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Independent Component Analysis A Tutorial Introduction.pdf
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英文原版书 独立分量分析 主要有1 independent component analysis and blind source separation 2 the geometry of mixtures 3 method for blind source separation 4 applications
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A Tutorial Introduction
INDEPENDENT COMPONENT ANALYSIS
James V. Stone
INDEPENDENT COMPONENT ANALYSIS A Tutorial Introduction James V. Stone
Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In
essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals,
or source signals. In so doing, this powerful method can extract the relatively small amount of useful information typ-
ically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical
brain signals to telecommunications and stock predictions.
In
Independent Component Analysis, Jim Stone presents the essentials of ICA and related techniques (projection
pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The
treatment fills the need for a basic primer on ICA that can be used by readers of varying levels of mathematical so-
phistication, including engineers, cognitive scientists, and neuroscientists who need to know the essentials of this
evolving method.
An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and de-
scribes how ICA is based on the key observation that different physical processes generate outputs that are statisti-
cally independent of each other. The book then describes what Stone calls “the mathematical nuts and bolts” of how
ICA works. Presenting only essential mathematical proofs, Stone guides the reader through an exploration of the fun-
damental characteristics of ICA.
Topics covered include the geometry of mixing and unmixing; methods for blind source separation; and appli-
cations of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector ma-
trix tutorial, plus basic demonstration computer code that allows the reader to see how each mathematical method
described in the text translates into working Matlab computer code.
James V. Stone is a Reader in the Psychology Department at the University of Sheffield, England.
INDEPENDENT COMPONENT ANALYSIS
Stone
This fantastic book provides a broad introduction to both the theory and applications of independent component
analysis. I recommend it to any student interested in exploring this emerging field.” —Martin J. McKeown, Associate
Professor of Medicine (Neurology), University of British Columbia
Independent component analysis is a recent and powerful addition to the methods that scientists and engineers have
available to explore large data sets in high-dimensional spaces. This book is a clearly written introduction to the foun-
dations of ICA and the practical issues that arise in applying it to a wide range of problems.” —Terrence J. Sejnowski,
Howard Hughes Medical Institute, Salk Institute for Biological Studies, and University of California, San Diego
This monograph provides a delightful tour, through the foothills of linear algebra to the higher echelons of inde-
pendent components analysis, in a graceful and deceptively simple way. Its careful construction, introducing concepts
as they are needed, discloses the fundamentals of source separation in a remarkably accessible and comprehen-
sive fashion.” —Karl J. Friston, University College London
The MIT Press
Massachusetts Institute of Technology
Cambridge, Massachusetts 02142
http://mitpress.mit.edu
0-262-69315-1
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A Bradford Book
cognitive neuroscience/psychology
Independent Component Analysis
A Tutorial Introduction
James V. Stone
A Bradford Book
The MIT Press
Cambridge, Massachusetts
London, England
Preface xi
Acknowledgments xiii
Abbreviations xv
Mathematical Symbols xvii
I Independent Component Analysis and Blind Source Separation 1
