Correspondence Analysis and Data Coding with

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.

Fionn Murtagh is a professor in the Department of Computer Science, Royal Holloway, University of London, UK

1 Introduction

1

(28)

1.1 Data Analysis

1

(2)

1.2 Notes on the History of Data Analysis

3

(6)

1.2.1 Biometry

4

(1)

1.2.2 Era Piscatoria

4

(1)

1.2.3 Psychometrics

5

(2)

1.2.4 Analysis of Proximities

7

(1)

1.2.5 Genesis of Correspondence Analysis

8

(1)

1.3 Correspondence Analysis or Principal Components Analysis

9

(8)

1.3.1 Similarities of These Two Algorithms

9

(1)

1.3.2 Introduction to Principal Components Analysis

10

(1)

1.3.3 An Illustrative Example

11

(2)

1.3.4 Principal Components Analysis of Globular Clusters

13

(1)

1.3.5 Correspondence Analysis of Globular Clusters

14

(3)

1.4 R Software for Correspondence Analysis and Clustering

17

(12)

1.4.1 Fuzzy or Piecewise Linear Coding

17

(1)

1.4.2 Utility for Plotting Axes

18

(1)

1.4.3 Correspondence Analysis Program

18

(2)

1.4.4 Running the Analysis and Displaying Results

20

(1)

1.4.5 Hierarchical Clustering

21

(6)

1.4.6 Handling Large Data Sets

27

(2)

2 Theory of Correspondence Analysis

29

(42)

2.1 Vectors and Projections

29

(3)

2.2 Factors

32

(6)

2.2.1 Review of Metric Spaces

32

(2)

2.2.2 Clouds of Points, Masses, and Inertia

34

(1)

2.2.3 Notation for Factors

35

(1)

2.2.4 Properties of Factors

36

(1)

2.2.5 Properties of Factors: Tensor Notation

36

(2)

2.3 Transform

38

(3)

2.3.1 Forward Transform

38

(1)

2.3.2 Inverse Transform

38

(1)

2.3.3 Decomposition of Inertia

38

(1)

2.3.4 Relative and Absolute Contributions

39

(1)

2.3.5 Reduction of Dimensionality

39

(1)

2.3.6 Interpretation of Results

39

(1)

2.3.7 Analysis of the Dual Spaces

40

(1)

2.3.8 Supplementary Elements

41

(1)

2.4 Algebraic Perspective

41

(5)

2.4.1 Processing

41

(1)

2.4.2 Motivation

41

(1)

2.4.3 Operations

42

(1)

2.4.4 Axes and Factors

43

(1)

2.4.5 Multiple Correspondence Analysis

44

(2)

2.4.6 Summary of Correspondence Analysis Properties

46

(1)

2.5 Clustering

46

(11)

2.5.1 Hierarchical Agglomerative Clustering

46

(3)

2.5.2 Minimum Variance Agglomerative Criterion

49

(1)

2.5.3 Lance-Williams Dissimilarity Update Formula

49

(3)

2.5.4 Reciprocal Nearest Neighbors and Reducibility

52

(1)

2.5.5 Nearest-Neighbor Chain Algorithm

53

(1)

2.5.6 Minimum Variance Method in Perspective

54

(1)

2.5.7 Minimum Variance Method: Mathematical Properties

55

(2)

2.5.8 Simultaneous Analysis of Factors and Clusters

57

(1)

2.6 Questions

57

(1)

2.7 Further R Software for Correspondence Analysis

58

(11)

2.7.1 Supplementary Elements

58

(3)

2.7.2 FACOR: Interpretation of Factors and Clusters

61

(3)

2.7.3 VACOR: Interpretation of Variables and Clusters

64

(3)

2.7.4 Hierarchical Clustering in C, Callable from R

67

(2)

2.8 Summary

69

(2)

3 Input Data Coding

71

(40)

3.1 Introduction

71

(6)

3.1.1 The Fundamental Role of Coding

72

(1)

3.1.2 "Semantic Embedding"

73

(2)

3.1.3 Input Data Encodings

75

(1)

3.1.4 Input Data Analyzed Without Transformation

76

(1)

3.2 From Doubling to Fuzzy Coding and Beyond

77

(15)

3.2.1 Doubling

77

(2)

3.2.2 Complete Disjunctive Form

79

(1)

3.2.3 Fuzzy, Piecewise Linear or Barycentric Coding

80

(5)

3.2.4 General Discussion of Data Coding

85

(1)

