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