Multiblock Data Fusion in Statistics and Machine Learning. Tormod Næs

      

Multiblock Data Fusion in Statistics and Machine Learning

      Applications in the Natural and Life Sciences

       Age K. Smilde

      Swammerdam Institute for Life Sciences, University of Amsterdam,

      Amsterdam, NL and

      Simula Metropolitan Center for Digital Engineering, Oslo, NO

       Tormod Næs

      Nofima

       Ås, NO

       Kristian Hovde Liland

      Norwegian University of Life Sciences

       Ås, NO

This edition first published 2022

      © 2022 John Wiley & Sons Ltd

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      A catalogue record for this book is available from the Library of Congress

      Hardback ISBN: 9781119600961; ePDF ISBN: 9781119600985; epub ISBN: 9781119600992;

      Obook ISBN: 9781119600978

      Cover image: © Professor Age K. Smilde

      Cover design by Wiley

      Set in 10/12pt WarnockPro-Regular by Integra Software Services Pvt. Ltd, Pondicherry, India

Contents

      1  Cover

      2  Title page

      3  Copyright

      4  Foreword

      5  Preface

      6  List of Figures

      7  List of Tables

      8 Part I Introductory Concepts and Theory1 Introduction1.1 Scope of the Book1.2 Potential Audience1.3 Types of Data and Analyses1.3.1 Supervised and Unsupervised Analyses1.3.2 High-, Mid- and Low-level Fusion1.3.3 Dimension Reduction1.3.4 Indirect Versus Direct Data1.3.5 Heterogeneous Fusion1.4 Examples1.4.1 Metabolomics1.4.2 Genomics1.4.3 Systems Biology1.4.4 Chemistry1.4.5 Sensory Science1.5 Goals of Analyses1.6 Some History1.7 Fundamental Choices1.8 Common and Distinct Components1.9 Overview and Links1.10 Notation and Terminology1.11 Abbreviations2 Basic Theory and Concepts2.i General Introduction2.1 Component Models2.1.1 General Idea of Component Models2.1.2 Principal Component Analysis2.1.3 Sparse PCA2.1.4 Principal Component Regression2.1.5 Partial Least Squares2.1.6 Sparse PLS2.1.7 Principal Covariates Regression2.1.8 Redundancy Analysis2.1.9 Comparing PLS, PCovR and RDA2.1.10 Generalised Canonical Correlation Analysis2.1.11 Simultaneous Component Analysis2.2 Properties of Data2.2.1 Data Theory2.2.2 Scale-types2.3 Estimation Methods2.3.1 Least-squares Estimation2.3.2 Maximum-likelihood Estimation2.3.3 Eigenvalue Decomposition-based Methods2.3.4 Covariance or Correlation-based Estimation Methods2.3.5 Sequential Versus Simultaneous Methods2.3.6 Homogeneous Versus Heterogeneous Fusion2.4 Within- and Between-block Variation2.4.1 Definition and Example2.4.2 MAXBET Solution2.4.3 MAXNEAR Solution2.4.4 PLS2 Solution2.4.5 CCA Solution2.4.6 Comparing the Solutions2.4.7 PLS, RDA and CCA Revisited2.5 Framework for Common and Distinct Components2.6 Preprocessing2.7 Validation2.7.1 Outliers2.7.1.1 Residuals2.7.1.2 Leverage2.7.2 Model Fit2.7.3 Bias-variance Trade-off2.7.4 Test Set Validation2.7.5 Cross-validation2.7.6 Permutation Testing2.7.7 Jackknife and Bootstrap2.7.8 Hyper-parameters and Penalties2.8 Appendix3 Structure of Multiblock Data3.i General Introduction3.1 Taxonomy3.2 Skeleton of a Multiblock Data Set3.2.1 Shared Sample Mode3.2.2 Shared Variable Mode3.2.3 Shared Variable or Sample Mode3.2.4 Shared Variable and Sample Mode3.3 Topology of a Multiblock Data Set3.3.1 Unsupervised Analysis3.3.2 Supervised Analysis3.4 Linking Structures3.4.1 Linking Structure for Unsupervised Analysis3.4.2 Linking Structures