Contents

1 Introduction 1.1 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Notes on the History of Data Analysis . . . . . . . . . . . . 1.2.1 Biometry . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Era Piscatoria . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Psychometrics . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Analysis of Proximities . . . . . . . . . . . . . . . . . 1.2.5 Genesis of Correspondence Analysis . . . . . . . . . 1.3 Correspondence Analysis or Principal Components Analysis 1.3.1 Similarities of These Two Algorithms . . . . . . . . . 1.3.2 Introduction to Principal Components Analysis . . . 1.3.3 An Illustrative Example . . . . . . . . . . . . . . . . 1.3.4 Principal Components Analysis of Globular Clusters 1.3.5 Correspondence Analysis of Globular Clusters . . . . 1.4 R Software for Correspondence Analysis and Clustering . . 1.4.1 Fuzzy or Piecewise Linear Coding . . . . . . . . . . . 1.4.2 Utility for Plotting Axes . . . . . . . . . . . . . . . . 1.4.3 Correspondence Analysis Program . . . . . . . . . . 1.4.4 Running the Analysis and Displaying Results . . . . 1.4.5 Hierarchical Clustering . . . . . . . . . . . . . . . . . 1.4.6 Handling Large Data Sets . . . . . . . . . . . . . . .

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1 1 3 4 4 5 7 8 9 9 10 11 13 14 17 17 18 18 20 21 27

2 Theory of Correspondence Analysis 2.1 Vectors and Projections . . . . . . . . . . . . 2.2 Factors . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Review of Metric Spaces . . . . . . . . 2.2.2 Clouds of Points, Masses, and Inertia . 2.2.3 Notation for Factors . . . . . . . . . . 2.2.4 Properties of Factors . . . . . . . . . . 2.2.5 Properties of Factors: Tensor Notation 2.3 Transform . . . . . . . . . . . . . . . . . . . . 2.3.1 Forward Transform . . . . . . . . . . . 2.3.2 Inverse Transform . . . . . . . . . . . 2.3.3 Decomposition of Inertia . . . . . . . . 2.3.4 Relative and Absolute Contributions . 2.3.5 Reduction of Dimensionality . . . . . .

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29 29 32 32 34 35 36 36 38 38 38 38 39 39

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xv

xvi

Correspondence Analysis and Data Coding

2.4

2.5

2.6 2.7

2.8

2.3.6 Interpretation of Results . . . . . . . . . . . . . . . . . 2.3.7 Analysis of the Dual Spaces . . . . . . . . . . . . . . . 2.3.8 Supplementary Elements . . . . . . . . . . . . . . . . . Algebraic Perspective . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Processing . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Operations . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4 Axes and Factors . . . . . . . . . . . . . . . . . . . . . 2.4.5 Multiple Correspondence Analysis . . . . . . . . . . . 2.4.6 Summary of Correspondence Analysis Properties . . . Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Hierarchical Agglomerative Clustering . . . . . . . . . 2.5.2 Minimum Variance Agglomerative Criterion . . . . . . 2.5.3 Lance-Williams Dissimilarity Update Formula . . . . . 2.5.4 Reciprocal Nearest Neighbors and Reducibility . . . . 2.5.5 Nearest-Neighbor Chain Algorithm . . . . . . . . . . . 2.5.6 Minimum Variance Method in Perspective . . . . . . . 2.5.7 Minimum Variance Method: Mathematical Properties 2.5.8 Simultaneous Analysis of Factors and Clusters . . . . Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further R Software for Correspondence Analysis . . . . . . . 2.7.1 Supplementary Elements . . . . . . . . . . . . . . . . . 2.7.2 FACOR: Interpretation of Factors and Clusters . . . . 2.7.3 VACOR: Interpretation of Variables and Clusters . . . 2.7.4 Hierarchical Clustering in C, Callable from R . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Input Data Coding 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 The Fundamental Role of Coding . . . . . . . . . . . 3.1.2 “Semantic Embedding” . . . . . . . . . . . . . . . . 3.1.3 Input Data Encodings . . . . . . . . . . . . . . . . . 3.1.4 Input Data Analyzed Without Transformation . . . 3.2 From Doubling to Fuzzy Coding and Beyond . . . . . . . . 3.2.1 Doubling . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Complete Disjunctive Form . . . . . . . . . . . . . . 3.2.3 Fuzzy, Piecewise Linear or Barycentric Coding . . . 3.2.4 General Discussion of Data Coding . . . . . . . . . . 3.2.5 From Fuzzy Coding to Possibility Theory . . . . . . 3.3 Assessment of Coding Methods . . . . . . . . . . . . . . . . 3.4 The Personal Equation and Double Rescaling . . . . . . . . 3.5 Case Study: DNA Exon and Intron Junction Discrimination 3.6 Conclusions on Coding . . . . . . . . . . . . . . . . . . . . . 3.7 Java Software . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Running the Java Software . . . . . . . . . . . . . .

