Taguchi Unsupervised Feature Extraction Applied to Bioinformatics

A PCA Based and TD Based Approach
1. Auflage 2019
ISBN: 978-3-030-22456-1
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 321 Seiten

Reihe: Unsupervised and Semi-Supervised Learning

This book proposes applications of tensor decomposition to unsupervised feature extraction and feature selection. The author posits that although supervised methods including deep learning have become popular, unsupervised methods have their own advantages. He argues that this is the case because unsupervised methods are easy to learn since tensor decomposition is a conventional linear methodology. This book starts from very basic linear algebra and reaches the cutting edge methodologies applied to difficult situations when there are many features (variables) while only small number of samples are available. The author includes advanced descriptions about tensor decomposition including Tucker decomposition using high order singular value decomposition as well as higher order orthogonal iteration, and train tenor decomposition. The author concludes by showing unsupervised methods and their application to a wide range of topics. 

• Allows readers to analyze data sets with small samples and many features;
• Provides a fast algorithm, based upon linear algebra, to analyze big data;
• Includes several applications to multi-view data analyses, with a focus on bioinformatics.

Autoren/Hrsg.

Taguchi, Y-h.

Inhaltsverzeichnis

1;Foreword;7
2;Preface;9
3;Acknowledgments;11
4;Contents;12
5;Acronyms;16
6;Part I Mathematical Preparations;18
6.1;1 Introduction to Linear Algebra;19
6.1.1;1.1 Introduction;19
6.1.2;1.2 Scalars;19
6.1.2.1;1.2.1 Scalars;19
6.1.2.2;1.2.2 Dummy Scalars;20
6.1.2.3;1.2.3 Generating New Features by Arithmetic;21
6.1.3;1.3 Vectors;21
6.1.3.1;1.3.1 Vectors;21
6.1.3.2;1.3.2 Geometrical Interpretation of Vectors: One Dimension;22
6.1.3.3;1.3.3 Geometrical Interpretation of Vectors: Two Dimensions;23
6.1.3.4;1.3.4 Geometrical Interpretation of Vectors: Features;25
6.1.3.5;1.3.5 Generating New Features by Arithmetic;26
6.1.3.6;1.3.6 Dummy Vectors;26
6.1.4;1.4 Matrices;27
6.1.4.1;1.4.1 Equivalences to Geometrical Representation;28
6.1.4.2;1.4.2 Matrix Manipulation and Feature Generation;29
6.1.5;1.5 Tensors;32
6.1.5.1;1.5.1 Introduction of Tensors;32
6.1.5.2;1.5.2 Geometrical Representation of Tensors;33
6.1.5.3;1.5.3 Generating New Features;35
6.1.5.4;1.5.4 Tensor Algebra;35
6.1.6;Appendix;38
6.1.6.1;Rank;38
6.2;2 Matrix Factorization;39
6.2.1;2.1 Introduction;39
6.2.2;2.2 Matrix Factorization;39
6.2.2.1;2.2.1 Rank Factorization;40
6.2.2.2;2.2.2 Singular Value Decomposition;41
6.2.2.2.1;2.2.2.1 How to Compute SVD;42
6.2.2.2.2;2.2.2.2 Applying SVD to Shop Data;44
6.2.3;2.3 Principal Component Analysis;46
6.2.4;2.4 Equivalence Between PCA and SVD;47
6.2.5;2.5 Geometrical Representation of PCA;49
6.2.5.1;2.5.1 PCA Selects the Axis with the Maximal Variance;49
6.2.5.2;2.5.2 PCA Selects the Axis with Minimum Residuals;52
6.2.5.3;2.5.3 Non-equivalence Between Two PCAs;53
6.2.6;2.6 PCA as a Clustering Method;54
6.2.7;Appendix;59
6.2.7.1;Proof of Theorem 2.1;59
6.2.8;References;61
6.3;3 Tensor Decomposition;62
6.3.1;3.1 Three Principal Realizations of TD;62
6.3.2;3.2 Performance of TDs as Tools Reducing the Degreesof Freedoms;66
6.3.2.1;3.2.1 Tucker Decomposition;66
6.3.2.2;3.2.2 CP Decomposition;68
6.3.2.3;3.2.3 Tensor Train Decomposition;70
6.3.2.4;3.2.4 TDs Are Not Always Interpretable;71
6.3.3;3.3 Various Algorithms to Compute TDs;72
6.3.3.1;3.3.1 CP Decomposition;73
6.3.3.2;3.3.2 Tucker Decomposition;77
6.3.3.3;3.3.3 Tensor Train Decomposition;80
6.3.4;3.4 Interpretation Using TD;82
6.3.5;3.5 Summary;86
6.3.5.1;3.5.1 CP Decomposition;87
6.3.5.1.1;3.5.1.1 Advantages;87
6.3.5.1.2;3.5.1.2 Disadvantages;87
6.3.5.2;3.5.2 Tucker Decomposition;87
6.3.5.2.1;3.5.2.1 Advantages;87
6.3.5.2.2;3.5.2.2 Disadvantages;88
6.3.5.3;3.5.3 Tensor Train Decomposition;88
6.3.5.3.1;3.5.3.1 Advantages;88
6.3.5.3.2;3.5.3.2 Disadvantages;88
6.3.5.4;3.5.4 Superiority of Tucker Decomposition;88
6.3.6;Appendix;89
6.3.6.1;Moore-Penrose Pseudoinverse;89
6.3.7;References;93
7;Part II Feature Extractions;94
7.1;4 PCA Based Unsupervised FE;95
