Correspondence Analysis and Data Coding with Java and R / Edition 1

by Fionn Murtagh

Overview

Developed by Jean-Paul Benzérci more than 30 years ago, correspondence analysis as a framework for analyzing data quickly found widespread popularity in Europe. The topicality and importance of correspondence analysis continue, and with the tremendous computing power now available and new fields of application emerging, its significance is greater than ever.

Correspondence Analysis and Data Coding with Java and R clearly demonstrates why this technique remains important and in the eyes of many, unsurpassed as an analysis framework. After presenting some historical background, the author presents a theoretical overview of the mathematics and underlying algorithms of correspondence analysis and hierarchical clustering. The focus then shifts to data coding, with a survey of the widely varied possibilities correspondence analysis offers and introduction of the Java software for correspondence analysis, clustering, and interpretation tools. A chapter of case studies follows, wherein the author explores applications to areas such as shape analysis and time-evolving data. The final chapter reviews the wealth of studies on textual content as well as textual form, carried out by Benzécri and his research lab. These discussions show the importance of correspondence analysis to artificial intelligence as well as to stylometry and other fields.

This book not only shows why correspondence analysis is important, but with a clear presentation replete with advice and guidance, also shows how to put this technique into practice. Downloadable software and data sets allow quick, hands-on exploration of innovative correspondence analysis applications.

Product Details

ISBN-13:	9780367392734
Publisher:	Taylor & Francis
Publication date:	09/05/2019
Series:	Chapman & Hall/CRC Computer Science & Data Analysis
Pages:	256
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Murtagh, Fionn

