Издательство MIT Press, 2004, -213 pp.
This book is intended to provide the essentials of independent component analysis (ICA) using intuitive examples described in simple geometric terms. The tutorial style adopted should make this book suitable for readers of varying mathematical sophistication, from the almost innumerate enthusiast to the research scientist.
In writing this book, I have not been overly conceed with much in the way of mathematical proofs, nor with unnecessary mathematical notation. This approach can be justified to some extent because the rapidly expanding field of independent component analysis is replete with such formal accounts. More generally, formal mathematical proofs require assumptions which are often physically untenable, as noted by Einstein,
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
Most importantly, disregarding all but the most important mathematical proofs leaves the reader free to explore the fundamental characteristics of independent component analysis without constantly tripping up the many caveats usually associated with highly mathematical treatments. The resultant tutorial account of independent component analysis is essentially true, even though such essential truths may not include certain technical details and caveats.
The tutorial approach adopted in this book has two consequences. First, important facts are repeated as appropriate in different sections of the book. I make no apology for this. What is obvious to the trained mathematician often bears a degree of repetition to the novice. Second, new topics are usually introduced on a need to know basis. This strategy of introducing new topics only when they are required ensures that the account of each new topic is well motivated by the problem at hand, and can be described in terms of relevant examples.
In attempting to understand the details of a particular method, it is often helpful to examine computer code which implements that method. This allows the reader to examine how a given mathematical method described in the text translates into working computer code. With this in mind, basic demonstration computer code is provided in appendices. This code, and more complete versions of it, can be obtained from my web site: http://www.shef.ac.uk/?pc1jvs.
Finally, my intention has been to cut through the distracting issues that inevitably accompany any new method (e.g., variants of independent component analysis methods that are smaller, faster, or cheaper), and to describe the essential core of independent component analysis in relation to a few intuitive examples. However, it must be acknowledged that there are a small number of variants of independent component analysis which, while not essential for understanding the principles of the method, are of considerable interest, and these are described briefly.
Independent Component Analysis and Blind Source Separation.
Overview of Independent Component Analysis.
Strategies for Blind Source Separation.
The Geometry of Mixtures.
Mixing and Unmixing.
Unmixing Using the Inner Product.
ndependence and Probability Density Functions.
Methods for Blind Source Separation.
Projection Pursuit.
ndependent Component Analysis.
Complexity Pursuit.
Gradient Ascent.
Principal Component Analysis and Factor Analysis.
Applications of ICA.
Appendices.
This book is intended to provide the essentials of independent component analysis (ICA) using intuitive examples described in simple geometric terms. The tutorial style adopted should make this book suitable for readers of varying mathematical sophistication, from the almost innumerate enthusiast to the research scientist.
In writing this book, I have not been overly conceed with much in the way of mathematical proofs, nor with unnecessary mathematical notation. This approach can be justified to some extent because the rapidly expanding field of independent component analysis is replete with such formal accounts. More generally, formal mathematical proofs require assumptions which are often physically untenable, as noted by Einstein,
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
Most importantly, disregarding all but the most important mathematical proofs leaves the reader free to explore the fundamental characteristics of independent component analysis without constantly tripping up the many caveats usually associated with highly mathematical treatments. The resultant tutorial account of independent component analysis is essentially true, even though such essential truths may not include certain technical details and caveats.
The tutorial approach adopted in this book has two consequences. First, important facts are repeated as appropriate in different sections of the book. I make no apology for this. What is obvious to the trained mathematician often bears a degree of repetition to the novice. Second, new topics are usually introduced on a need to know basis. This strategy of introducing new topics only when they are required ensures that the account of each new topic is well motivated by the problem at hand, and can be described in terms of relevant examples.
In attempting to understand the details of a particular method, it is often helpful to examine computer code which implements that method. This allows the reader to examine how a given mathematical method described in the text translates into working computer code. With this in mind, basic demonstration computer code is provided in appendices. This code, and more complete versions of it, can be obtained from my web site: http://www.shef.ac.uk/?pc1jvs.
Finally, my intention has been to cut through the distracting issues that inevitably accompany any new method (e.g., variants of independent component analysis methods that are smaller, faster, or cheaper), and to describe the essential core of independent component analysis in relation to a few intuitive examples. However, it must be acknowledged that there are a small number of variants of independent component analysis which, while not essential for understanding the principles of the method, are of considerable interest, and these are described briefly.
Independent Component Analysis and Blind Source Separation.
Overview of Independent Component Analysis.
Strategies for Blind Source Separation.
The Geometry of Mixtures.
Mixing and Unmixing.
Unmixing Using the Inner Product.
ndependence and Probability Density Functions.
Methods for Blind Source Separation.
Projection Pursuit.
ndependent Component Analysis.
Complexity Pursuit.
Gradient Ascent.
Principal Component Analysis and Factor Analysis.
Applications of ICA.
Appendices.