Advances in Principal Component Analysis (eBook)

Ganesh R Naik: Ganesh R. Naik received B.E. degree in Electronics and Communication Engineering from the University of Mysore, India, in 1997. M.E. degree in Communication and Information Engineering from Griffith University, Brisbane, Australia, in 2002, and the PhD degree in the area of Electronics Engineering, specialised in Biomedical Engineering and Signal processing from RMIT University, Melbourne, Australia, in 2009. He is currently Postdoctoral research fellow at MARCS institute, Western Sydney University. Prior to that he held Chancellor's Post-Doctoral Research Fellow position Centre for Health Technologies (CHT), University of Technology Sydney (UTS). As an early mid-career researcher, he has edited 10 books, authored more than 100 papers in peer reviewed journals, conferences, and book chapters over the last seven years. His research interests include EMG signal processing, Pattern recognition, Blind Source Separation (BSS) techniques, Biomedical signal processing, Human Computer Interface (HCI) and Audio signal processing. 

Preface 5
Contents 7
Sparse Principal Component Analysis via Rotation and Truncation 8
1 Motivation of Sparse PCA 8
2 Involved Issues 9
3 Related Work 10
3.1 SPCArt 11
4 SPCArt: Sparse PCA via Rotation and Truncation 13
4.1 Motivation 13
4.2 Objective and Optimization 14
4.3 Truncation Types 16
4.4 Performance Analysis 17
5 A Unified View to Some Prior Work 21
6 Conclusion 23
References 24
PCA, Kernel PCA and Dimensionality Reduction in Hyperspectral Images 26
1 Introduction 26
2 Principal Component Analysis (PCA) Based Feature Extraction Method 28
3 Segmented Principal Component Analysis (SPCA) Based Feature Extraction Method 29
4 Kernel Principal Component Analysis (KPCA) Based Feature Extraction Method 30
5 Clustering Oriented Kernel Principal Component Analysis (KPCA) Based Feature Extraction Method 33
6 Experimental Evaluation 36
6.1 Description of Data Sets 36
6.2 Performance Measures 40
6.3 Parameter Details 42
6.4 Analysis of Results 44
7 Conclusions 51
References 51
Principal Component Analysis in the Presence of Missing Data 54
1 Introduction 54
2 Missing Data Mechanisms 56
2.1 Missing Completely at Random 58
2.2 Missing at Random 58
2.3 Missing Not at Random 59
3 Methods to Handle Missing Data in Principal Component Analysis 61
3.1 Missing (Completely) at Random 62
3.2 Missing Not at Random 67
4 Conclusion 73
References 76
Robust PCAs and PCA Using Generalized Mean 78
1 Introduction 78
2 PCA and Robust PCAs 80
3 Robust Principal Component Analysis Based on Generalized Mean 82
3.1 Generalized Mean 82
3.2 Generalized Sample Mean 83
3.3 Principal Component Analysis Using Generalized Mean 86
4 Experiments 91
4.1 Face Reconstruction 91
4.2 Clustering 94
4.3 Object Categorization 97
5 Conclusion and Discussion 100
References 104
Principal Component Analysis Techniques for Visualization of Volumetric Data 106
1 Introduction 106
2 Related Work 107
3 Concepts 110
4 Cell-Based PCA for Volume Data 112
5 Band-Based PCA 117
6 Conclusions and Future Work 124
References 126
Outlier-Resistant Data Processing with L1-Norm Principal Component Analysis 128
1 Introduction and Problem Formulation 129
2 Exact Solution of L1-PCA 130
2.1 Special Case: Non-negative Data 132
3 Approximate Algorithms 132
3.1 Sequential Fixed-Point Iterations 17 132
3.2 Joint Fixed-Point Iterations (``non-greedy'' approach) 320pt 133
3.3 Semi-definite Programming Relaxation 30 134
3.4 Bit-Flipping Iterations 16,27,29 134
4 Numerical Studies 136
4.1 Line-Fitting 136
4.2 Direction-of-Arrival (DoA) Estimation 137
4.3 L1-PCA Computation Accuracy 139
5 Conclusions 139
References 140
Damage and Fault Detection of Structures Using Principal Component Analysis and Hypothesis Testing 143
1 Introduction 143
2 Experimental Set-Up and Reference Wind Turbine 145
2.1 Experimental Set-Up 145
2.2 Reference Wind Turbine 146
3 Fault Detection Strategy 151
3.1 Data Driven Baseline Modeling Based on PCA 153
3.2 Fault Detection Based on Univariate Hypothesis Testing 158
3.3 Fault Detection Based on Multivariate Hypothesis Testing 164
4 Results 173
4.1 Aluminum Plate and Univariate HT 174
4.2 Aluminum Plate and Multivariate HT 180
4.3 Wind Turbine and Univariate HT 190
4.4 Wind Turbine and Multivariate HT 193
5 Concluding Remarks 195
References 196
Principal Component Analysis for Exponential Family Data 198
1 A Probabilistic Model for Exponential Family Principal Component Analysis (ePCA) 198
1.1 A Probabilistic View of PCA 199
1.2 Exponential Family PCA 199
2 Two Computational Algorithms for ePCA 201
2.1 Sequential Optimization 201
2.2 Transformation by Convex Conjugate 203
3 A Special Case: Logistic PCA 206
4 An Alternative Formulation: Projection of Saturated Model Parameters 209
5 Applications: Dimension Reduction and Aggregate Association Study 213
6 Sparse ePCA Through Penalization 215
7 Two Computational Algorithms for Sparse ePCA 216
7.1 Majorization-Minimization 217
7.2 Transformation by Convex Conjugate 219
8 Connection of Sparse ePCA with ePCA and Sparse PCA 223
9 Application: Clustering of Facial Images 224
10 Conclusions and Future Directions 226
References 227
Application and Extension of PCA Concepts to Blind Unmixing of Hyperspectral Data with Intra-class Variability 229
1 Introduction 230
2 Mixing Models for Earth Observation 232
2.1 Standard Model 232
2.2 Extended Model: Intra-class Variability 234
3 Experimental Characterization of Spectral Variability with PCA 236
4 A New PCA-related Blind Source Separation Method for Handling Spectral Variability 241
4.1 Background: Nonnegative Matrix Factorization (NMF) 241
4.2 Proposed Unconstrained Pixel-by-pixel NMF Method 241
4.3 Proposed Inertia-Constrained Pixel-by-pixel NMF Method 244
5 Analyzing Source Separation Results with PCA 249
6 Conclusion 253
References 254