Dr JV Stone

Independent Component Analysis

A Tutorial Introduction

by James V Stone.

Published September 2004 by MIT Press.

ISBN: 0262693151

Contents

Part I Independent Component Analysis and Blind Source Separation

Chapter 1 Overview of Independent Component Analysis

1.1: Introduction
1.2: Independent Component Analysis: What Is It?
1.3: How Independent Component Analysis Works
1.4: Independent Component Analysis and Perception
1.5: Principal Component Analysis and Factor Analysis
1.6: Independent Component Analysis: What Is It Good For?

Chapter 2 Strategies for Blind Source Separation

2.1: Introduction
2.2: Mixing Signals
2.3: Unmixing Signals
2.4: The Number of Sources and Mixtures
2.5: Comparing Strategies
2.6: Summary

Part II The Geometry of Mixtures

Chapter 3 Mixing and Unmixing

3.1: Introduction
3.2: Signals, Variables, and Scalars
3.3: The Geometry of Signals
3.4: Summary

Chapter 4 Unmixing Using the Inner Product

4.1: Introduction
4.2: Unmixing Coefficients as Weight Vectors
4.3: The Inner Product
4.4: Matrices as Geometric Transformations
4.5: The Mixing Matrix Transforms Source Signal Axes
4.6: Summary

Chapter 5 Independence and Probability Density Functions

5.1: Introduction
5.2: Histograms
5.3: Histograms and Probability Density Functions
5.4: The Central Limit Theorem
5.5: Cumulative Density Functions
5.6: Moments: Mean, Variance, Skewness and Kurtosis
5.7: Independence and Correlation
5.8: Uncorrelated Pendulums
5.9: Summary

Part III Methods for Blind Source Separation

Chapter 6 Projection Pursuit

6.1: Introduction
6.2: Mixtures Are Gaussian
6.3: Gaussian Signals: Good News, Bad News
6.4: Kurtosis as a Measure of Non-Normality
6.5: Weight Vector Angle and Kurtosis
6.6: Using Kurtosis to Recover Multiple Source Signals
6.7: Projection Pursuit and ICA Extract the Same Signals
6.8: When to Stop Extracting Signals
6.9: Summary

Chapter 7 Independent Component Analysis

7.1: Introduction
7.2: Independence of Joint and Marginal Distributions
7.3: Infomax: Independence and Entropy
7.4: Maximum Likelihood ICA
7.5: Maximum Likelihood and Infomax Equivalence
7.6: Extracting Source Signals Using Gradient Ascent
7.7: Temporal and Spatial ICA
7.8: Summary

Chapter 8 Complexity Pursuit

8.1: Introduction
8.2: Predictability and Complexity
8.3: Measuring Complexity Using Signal Predictability
8.4: Extracting Signals by Maximizing Predictability
8.5: Summary

Chapter 9 Gradient Ascent

9.1: Introduction
9.2: Gradient Ascent on a Line
9.3: Gradient Ascent on a Hill
9.4: Second Order Methods
9.5: The Natural Gradient
9.6: Global and Local Maxima
9.7: Summary

Chapter 10 Principal Component Analysis and Factor Analysis

10.1: Introduction
10.2: ICA and PCA
10.3: Eigenvectors and Eigenvalues
10.4: PCA Applied to Speech Signal Mixtures
10.5: Factor Analysis
10.6: Summary

PartIV Applications

Chapter 11 Applications of ICA

11.1: Introduction
11.2: Temporal ICA of Voice Mixtures
11.3: Temporal ICA of Electroencephalograms158
11.4: Spatial ICA of fMRI Data
11.5: Spatial ICA for Color MRI Data
11.6: Complexity Pursuit for Fetal Heart Monitoring
11.7: Complexity Pursuit for Learning Stereo Disparity

PartV Appendices

Appendix A: A Vector Matrix Tutorial

Appendix B: Projection Pursuit Gradient Ascent

Appendix C: Projection Pursuit: Stepwise Separation of Sources

Appendix D: ICA Gradient Ascent

Appendix E: Complexity Pursuit Gradient Ascent

Appendix F: Principal Component Analysis for Preprocessing Data

Appendix G: Independent Component Analysis Resources

Appendix H: Recommended Reading