7.1.1;4.1 Introduction: Feature Extraction vs Feature Selection;95
7.1.2;4.2 Various Feature Selection Procedures;96
7.1.3;4.3 PCA Applied to More Complicated Patterns;99
7.1.4;4.4 Identification of Non-sinusoidal Periodicity by PCA Based Unsupervised FE;106
7.1.5;4.5 Null Hypothesis;111
7.1.6;4.6 Feature Selection with Considering P-Values;112
7.1.7;4.7 Stability;115
7.1.8;4.8 Summary;116
7.1.9;Reference;116
7.2;5 TD Based Unsupervised FE;117
7.2.1;5.1 TD as a Feature Selection Tool;117
7.2.2;5.2 Comparisons with Other TDs;121
7.2.3;5.3 Generation of a Tensor From Matrices;123
7.2.4;5.4 Reduction of Number of Dimensions of Tensors;124
7.2.5;5.5 Identification of Correlated Features Using Type I Tensor;125
7.2.6;5.6 Identification of Correlated Features Using Type II Tensor;128
7.2.7;5.7 Summary;129
7.2.8;Reference;130
8;Part III Applications to Bioinformatics;131
8.1;6 Applications of PCA Based Unsupervised FE to Bioinformatics;132
8.1.1;6.1 Introduction;132
8.1.2;6.2 Some Introduction to Genomic Science;132
8.1.2.1;6.2.1 Central Dogma;133
8.1.2.2;6.2.2 Regulation of Transcription;133
8.1.2.3;6.2.3 The Technologies to Measure the Amount of Transcript;134
8.1.2.4;6.2.4 Various Factors that Regulate the Amount of Transcript;134
8.1.2.5;6.2.5 Other Factors to Be Considered;135
8.1.3;6.3 Biomarker Identification;136
8.1.3.1;6.3.1 Biomarker Identification Using Circulating miRNA;136
8.1.3.1.1;6.3.1.1 Biomarker Identification Using Serum miRNA;136
8.1.3.2;6.3.2 Circulating miRNAs as Universal Disease Biomarker;148
8.1.3.3;6.3.3 Biomarker Identification Using Exosomal miRNAs;150
8.1.4;6.4 Integrated Analysis of mRNA and miRNA Expression;158
8.1.4.1;6.4.1 Understanding Soldier's Heart From the mRNA and miRNA;158
8.1.4.2;6.4.2 Identifications of Interactions Between miRNAs and mRNAs in Multiple Cancers;171
8.1.5;6.5 Integrated Analysis of Methylation and Gene Expression;175
8.1.5.1;6.5.1 Aberrant Promoter Methylation and Expression Associated with Metastasis;176
8.1.5.2;6.5.2 Epigenetic Therapy Target Identification Based upon Gene Expression and Methylation Profile;180
8.1.5.3;6.5.3 Identification of Genes Mediating Transgenerational Epigenetics Based upon Integrated Analysis of mRNA Expression and Promoter Methylation;191
8.1.6;6.6 Time Development Analysis;195
8.1.6.1;6.6.1 Identification of Cell Division Cycle Genes;198
8.1.6.2;6.6.2 Identification of Disease Driving Genes;207
8.1.7;6.7 Gene Selection for Single Cell RNA-seq;215
8.1.8;6.8 Summary;219
8.1.9;References;220
8.2;7 Application of TD Based Unsupervised FE to Bioinformatics;225
8.2.1;7.1 Introduction;225
8.2.2;7.2 PTSD Mediated Heart Diseases;225
8.2.3;7.3 Drug Discovery From Gene Expression;231
8.2.4;7.4 Universarity of miRNA Transfection;239
8.2.5;7.5 One-Class Differential Expression Analysis for Multiomics Data Set;243
8.2.6;7.6 General Examples of Case I and II Tensors;251
8.2.6.1;7.6.1 Integrated Analysis of mRNA and miRNA;251
8.2.6.2;7.6.2 Temporally Differentially Expressed Genes;259
8.2.7;7.7 Gene Expression and Methylation in Social Insects;264
8.2.8;7.8 Drug Discovery From Gene Expression: II;269
8.2.9;7.9 Integrated Analysis of miRNA Expression and Methylation;273
8.2.10;7.10 Summary;279
8.2.11;Appendix;280
8.2.11.1;Universarity of miRNA Transfection;280
8.2.11.1.1;Study 1;280
8.2.11.1.2;Study 2;282
8.2.11.1.3;Study 3;283
8.2.11.1.4;Study 4;284
8.2.11.1.5;Study 5;284
8.2.11.1.6;Study 6;284
8.2.11.1.7;Study 7;287
8.2.11.1.8;Study 8;288
8.2.11.1.9;Study 9;289
8.2.11.1.10;Study 10;290
8.2.11.1.11;Study 11;291
8.2.11.2;Drug Discovery From Gene Expression: II;292
8.2.11.2.1;Heart Failure;292
8.2.11.2.2;PTSD;293
8.2.11.2.3;ALL;296
8.2.11.2.4;Diabetes;299
8.2.11.2.5;Renal Carcinoma;300
8.2.11.2.6;Cirrhosis;304
8.2.12;References;306
9;A Various Implementations of TD;309
9.1;A.1 Introduction;309
9.2;A.2 R;309
9.2.1;A.2.1 rTensor;309
9.2.2;A.2.2 ttTensor;310
9.3;A.3 Python;310
9.3.1;A.3.1 HOTTBOX;310
9.4;A.4 MATLAB;310
9.4.1;A.4.1 Tensor Toolbox;310
9.5;A.5 julia;311
9.5.1;A.5.1 TensorDecompositions.jl;311
9.6;A.6 TensorFlow;311
9.6.1;A.6.1 t3f;311
10;B List of Published Papers Related to the Methods;312
10.1;References;312
11;Glossary;315
12;Solutions;316
12.1;Problems of Chap.1;316
12.2;Problems of Chap.2;320
12.3;Problems of Chap.3;322
13;Index;327