Multiblock Data Fusion in Statistics and Machine Learning: Applications in the Natural and Life Sciences

Description

Multiblock Data Fusion in Statistics and Machine Learning Explore the advantages and shortcomings of various forms of multiblock analysis, and the relationships between them, with this expert guide Arising out of fusion problems that exist in a variety of fields in the natural and life sciences, the methods available to fuse multiple data sets have expanded dramatically in recent years. Older methods, rooted in psychometrics and chemometrics, also exist. Multiblock Data Fusion in Statistics and Machine Learning: Applications in the Natural and Life Sciences is a detailed overview of all relevant multiblock data analysis methods for fusing multiple data sets. It focuses on methods based on components and latent variables, including both well-known and lesser-known methods with potential applications in different types of problems. Many of the included methods are illustrated by practical examples and are accompanied by a freely available R-package. The distinguished authors have created an accessible and useful guide to help readers fuse data, develop new data fusion models, discover how the involved algorithms and models work, and understand the advantages and shortcomings of various approaches. This book includes: A thorough introduction to the different options available for the fusion of multiple data sets, including methods originating in psychometrics and chemometricsPractical discussions of well-known and lesser-known methods with applications in a wide variety of data problemsIncluded, functional R-code for the application of many of the discussed methods Perfect for graduate students studying data analysis in the context of the natural and life sciences, including bioinformatics, sensometrics, and chemometrics, Multiblock Data Fusion in Statistics and Machine Learning: Applications in the Natural and Life Sciences is also an indispensable resource for developers and users of the results of multiblock methods. Multiblock Data Fusion in Statistics and Machine Learning Contents Foreword Preface List of Figures List of Tables Part I Introductory Concepts and Theory chapnumcolor1 Introduction 1.1 Scope of the Book 1.2 Potential Audience 1.3 Types of Data and Analyses 1.3.1 Supervised and Unsupervised Analyses 1.3.2 High-, Mid- and Low-level Fusion 1.3.3 Dimension Reduction 1.3.4 Indirect Versus Direct Data 1.3.5 Heterogeneous Fusion 1.4 Examples 1.4.1 Metabolomics 1.4.2 Genomics 1.4.3 Systems Biology 1.4.4 Chemistry 1.4.5 Sensory Science 1.5 Goals of Analyses 1.6 Some History 1.7 Fundamental Choices 1.8 Common and Distinct Components 1.9 Overview and Links 1.10 Notation and Terminology 1.11 Abbreviations chapnumcolor2 Basic Theory and Concepts 2.i General Introduction 2.1 Component Models 2.1.1 General Idea of Component Models 2.1.2 Principal Component Analysis 2.1.3 Sparse PCA 2.1.4 Principal Component Regression 2.1.5 Partial Least Squares 2.1.6 Sparse PLS 2.1.7 Principal Covariates Regression 2.1.8 Redundancy Analysis 2.1.9 Comparing PLS, PCovR and RDA 2.1.10 Generalised Canonical Correlation Analysis 2.1.11 Simultaneous Component Analysis 2.2 Properties of Data 2.2.1 Data Theory 2.2.2 Scale-types 2.3 