1 Overview of Independent Component Analysis 5
1.1 Introduction 5
1.2 Independent Component Analysis: What Is It? 5
1.3 How Independent Component Analysis Works 8
1.4 Independent Component Analysis and Perception 8
1.5 Principal Component Analysis and Factor Analysis 9
1.6 Independent Component Analysis: What Is It Good For? 10
2 Strategies for Blind Source Separation 13
2.1 Introduction 13
2.2 Mixing Signals 13
2.3 Unmixing Signals 14
2.4 The Number of Sources and Mixtures 17
2.5 Comparing Strategies 18
2.6 Summary 18
II The Geometry of Mixtures 19
3 Mixing and Unmixing 21
3.1 Introduction 21
3.2 Signals, Variables, and Scalars 21
3.2.1 Images as Signals 21
3.2.2 Representing Signals: Vectors and Vector Variables 22
3.3 The Geometry of Signals 24
3.3.1 Mixing Signals 24
3.3.2 Unmixing Signals 27
3.4 Summary 29
4 Unmixing Using the Inner Product 31
4.1 Introduction 31
4.2 Unmixing Coeffi cients as Weight Vectors 33
4.2.1 Extracted Signals Depend on the Orientation of Weight Vectors 34
4.3 The Inner Product 35
4.3.1 The Geometry of the Inner Product 38
4.4 Matrices as Geometric Transformations 39
Contents
viii Contents
4.4.1 Geometric Transformation of Signals 39
4.4.2 The Unmixing Matrix 40
4.4.3 The Mixing Matrix 42
4.5 The Mixing Matrix Transforms Source Signal Axes 43
4.5.1 Extracting One Source Signal from Two Mixtures 44
4.5.2 Extracting Source Signals from Three Mixtures 46
4.6 Summary 49
5 Independence and Probability Density Functions 51
5.1 Introduction 51
5.2 Histograms 51
5.3 Histograms and Probability Density Functions 54
5.4 The Central Limit Theorem 56
5.5 Cumulative Density Functions 57
5.6 Moments: Mean, Variance, Skewness and Kurtosis 58
5.7 Independence and Correlation 61
5.8 Uncorrelated Pendulums 63
5.9 Summary 65
III Methods for Blind Source Separation 69
6 Projection Pursuit 71
6.1 Introduction 71
6.2 Mixtures Are Gaussian 71
6.3 Gaussian Signals: Good News, Bad News 72
6.4 Kurtosis as a Measure of Non-Normality 73
6.5 Weight Vector Angle and Kurtosis 73
6.6 Using Kurtosis to Recover Multiple Source Signals 75
6.7 Projection Pursuit and ICA Extract the Same Signals 75
6.8 When to Stop Extracting Signals 76
6.9 Summary 77
7 Independent Component Analysis 79
7.1 Introduction 79
7.2 Independence of Joint and Marginal Distributions 79
7.2.1 Independent Events: Coin Tossing 79
7.2.2 Independent Signals: Speech 80
7.3 Infomax: Independence and Entropy 83
7.3.1 Infomax Overview 84
7.3.2 Entropy 86
7.3.3 Entropy of Univariate pdfs 90
Contents ix
7.3.4 Entropy of Multivariate pdfs 93
7.3.5 Using Entropy to Extract Independent Signals 99
7.4 Maximum Likelihood ICA 99
7.5 Maximum Likelihood and Infomax Equivalence 103
7.6 Extracting Source Signals Using Gradient Ascent 103
7.7 Temporal and Spatial ICA 103
7.7.1 Temporal ICA 106
7.7.2 Spatial ICA 108
7.7.3 Spatiotemporal ICA 109
7.7.4 The Size of the Unmixing Matrix 109
7.8 Summary 110
8 Complexity Pursuit 111
8.1 Introduction 111
8.2 Predictability and Complexity 112
8.3 Measuring Complexity Using Signal Predictability 113
8.4 Extracting Signals by Maximizing Predictability 115
8.5 Summary 118
9 Gradient Ascent 119
9.1 Introduction 119
9.2 Gradient Ascent on a Line 120
9.3 Gradient Ascent on a Hill 122
9.4 Second Order Methods 126
9.5 The Natural Gradient 127
9.6 Global and Local Maxima 127
9.7 Summary 128
10 Principal Component Analysis and Factor Analysis 129
10.1 Introduction 129
10.2 ICA and PCA 129
10.3 Eigenvectors and Eigenvalues 130
10.4 PCA Applied to Speech Signal Mixtures 131
10.5 Factor Analysis 133
10.6 Summary 135
IV Applications 137
11 Applications of ICA 139
11.1 Introduction 139
11.2 Temporal ICA of Voice Mixtures 139
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资源评论
- 乖灬小狐2018-08-07内容很完整,需要慢慢啃。
- pyx77_882012-05-08内容很齐全,对我目前的学习很有帮助,谢谢分享啊!
- idonotknowit2014-06-07这个东东的确是好东西,不过要价也很高啊。
- ajie1234567892014-11-22好书,值得仔细看!
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