able to use the book. We have made

everyeffortto make this book self-contained, so that a readerwith a basic background

in college calculus, matrix algebra, probability theory, and statistics will be able to

read it. This book is also suitable for a graduate level university course on ICA,

which is facilitated by the exercise problems and computer assignments given in

many chapters.

Scope and contents of this book

This book provides a comprehensive introduction to ICA as a statistical and compu-

tational technique. The emphasis is on the fundamental mathematical principles and

basic algorithms. Much of the material is based on the original research conducted

in the authors’ own research group, which is naturally reﬂected in the weighting of

the different topics. We give a wide coverage especially to those algorithms that are

scalable to large problems, that is, work even with a large number of observed vari-

ables and data points. These will be increasingly used in the near future when ICA

is extensively applied in practical real-world problems instead of the toy problems

or small pilot studies that have been predominant until recently. Respectively, some-

PREFACE

xix

what less emphasis is given to more specialized signal processing methods involving

convolutivemixtures, delays, and other blind source separation techniques than ICA.

As ICA is a fast growing research area, it is impossible to include every reported

development in a textbook. We have tried to cover the central contributions by other

workers in the ﬁeld in their appropriatecontext and present an extensive bibliography

for further reference. We apologize for any omissions of important contributions that

we may have overlooked.

For easier reading, the book is divided into four parts.



Part I gives the mathematical preliminaries. It introduces the general math-

ematical concepts needed in the rest of the book. We start with a crash course

on probability theory in Chapter 2. The reader is assumed to be familiar with

most of the basic material in this chapter, but also some concepts more spe-

ciﬁc to ICA are introduced, such as higher-order cumulants and multivariate

probability theory. Next, Chapter 3 discusses essential concepts in optimiza-

tion theory and gradient methods, which are needed when developing ICA

algorithms. Estimation theory is reviewed in Chapter 4. A complementary

theoretical framework for ICA is information theory, covered in Chapter 5.

Part I is concluded by Chapter 6, which discusses methods related to principal

component analysis, factor analysis, and decorrelation.

More conﬁdent readers may prefer to skip some or all of the introductory

chapters in Part I and continue directly to the principles of ICA in Part II.



In Part II, the basic ICA model is covered and solved. This is the linear

instantaneousnoise-freemixing modelthat is classicin ICA, and formsthe core

of the ICA theory. The modelis introduced and the question of identiﬁability of

the mixing matrix is treated in Chapter 7. The followingchapters treat different

methods of estimating the model. A central principle is nongaussianity, whose

relationto ICA is ﬁrst discussedin Chapter 8. Next, the principlesof maximum

likelihood (Chapter 9) and minimum mutual information (Chapter 10) are

reviewed, and connections between these three fundamental principles are

shown. Material that is less suitable for an introductory course is covered

in Chapter 11, which discusses the algebraic approach using higher-order

cumulant tensors, and Chapter 12, which reviews the early work on ICA based

on nonlinear decorrelations, as well as the nonlinear principal component

approach. Practical algorithms for computing the independent components

and the mixing matrix are discussed in connection with each principle. Next,

some practical considerations, mainly related to preprocessing and dimension

reduction of the data arediscussed in Chapter13,including hintsto practitioners

on howto really apply ICA to their ownproblem. An overviewand comparison

of the various ICA methods is presented in Chapter 14, which thus summarizes

Part II.



In PartIII, differentextensions of the basicICA modelare given. This part is by

its nature more speculative than Part II, since most of the extensions have been

introduced very recently, and many open problems remain. In an introductory

PREFACE

course on ICA, only selected chapters from this part may be covered. First,

in Chapter 15, we treat the problem of introducing explicit observational noise

in the ICA model. Then the situation where there are more independent

components than observed mixtures is treated in Chapter 16. In Chapter 17,

the model is widely generalized to the case where the mixing process can be of

a very general nonlinear form. Chapter 18 discusses methods that estimate a

linear mixing model similar to thatof ICA, but with quitedifferentassumptions:

the components are not nongaussianbut have some time dependencies instead.

Chapter 19 discusses the case where the mixing system includes convolutions.

Further extensions, in particular models where the components are no longer

required to be exactly independent, are given in Chapter 20.



Part IV treats some applications of ICA methods. Feature extraction (Chap-

ter 21) is relevant to both image processing and vision research. Brain imaging

applications (Chapter 22) concentrate on measurements of the electrical and

magnetic activity of the human brain. Telecommunications applications are

treated in Chapter 23. Some econometric and audio signal processing applica-

tions, together with pointers to miscellaneous other applications, are treated in

Chapter 24.

Throughout the book, we have marked with an asterisk some sections that are

rather involved and can be skipped in an introductory course.

Several of the algorithms presented in this book are available as public domain

software through the World Wide Web, both on our own Web pages and those of

other ICA researchers. Also, databases of real-world data can be found there for

testing the methods. We have made a special Web page for this book, which contains

appropriate pointers. The address is

www.cis.hut.fi/projects/ica/book

The reader is advised to consult this page for further information.

This book was written in cooperation between the three authors. A. Hyv

arinen

was responsible for the chapters 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 20, 21, and 22;

J. Karhunen was responsible for the chapters 2, 4, 17, 19, and 23; while E. Oja was

responsible for the chapters 3, 6, and 12. The Chapters 1 and 24 were written jointly

by the authors.

Acknowledgments

We are grateful to the many ICA researchers whose original contributions form the

foundations of ICA and who have made this book possible. In particular, we wish to

expressour gratitude to the Series Editor Simon Haykin, whose articles and books on

signal processing and neural networks have been an inspiration to us over the years.

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