Estimation Methods 2.3.1 Least-squares Estimation 2.3.2 Maximum-likelihood Estimation 2.3.3 Eigenvalue Decomposition-based Methods 2.3.4 Covariance or Correlation-based Estimation Methods 2.3.5 Sequential Versus Simultaneous Methods 2.3.6 Homogeneous Versus Heterogeneous Fusion 2.4 Within- and Between-block Variation 2.4.1 Definition and Example 2.4.2 MAXBET Solution 2.4.3 MAXNEAR Solution 2.4.4 PLS2 Solution 2.4.5 CCA Solution 2.4.6 Comparing the Solutions 2.4.7 PLS, RDA and CCA Revisited 2.5 Framework for Common and Distinct Components 2.6 Preprocessing 2.7 Validation 2.7.1 Outliers 2.7.1.1 Residuals 2.7.1.2 Leverage 2.7.2 Model Fit 2.7.3 Bias-variance Trade-off 2.7.4 Test Set Validation 2.7.5 Cross-validation 2.7.6 Permutation Testing 2.7.7 Jackknife and Bootstrap 2.7.8 Hyper-parameters and Penalties 2.8 Appendix chapnumcolor3 Structure of Multiblock Data 3.i General Introduction 3.1 Taxonomy 3.2 Skeleton of a Multiblock Data Set 3.2.1 Shared Sample Mode 3.2.2 Shared Variable Mode 3.2.3 Shared Variable or Sample Mode 3.2.4 Shared Variable and Sample Mode 3.3 Topology of a Multiblock Data Set 3.3.1 Unsupervised Analysis 3.3.2 Supervised Analysis 3.4 Linking Structures 3.4.1 Linking Structure for Unsupervised Analysis 3.4.2 Linking Structures for Supervised Analysis 3.5 Summary chapnumcolor4 Matrix Correlations 4.i General Introduction 4.1 Definition 4.2 Most Used Matrix Correlations 4.2.1 Inner Product Correlation 4.2.2 GCD coefficient 4.2.3 RV-coefficient 4.2.4 SMI-coefficient 4.3 Generic Framework of Matrix Correlations 4.4 Generalised Matrix Correlations 4.4.1 Generalised RV-coefficient 4.4.2 Generalised Association Coefficient 4.5 Partial Matrix Correlations 4.6 Conclusions and Recommendations 4.7 Open Issues Part II Selected Methods for Unsupervised and Supervised Topologies chapnumcolor5 Unsupervised Methods 5.i General Introduction 5.ii Relations to the General Framework 5.1 Shared Variable Mode 5.1.1 Only Common Variation 5.1.1.1 Simultaneous Component Analysis 5.1.1.2 Clustering and SCA 5.1.1.3 Multigroup Data Analysis 5.1.2 Common, Local, and Distinct Variation 5.1.2.1 Distinct and Common Components 5.1.2.2 Multivariate Curve Resolution 5.2 Shared Sample Mode 5.2.1 Only Common Variation 5.2.1.1 SUM-PCA 5.2.1.2 Multiple Factor Analysis and STATIS 5.2.1.3 Generalised Canonical Analysis 5.2.1.4 Regularised Generalised Canonical Correlation Analysis 5.2.1.5 Exponential Family SCA 5.2.1.6 Optimal-scaling 5.2.2 Common, Local, and Distinct Variation 5.2.2.1 Joint and Individual Variation Explained 5.2.2.2 Distinct and Common Components 5.2.2.3 PCA-GCA 5.2.2.4 Advanced Coupled Matrix and Tensor Factorisation 5.2.2.5 Penalised-ESCA 5.2.2.6 Multivariate Curve Resolution 5.3 Generic Framework 5.3.1 Framework for Simultaneous Unsupervised Methods 5.3.1.1 Description of the Framework 5.3.1.2 Framework Applied to Simultaneous Unsupervised Data Analysis Methods 5.3.1.3 Framework of Common/Distinct Applied to Simultaneous Unsupervised Multiblock Data Analysis Methods 5.4 Conclusions and Recommendations 5.5 Open Issues chapnumcolor6 ASCA and Extensions 6.i General Introduction 6.ii Relations to the General Framework 6.1 ANOVA-Simultaneous Component Analysis 6.1.1 The ASCA Method 6.1.2 Validation of ASCA 6.1.2.1 Permutation Testing 