Table of Contents

About the Authors xiii Preface xv Acknowledgements xvii Glossary xix 1 Introduction 1

1.1 Overview of Blind Source Separation 1

1.2 History of BSS 4

1.3 Applications of BSS 8

1.4 Contents of the Book 10

References 11

Part I BASIC THEORY OF BSS 2 Mathematical Foundation of Blind Source Separation 19

2.1 Matrix Analysis and Computing 19

2.2 Foundation of Probability Theory for Higher-Order Statistics 28

2.3 Basic Concepts of Information Theory 33

2.4 Distance Measure 37

2.5 Solvability of the Signal Blind Source Separation Problem 40

Further Reading 41

3 General Model and Classical Algorithm for BSS 43

3.1 Mathematical Model 43

3.2 BSS Algorithm 46

References 51

4 Evaluation Criteria for the BSS Algorithm 53

4.1 Evaluation Criteria for Objective Functions 53

4.2 Evaluation Criteria for Correlations 57

4.3 Evaluation Criteria for Signal-to-Noise Ratio 57

References 58

Part II INDEPENDENT COMPONENT ANALYSIS AND APPLICATIONS 5 Independent Component Analysis 61

5.1 History of ICA 61

5.2 Principle of ICA 65

5.3 Chapter Summary 82

References 83

6 Fast Independent Component Analysis and Its Application 85

6.1 Overview 85

6.2 FastICA Algorithm 89

6.3 Application and Analysis 92

6.4 Conclusion 118

References 119

7 Maximum Likelihood Independent Component Analysis and Its Application 121

7.1 Overview 121

7.2 Algorithms for Maximum Likelihood Estimation 123

7.3 Application and Analysis 130

7.4 Chapter Summary 133

References 133

8 Overcomplete Independent Component Analysis Algorithms and Applications 135

8.1 Overcomplete ICA Algorithms 135

8.2 Applications and Analysis 139

8.3 Chapter Summary 143

References 144

9 Kernel Independent Component Analysis 145

9.1 KICA Algorithm 145

9.2 Application and Analysis 147

9.3 Concluding Remarks 149

References 152

10 Natural Gradient Flexible ICA Algorithm and Its Application 153

10.1 Natural Gradient Flexible ICA Algorithm 153

10.2 Application and Analysis 156

10.3 Chapter Summary 166

References 166

11 Non-negative Independent Component Analysis and Its Application 167

11.1 Non-negative Independent Component Analysis 168

11.2 Application and Analysis 169

11.3 Chapter Summary 182

References 182

12 Constraint Independent Component Analysis Algorithms and Applications 183

12.1 Overview 183

12.2 CICA Algorithm 185

12.3 Application and Analysis 189

12.4 Chapter Summary 196

References 196

13 Optimized Independent Component Analysis Algorithms and Applications 199

13.1 Overview 199

13.2 Optimized ICA Algorithm 200

13.3 Application and Analysis 205

13.4 Chapter Summary 221

References 222

14 Supervised Learning Independent Component Analysis Algorithms and Applications 225

14.1 Overview 225

14.2 Mathematical Model 226

14.3 Principles of SL-ICA 227

14.4 SL-ICA Implementation Process 230

14.5 The Experiment 230

14.6 Chapter Summary 239

Appendix 14.A Polarization Channel SAR Images of Beijing and the Decomposition Results using SL-ICA 239

References 242

Part III ADVANCES AND APPLICATIONS OF BSS 15 Non-negative Matrix Factorization Algorithms and Applications 247

15.1 Introduction 247

15.2 NMF Algorithms 251

15.3 Applications and Analysis 276

15.4 Chapter Summary 309

References 310

16 Sparse Component Analysis and Applications 313

16.1 Overview 314

16.2 Linear Clustering SCA (LC-SCA) 321

16.3 Plane Clustering SCA (PC-SCA) 332

16.4 Over-Complete SCA Based on Plane Clustering (PCO-SCA) 336

16.5 Blind Image Separation Based on Wavelets and SCA (WL-SCA) 340

16.6 New BSS Algorithm Based on Feedback SCA 343

16.7 Remote Sensing Image Classification Based on SCA 351

16.8 Chapter Summary 357

References 357 Index 361

About the Author

Xianchuan Yu, Beijing Normal University, P. R. China Dan Hu, Beijing Normal University, P. R. China Jindong Xu, Beijing Normal University, P. R. China