3.2.5 From Fuzzy Coding to Possibility Theory

86

(6)

3.3 Assessment of Coding Methods

92

(6)

3.4 The Personal Equation and Double Resealing

98

(1)

3.5 Case Study: DNA Exon and Intron Junction Discrimination

99

(4)

3.6 Conclusions on Coding

103

(1)

3.7 Java Software

104

(7)

3.7.1 Running the Java Software

105

(6)

4 Examples and Case Studies

111

(50)

4.1 Introduction to Analysis of Size and Shape

111

(7)

4.1.1 Morphometry of Prehistoric Thai Goblets

111

(5)

4.1.2 Software Used

116

(2)

4.2 Comparison of Prehistoric and Modern Groups of Canids

118

(17)

4.2.1 Software Used

130

(5)

4.3 Craniometric Data from Ancient Egyptian Tombs

135

(5)

4.3.1 Software Used

139

(1)

4.4 Time-Varying Data Analysis: Examples from Economics

140

(8)

4.4.1 Imports and Exports of Phosphates

140

(5)

4.4.2 Services and Other Sectors in Economic Growth

145

(3)

4.5 Financial Modeling and Forecasting

148

(13)

4.5.1 Introduction

148

(1)

4.5.2 Brownian Motion

149

(1)

4.5.3 Granularity of Coding

150

(8)

4.5.4 Fingerprinting the Price Movements

158

(2)

4.5.5 Conclusions

160

(1)

5 Content Analysis of Text

161

(60)

5.1 Introduction

161

(3)

5.1.1 Accessing Content

161

(1)

5.1.2 The Work of J.-P. Benzécri

161

(2)

5.1.3 Objectives and Some Findings

163

(1)

5.1.4 Outline of the Chapter

164

(1)

5.2 Correspondence Analysis

164

(2)

5.2.1 Analyzing Data

164

(1)

5.2.2 Textual Data Preprocessing

165

(1)

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

166

(6)

5.3.1 Tool Words versus Full Words

166

(1)

5.3.2 Tool Words in Various Languages

167

(1)

5.3.3 Tool Words versus Metalanguages or Ontologies

168

(2)

5.3.4 Refinement of Tool Words

170

(1)

5.3.5 Tool Words in Survey Analysis

171

(1)

5.3.6 The Text Aggregates Studied

172

(1)

5.4 Towards Content Analysis

172

(8)

5.4.1 Intra-Document Analysis of Content

172

(2)

5.4.2 Comparative Semantics: Diagnosis versus Prognosis

174

(1)

5.4.3 Semantics of Connotation and Denotation

175

(1)

5.4.4 Discipline-Based Theme Analysis

175

(1)

5.4.5 Mapping Cognitive Processes

176

(1)

5.4.6 History and Evolution of Ideas

176

(1)

5.4.7 Doctrinal Content and Stylistic Expression

177

(2)

5.4.8 Interpreting Antinomies Through Cluster Branchings

179

(1)

5.4.9 The Hypotheses of Plato on The One

179

(1)

5.5 Textual and Documentary Typology

180

(6)

5.5.1 Assessing Authorship

180

(4)

5.5.2 Further Studies with Tool Words and Miscellaneous Approaches

184

(2)

5.6 Conclusion: Methodology in Free Text Analysis

186

(2)

5.7 Software for Text Processing

188

(1)

5.8 Introduction to the Text Analysis Case Studies

189

(1)

5.9 Eight Hypotheses of Parmenides Regarding the One

190

(7)

5.10 Comparative Study of Reality, Fable and Dream

197

(10)

5.10.1 Aviation Accidents

198

(1)

5.10.2 Dream Reports

198

(1)

5.10.3 Grimm Fairy Tales

199

(1)

5.10.4 Three Jane Austen Novels

199

(1)

5.10.5 Set of Texts

200

(1)

5.10.6 Tool Words

200

(1)

5.10.7 Domain Content Words

201

(4)

5.10.8 Analysis of Domains through Content-Oriented Words

205

(2)

5.11 Single Document Analysis

207

(13)

5.11.1 The Data: Aristotle's Categories

207

(3)

5.11.2 Structure of Presentation

210

(4)

5.11.3 Evolution of Presentation

214

(6)

5.12 Conclusion on Text Analysis Case Studies

220

(1)

6 Concluding Remarks

221

(2)

References

223

(6)

Index

229

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Correspondence Analysis and Data Coding with JAVA and R

Summary

Author Biography

Table of Contents

Supplemental Materials