6.1.2.2 Back-projection 6.1.2.3 Confidence Ellipsoids 6.1.3 The ASCA+ and LiMM-PCA Methods 6.2 Multilevel-SCA 6.3 Penalised-ASCA 6.4 Conclusions and Recommendations 6.5 Open Issues chapnumcolor7 Supervised Methods 7.i General Introduction 7.ii Relations to the General Framework 7.1 Multiblock Regression: General Perspectives 7.1.1 Model and Assumptions 7.1.2 Different Challenges and Aims 7.2 Multiblock PLS Regression 7.2.1 Standard Multiblock PLS Regression 7.2.2 MB-PLS Used for Classification 7.2.3 Sparse Multiblock PLS Regression (sMB-PLS) 7.3 The Family of SO-PLS Regression Methods (Sequential and Orthogonalised PLS Regression) 7.3.1 The SO-PLS Method 7.3.2 Order of Blocks 7.3.3 Interpretation Tools 7.3.4 Restricted PLS Components and their Application in SO-PLS 7.3.5 Validation and Component Selection 7.3.6 Relations to ANOVA 7.3.7 Extensions of SO-PLS to Handle Interactions Between Blocks 7.3.8 Further Applications of SO-PLS 7.3.9 Relations Between SO-PLS and ASCA 7.4 Parallel and Orthogonalised PLS (PO-PLS) Regression 7.5 Response Oriented Sequential Alternation 7.5.1 The ROSA Method 7.5.2 Validation 7.5.3 Interpretation 7.6 Conclusions and Recommendations 7.7 Open Issues Part III Methods for Complex Multiblock Structures chapnumcolor8 Complex Block Structures; with Focus on L-Shape Relations 8.i General Introduction 8.ii Relations to the General Framework 8.1 Analysis of L-shape Data: General Perspectives 8.2 Sequential Procedures for L-shape Data Based on PLS/PCR and ANOVA 8.2.1 Interpretation of X1, Quantitative X2-data, Horizontal Axis First 8.2.2 Interpretation of X1, Categorical X2-data, Horizontal Axis First 8.2.3 Analysis of Segments/Clusters of X1 Data 8.3 The L-PLS Method for Joint Estimation of Blocks in L-shape Data 8.3.1 The Original L-PLS Method, Endo-L-PLS 8.3.2 Exo- Versus Endo-L-PLS 8.4 Modifications of the Original L-PLS Idea 8.4.1 Weighting Information from X3 and X1 in L-PLS Using a Parameter "α 8.4.2 Three-blocks Bifocal PLS 8.5 Alternative L-shape Data Analysis Methods 8.5.1 Principal Component Analysis with External Information 8.5.2 A Simple PCA Based Procedure for Using Unlabelled Data in Calibration 8.5.3 Multivariate Curve Resolution for Incomplete Data 8.5.4 An Alternative Approach in Consumer Science Based on Correlations Between X3 and X1 8.6 Domino PLS and More Complex Data Structures 8.7 Conclusions and Recommendations 8.8 Open Issues Part IV Alternative Methods for Unsupervised and Supervised Topologies chapnumcolor9 Alternative Unsupervised Methods 9.i General Introduction 9.ii Relationship to the General Framework 9.1 Shared Variable Mode 9.2 Shared Sample Mode 9.2.1 Only Common Variation 9.2.1.1 DIABLO 9.2.1.2 Generalised Coupled Tensor Factorisation 9.2.1.3 Representation Matrices 9.2.1.4 Extended PCA 9.2.2 Common, Local, and Distinct Variation 9.2.2.1 Generalised SVD 9.2.2.2 Structural Learning and Integrative Decomposition 9.2.2.3 Bayesian Inter-battery Factor Analysis 9.2.2.4 Group Factor Analysis 9.2.2.5 OnPLS 9.2.2.6 Generalised Association Study 9.2.2.7 Multi-Omics Factor Analysis 9.3 Two Shared Modes and Only Common Variation 9.3.1 Generalised Procrustes Analysis 9.3.2 Three-way Methods 9.4 Conclusions and Recommendations 9.4.1 Open Issues chapnumcolor10 Alternative Supervised Methods 