Unsupervised Feature Extraction Applied to Bioinformatics (eBook)

Foreword 7
Preface 9
Acknowledgments 11
Contents 12
Acronyms 16
Part I Mathematical Preparations 18
1 Introduction to Linear Algebra 19
1.1 Introduction 19
1.2 Scalars 19
1.2.1 Scalars 19
1.2.2 Dummy Scalars 20
1.2.3 Generating New Features by Arithmetic 21
1.3 Vectors 21
1.3.1 Vectors 21
1.3.2 Geometrical Interpretation of Vectors: One Dimension 22
1.3.3 Geometrical Interpretation of Vectors: Two Dimensions 23
1.3.4 Geometrical Interpretation of Vectors: Features 25
1.3.5 Generating New Features by Arithmetic 26
1.3.6 Dummy Vectors 26
1.4 Matrices 27
1.4.1 Equivalences to Geometrical Representation 28
1.4.2 Matrix Manipulation and Feature Generation 29
1.5 Tensors 32
1.5.1 Introduction of Tensors 32
1.5.2 Geometrical Representation of Tensors 33
1.5.3 Generating New Features 35
1.5.4 Tensor Algebra 35
Appendix 38
Rank 38
2 Matrix Factorization 39
2.1 Introduction 39
2.2 Matrix Factorization 39
2.2.1 Rank Factorization 40
2.2.2 Singular Value Decomposition 41
2.2.2.1 How to Compute SVD 42
2.2.2.2 Applying SVD to Shop Data 44
2.3 Principal Component Analysis 46
2.4 Equivalence Between PCA and SVD 47
2.5 Geometrical Representation of PCA 49
2.5.1 PCA Selects the Axis with the Maximal Variance 49
2.5.2 PCA Selects the Axis with Minimum Residuals 52
2.5.3 Non-equivalence Between Two PCAs 53
2.6 PCA as a Clustering Method 54
Appendix 59
Proof of Theorem 2.1 59
References 61
3 Tensor Decomposition 62
3.1 Three Principal Realizations of TD 62
3.2 Performance of TDs as Tools Reducing the Degreesof Freedoms 66
3.2.1 Tucker Decomposition 66
3.2.2 CP Decomposition 68
3.2.3 Tensor Train Decomposition 70
3.2.4 TDs Are Not Always Interpretable 71
3.3 Various Algorithms to Compute TDs 72
3.3.1 CP Decomposition 73
3.3.2 Tucker Decomposition 77
3.3.3 Tensor Train Decomposition 80
3.4 Interpretation Using TD 82
3.5 Summary 86
3.5.1 CP Decomposition 87
3.5.1.1 Advantages 87
3.5.1.2 Disadvantages 87
3.5.2 Tucker Decomposition 87
3.5.2.1 Advantages 87
3.5.2.2 Disadvantages 88
3.5.3 Tensor Train Decomposition 88
3.5.3.1 Advantages 88
3.5.3.2 Disadvantages 88
3.5.4 Superiority of Tucker Decomposition 88
Appendix 89
Moore-Penrose Pseudoinverse 89
References 93
Part II Feature Extractions 94
4 PCA Based Unsupervised FE 95
4.1 Introduction: Feature Extraction vs Feature Selection 95
4.2 Various Feature Selection Procedures 96
4.3 PCA Applied to More Complicated Patterns 99
4.4 Identification of Non-sinusoidal Periodicity by PCA Based Unsupervised FE 106
4.5 Null Hypothesis 111
4.6 Feature Selection with Considering P-Values 112
4.7 Stability 115
4.8 Summary 116
Reference 116
5 TD Based Unsupervised FE 117
5.1 TD as a Feature Selection Tool 117
5.2 Comparisons with Other TDs 121
5.3 Generation of a Tensor From Matrices 123
5.4 Reduction of Number of Dimensions of Tensors 124
5.5 Identification of Correlated Features Using Type I Tensor 125
5.6 Identification of Correlated Features Using Type II Tensor 128
5.7 Summary 129
Reference 130
Part III Applications to Bioinformatics 131
6 Applications of PCA Based Unsupervised FE to Bioinformatics 132
6.1 Introduction 132
6.2 Some Introduction to Genomic Science 132
6.2.1 Central Dogma 133
6.2.2 Regulation of Transcription 133
6.2.3 The Technologies to Measure the Amount of Transcript 134
6.2.4 Various Factors that Regulate the Amount of Transcript 134
6.2.5 Other Factors to Be Considered 135
6.3 Biomarker Identification 136
6.3.1 Biomarker Identification Using Circulating miRNA 136
6.3.1.1 Biomarker Identification Using Serum miRNA 136
6.3.2 Circulating miRNAs as Universal Disease Biomarker 148
6.3.3 Biomarker Identification Using Exosomal miRNAs 150
6.4 Integrated Analysis of mRNA and miRNA Expression 158
6.4.1 Understanding Soldier's Heart From the mRNA and miRNA 158
6.4.2 Identifications of Interactions Between miRNAs and mRNAs in Multiple Cancers 171
6.5 Integrated Analysis of Methylation and Gene Expression 175
6.5.1 Aberrant Promoter Methylation and Expression Associated with Metastasis 176
6.5.2 Epigenetic Therapy Target Identification Based upon Gene Expression and Methylation Profile 180
6.5.3 Identification of Genes Mediating Transgenerational Epigenetics Based upon Integrated Analysis of mRNA Expression and Promoter Methylation 191
6.6 Time Development Analysis 195
6.6.1 Identification of Cell Division Cycle Genes 198
6.6.2 Identification of Disease Driving Genes 207
6.7 Gene Selection for Single Cell RNA-seq 215
6.8 Summary 219
References 220
7 Application of TD Based Unsupervised FE to Bioinformatics 225
7.1 Introduction 225
7.2 PTSD Mediated Heart Diseases 225
7.3 Drug Discovery From Gene Expression 231
7.4 Universarity of miRNA Transfection 239
7.5 One-Class Differential Expression Analysis for Multiomics Data Set 243
7.6 General Examples of Case I and II Tensors 251
7.6.1 Integrated Analysis of mRNA and miRNA 251
7.6.2 Temporally Differentially Expressed Genes 259
7.7 Gene Expression and Methylation in Social Insects 264
7.8 Drug Discovery From Gene Expression: II 269
7.9 Integrated Analysis of miRNA Expression and Methylation 273
7.10 Summary 279
Appendix 280
Universarity of miRNA Transfection 280
Study 1 280
Study 2 282
Study 3 283
Study 4 284
Study 5 284
Study 6 284
Study 7 287
Study 8 288
Study 9 289
Study 10 290
Study 11 291
Drug Discovery From Gene Expression: II 292
Heart Failure 292
PTSD 293
ALL 296
Diabetes 299
Renal Carcinoma 300
Cirrhosis 304
References 306
A Various Implementations of TD 309
A.1 Introduction 309
A.2 R 309
A.2.1 rTensor 309
A.2.2 ttTensor 310
A.3 Python 310
A.3.1 HOTTBOX 310
A.4 MATLAB 310
A.4.1 Tensor Toolbox 310
A.5 julia 311
A.5.1 TensorDecompositions.jl 311
A.6 TensorFlow 311
A.6.1 t3f 311
B List of Published Papers Related to the Methods 312
References 312
Glossary 315
Solutions 316
Problems of Chap.1 316
Problems of Chap.2 320
Problems of Chap.3 322
Index 327