Table of Contents

1 Introduction 1

1.1 Data Analysis 1

1.2 Notes on the History of Data Analysis 3

1.2.1 Biometry 4

1.2.2 Era Piscatoria 4

1.2.3 Psychometrics 5

1.2.4 Analysis of Proximities 7

1.2.5 Genesis of Correspondence Analysis 8

1.3 Correspondence Analysis or Principal Components Analysis 9

1.3.1 Similarities of These Two Algorithms 9

1.3.2 Introduction to Principal Components Analysis 10

1.3.3 An Illustrative Example 11

1.3.4 Principal Components Analysis of Globular Clusters 13

1.3.5 Correspondence Analysis of Globular Clusters 14

1.4 R Software for Correspondence Analysis and Clustering 17

1.4.1 Fuzzy or Piecewise Linear Coding 17

1.4.2 Utility for Plotting Axes 18

1.4.3 Correspondence Analysis Program 18

1.4.4 Running the Analysis and Displaying Results 20

1.4.5 Hierarchical Clustering 21

1.4.6 Handling Large Data Sets 27

2 Theory of Correspondence Analysis 29

2.1 Vectors and Projections 29

2.2 Factors 32

2.2.1 Review of Metric Spaces 32

2.2.2 Clouds of Points, Masses, and Inertia 34

2.2.3 Notation for Factors 35

2.2.4 Properties of Factors 36

2.2.5 Properties of Factors: Tensor Notation 36

2.3 Transform 38

2.3.1 Forward Transform 38

2.3.2 Inverse Transform 38

2.3.3 Decomposition of Inertia 38

2.3.4 Relative and Absolute Contributions 39

2.3.5 Reduction of Dimensionality 39

2.3.6 Interpretation of Results 39

2.3.7 Analysis of the Dual Spaces 40

2.3.8 Supplementary Elements 41

2.4 Algebraic Perspective 41

2.4.1 Processing 41

2.4.2 Motivation 41

2.4.3 Operations 42

2.4.4 Axes and Factors 43

2.4.5 Multiple Correspondence Analysis 44

2.4.6 Summary of Correspondence Analysis Properties 46

2.5 Clustering 46

2.5.1 Hierarchical Agglomerative Clustering 46

2.5.2 Minimum Variance Agglomerative Criterion 49

2.5.3 Lance-Williams Dissimilarity Update Formula 49

2.5.4 Reciprocal Nearest Neighbors and Reductibility 52

2.5.5 Nearest-Neighbor Chain Algorithm 53

2.5.6 Minimum Variance Method in Perspective 54

2.5.7 Minimum Variance Method: Mathematical Properties 55

2.5.8 Simultaneous Analysis of Factors and Clusters 57

2.6 Questions 57

2.7 Further R Software for Correspondence Analysis 58

2.7.1 Supplementary Elements 58

2.7.2 FACOR: Interpretation of Factors and Clusters 61

2.7.3 VACOR: Interpretation of Variables and Clusters 64

2.7.4 Hierarchical Clustering in C, Callable from R 67

2.8 Summary 69

3 Input Data Coding 71

3.1 Introduction 71

3.1.1 The Fundamental Role of Coding 72

3.1.2 "Semantic Embedding" 73

3.1.3 Input Data Encodings 75

3.1.4 Input Data Analyzed Without Transformation 76

3.2 From Doubling to Fuzzy Coding and Beyond 77

3.2.1 Doubling 77

3.2.2 Complete Disjunctive Form 79

3.2.3 Fuzzy, Piecewise Linear or Barycentric Coding 80

3.2.4 General Discussion of Data Coding 85

3.2.5 From Fuzzy Coding to Possibility Theory 86

3.3 Assessment of Coding Methods 92

3.4 The Personal Equation and Double Rescaling 98

3.5 Case Study: DNA Exon and Intron Junction Discrimination 99

3.6 Conclusions on Coding 103

3.7 Java Software 104

3.7.1 Running the Java Software 105

4 Examples and Case Studies 111

4.1 Introduction to Analysis of Size and Shape 111

4.1.1 Morphometry of Prehistoric Thai Goblets 111

4.1.2 Software Used 116

4.2 Comparison of Prehistoric and Modern Groups of Canids 118

4.2.1 Software Used 130

4.3 Craniometric Data from Ancient Egyptian Tombs 135

4.3.1 Software Used 139

4.4 Time-Varying Data Analysis: Examples from Economics 140

4.4.1 Imports and Exports of Phosphates 140

4.4.2 Services and Other Sectors in Economic Growth 145

4.5 Financial Modeling and Forecasting 148

4.5.1 Introduction 148

4.5.2 Brownian Motion 149

4.5.3 Granularity of Coding 150

4.5.4 Fingerprinting the Price Movements 158

4.5.5 Conclusions 160

5 Content Analysis of Text 161

5.1 Introduction 161

5.1.1 Accessing Content 161

5.1.2 The Work of J.-P. Benzécri 161

5.1.3 Objectives and Some Findings 163

5.1.4 Outline of the Chapter 164

5.2 Correspondence Analysis 164

5.2.1 Analyzing Data 164

5.2.2 Textual Data Preprocessing 165

5.3 Tool Words: Between Analysis of Form and Analysis of Content 166

5.3.1 Tool Words versus Full Words 166

5.3.2 Tool Words in Various Languages 167

5.3.3 Tool Words versus Metalanguages or Ontologies 168

5.3.4 Refinement of Tool Words 170

5.3.5 Tool Words in Survey Analysis 171

5.3.6 The Text Aggregates Studied 172

5.4 Towards Content Analysis 172

5.4.1 Intra-Document Analysis of Content 172

5.4.2 Comparative Semantics: Diagnosis versus Prognosis 174

5.4.3 Semantics of Connotation and Denotation 175

5.4.4 Discipline-Based Theme Analysis 175

5.4.5 Mapping Cognitive Processes 176

5.4.6 History and Evolution of Ideas 176

5.4.7 Doctrinal Content and Stylistic Expression 177

5.4.8 Interpreting Antinomies Through Cluster Branchings 179

5.4.9 The Hypotheses of Plato on The One 179

5.5 Textual and Documentary Typology 180

5.5.1 Assessing Authorship 180

5.5.2 Further Studies with Tool Words and Miscellaneous Approaches 184

5.6 Conclusion: Methodology in Free Text Analysis 186

5.7 Software for Text Processing 188

5.8 Introduction to the Text Analysis Case Studies 189

5.9 Eight Hypotheses of Parmenides Regarding the One 190

5.10 Comparative Study of Reality, Fable and Dream 197

5.10.1 Aviation Accidents 198

5.10.2 Dream Reports 198

5.10.3 Grimm Fairy Tales 199

5.10.4 Three Jane Austen Novels 199

5.10.5 Set of Texts 200

5.10.6 Tool Words 200

5.10.7 Domain Content Words 201

5.10.8 Analysis of Domains through Content-Oriented Words 205

5.11 Single Document Analysis 207

5.11.1 The Data: Aristotle's Categories 207

5.11.2 Structure of Presentation 210

5.11.3 Evolution of Presentation 214

5.12 Conclusion on Text Analysis Case Studies 220

6 Concluding Remarks 221

References 223

Index 229

Editorial Reviews

"Detailed examples of its application to data are drawn from an astonishingly wide variety of fields; astronomy, financial modeling and forecasting, comparisons of prehistoric and modern groups of dogs, ancient goblets and measurements on ancient Egyptian skulls. …All in all this book can be recommended as a succinct reference on all aspects of correspondence analysis, theoretical, computational, and practical."
-J.M. Juritz, Short Book Reviews of the ISI

"This book plays an important role in bridging the gap between learning a method and actually implementing it . . . could serve as either a text for an introductory course on CA or as a supplementary text to a more advanced graduate course in CA or multivariate techniques in general . . . The author should be commended for bringing these issues to the forefront."

– Douglas Steinley, University of Missouri-Columbia, in Psychometrika, March 2007, Vol. 74, No. 1

From the Publisher