10.i General Introduction 10.ii Relations to the General Framework 10.1 Model and Focus 10.2 Extension of PCovR 10.2.1 Sparse Multiblock Principal Covariates Regression, Sparse PCovR 10.2.2 Multiway Multiblock Covariates Regression 10.3 Multiblock Redundancy Analysis 10.3.1 Standard Multiblock Redundancy Analysis 10.3.2 Sparse Multiblock Redundancy Analysis 10.4 Miscellaneous Multiblock Regression Methods 10.4.1 Multiblock Variance Partitioning 10.4.2 Network Induced Supervised Learning 10.4.3 Common Dimensions for Multiblock Regression 10.5 Modifications and Extensions of the SO-PLS Method 10.5.1 Extensions of SO-PLS to Three-Way Data 10.5.2 Variable Selection for SO-PLS 10.5.3 More Complicated Error Structure for SO-PLS 10.5.4 SO-PLS Used for Path Modelling 10.6 Methods for Data Sets Split Along the Sample Mode, Multigroup Methods 10.6.1 Multigroup PLS Regression 10.6.2 Clustering of Observations in Multiblock Regression 10.6.3 Domain-Invariant PLS, DI-PLS 10.7 Conclusions and Recommendations 10.8 Open Issues Part V Software chapnumcolor11 Algorithms and Software 11.1 Multiblock Software 11.2 R package multiblock 11.3 Installing and Starting the Package 11.4 Data Handling 11.4.1 Read From File 11.4.2 Data Pre-processing 11.4.3 Re-coding Categorical Data 11.4.4 Data Structures for Multiblock Analysis 11.4.4.1 Create List of Blocks 11.4.4.2 Create data.frame of Blocks 11.5 Basic Methods 11.5.1 Prepare Data 11.5.2 Modelling 11.5.3 Common Output Elements Across Methods 11.5.4 Scores and Loadings 11.6 Unsupervised Methods 11.6.1 Formatting Data for Unsupervised Data Analysis 11.6.2 Method Interfaces 11.6.3 Shared Sample Mode Analyses 11.6.4 Shared Variable Mode 11.6.5 Common Output Elements Across Methods 11.6.6 Scores and Loadings 11.6.7 Plot From Imported Package 11.7 ANOVA Simultaneous Component Analysis 11.7.1 Formula Interface 11.7.2 Simulated Data 11.7.3 ASCA Modelling 11.7.4 ASCA Scores 11.7.5 ASCA Loadings 11.8 Supervised Methods 11.8.1 Formatting Data for Supervised Analyses 11.8.2 Multiblock Partial Least Squares 11.8.2.1 MB-PLS Modelling 11.8.2.2 MB-PLS Summaries and Plotting 11.8.3 Sparse Multiblock Partial Least Squares 11.8.3.1 Sparse MB-PLS Modelling 11.8.3.2 Sparse MB-PLS Plotting 11.8.4 Sequential and Orthogonalised Partial Least Squares 11.8.4.1 SO-PLS Modelling 11.8.4.2 Mge Plot 11.8.4.3 SO-PLS Loadings 11.8.4.4 SO-PLS Scores 11.8.4.5 SO-PLS Prediction 11.8.4.6 SO-PLS Validation 11.8.4.7 Principal Components of Predictions 11.8.4.8 CVANOVA 11.8.5 Parallel and Orthogonalised Partial Least Squares 11.8.5.1 PO-PLS Modelling 11.8.5.2 PO-PLS Scores and Loadings 11.8.6 Response Optimal Sequential Alternation 11.8.6.1 ROSA Modelling 11.8.6.2 ROSA Loadings 11.8.6.3 ROSA Scores 11.8.6.4 ROSA Prediction 11.8.6.5 ROSA Validation 11.8.6.6 ROSA Image Plots 11.8.7 Multiblock Redundancy Analysis 11.8.7.1 MB-RDA Modelling 11.8.7.2 MB-RDA Loadings and Scores 11.9 Complex Data Structures 11.9.1 L-PLS 11.9.1.1 Simulated L-shaped Data 11.9.1.2 Exo-L-PLS 11.9.1.3 Endo-L-PLS 11.9.1.4 L-PLS Cross-validation 11.9.2 SO-PLS-PM 11.9.2.1 Single SO-PLS-PM Model 11.9.2.2 Multiple Paths in an SO-PLS-PM Model 11.10 Software Packages 11.10.1 R Packages 11.10.2 MATLAB Toolboxes 11.10.3 Python 11.10.4 Commercial Software References Index EULA