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39 40 41 41 41 41 42 43 44 46 46 46 49 49 52 53 54 55 57 57 58 58 61 64 67 69 71 71 72 73 75 76 77 77 79 80 85 86 92 98 99 103 104 105

Table of Contents 4 Examples and Case Studies 4.1 Introduction to Analysis of Size and Shape . . . . . . . 4.1.1 Morphometry of Prehistoric Thai Goblets . . . . 4.1.2 Software Used . . . . . . . . . . . . . . . . . . . . 4.2 Comparison of Prehistoric and Modern Groups of Canids 4.2.1 Software Used . . . . . . . . . . . . . . . . . . . . 4.3 Craniometric Data from Ancient Egyptian Tombs . . . . 4.3.1 Software Used . . . . . . . . . . . . . . . . . . . . 4.4 Time-Varying Data Analysis: Examples from Economics 4.4.1 Imports and Exports of Phosphates . . . . . . . 4.4.2 Services and Other Sectors in Economic Growth 4.5 Financial Modeling and Forecasting . . . . . . . . . . . . 4.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . 4.5.2 Brownian Motion . . . . . . . . . . . . . . . . . . 4.5.3 Granularity of Coding . . . . . . . . . . . . . . . 4.5.4 Fingerprinting the Price Movements . . . . . . . 4.5.5 Conclusions . . . . . . . . . . . . . . . . . . . . .

xvii 111 . . . 111 . . . 111 . . . 116 . . 118 . . . 130 . . . 135 . . . 139 . . . 140 . . . 140 . . . 145 . . . 148 . . . 148 . . . 149 . . . 150 . . . 158 . . . 160

5 Content Analysis of Text 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Accessing Content . . . . . . . . . . . . . . . . . . . 5.1.2 The Work of J.-P. Benz´ecri . . . . . . . . . . . . . . 5.1.3 Objectives and Some Findings . . . . . . . . . . . . 5.1.4 Outline of the Chapter . . . . . . . . . . . . . . . . . 5.2 Correspondence Analysis . . . . . . . . . . . . . . . . . . . . 5.2.1 Analyzing Data . . . . . . . . . . . . . . . . . . . . . 5.2.2 Textual Data Preprocessing . . . . . . . . . . . . . . 5.3 Tool Words: Between Analysis of Form and Analysis of Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Tool Words versus Full Words . . . . . . . . . . . . . 5.3.2 Tool Words in Various Languages . . . . . . . . . . . 5.3.3 Tool Words versus Metalanguages or Ontologies . . . 5.3.4 Refinement of Tool Words . . . . . . . . . . . . . . . 5.3.5 Tool Words in Survey Analysis . . . . . . . . . . . . 5.3.6 The Text Aggregates Studied . . . . . . . . . . . . . 5.4 Towards Content Analysis . . . . . . . . . . . . . . . . . . . 5.4.1 Intra-Document Analysis of Content . . . . . . . . . 5.4.2 Comparative Semantics: Diagnosis versus Prognosis 5.4.3 Semantics of Connotation and Denotation . . . . . . 5.4.4 Discipline-Based Theme Analysis . . . . . . . . . . . 5.4.5 Mapping Cognitive Processes . . . . . . . . . . . . . 5.4.6 History and Evolution of Ideas . . . . . . . . . . . . 5.4.7 Doctrinal Content and Stylistic Expression . . . . . 5.4.8 Interpreting Antinomies Through Cluster Branchings 5.4.9 The Hypotheses of Plato on The One . . . . . . . .

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161 161 161 161 163 164 164 164 165

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166 166 167 168 170 171 172 172 172 174 175 175 176 176 177 179 179

xviii 5.5

Correspondence Analysis and Data Coding

Textual and Documentary Typology . . . . . . . . . . . . . . 5.5.1 Assessing Authorship . . . . . . . . . . . . . . . . . . . 5.5.2 Further Studies with Tool Words and Miscellaneous Approaches . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Conclusion: Methodology in Free Text Analysis . . . . . . . . 5.7 Software for Text Processing . . . . . . . . . . . . . . . . . . . 5.8 Introduction to the Text Analysis Case Studies . . . . . . . . 5.9 Eight Hypotheses of Parmenides Regarding the One . . . . . 5.10 Comparative Study of Reality, Fable and Dream . . . . . . . 5.10.1 Aviation Accidents . . . . . . . . . . . . . . . . . . . . 5.10.2 Dream Reports . . . . . . . . . . . . . . . . . . . . . . 5.10.3 Grimm Fairy Tales . . . . . . . . . . . . . . . . . . . . 5.10.4 Three Jane Austen Novels . . . . . . . . . . . . . . . . 5.10.5 Set of Texts . . . . . . . . . . . . . . . . . . . . . . . . 5.10.6 Tool Words . . . . . . . . . . . . . . . . . . . . . . . . 5.10.7 Domain Content Words . . . . . . . . . . . . . . . . . 5.10.8 Analysis of Domains through Content-Oriented Words 5.11 Single Document Analysis . . . . . . . . . . . . . . . . . . . . 5.11.1 The Data: Aristotle’s Categories . . . . . . . . . . . . 5.11.2 Structure of Presentation . . . . . . . . . . . . . . . . 5.11.3 Evolution of Presentation . . . . . . . . . . . . . . . . 5.12 Conclusion on Text Analysis Case Studies . . . . . . . . . . .

180 180 184 186 188 189 190 197 198 198 199 199 200 200 201 205 207 207 210 214 220

6 Concluding Remarks

221

References

223

Index

229

Contents - multiresolutions.com

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.
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