Analysis of symbolic data : exploratory methods for extracting statistical information from complex data

목차 (Table of Contents)

• CONTENTS
• Preface of the Scientific Editors = ⅴ
• Preface of the Project Managers = ⅷ
• 1. Symbolic Data Analysis and the SODAS Project : Purpose, History, Perspective / E. Diday = 1
• 1.1 Introduction = 1
• 1.2 Symbolic Data Tables and Symbolic Objects = 2
• 1.2.1 The Input of SDA : Symbolic Data Tables, Rules and Taxonomies = 2
• 1.2.2 Sources of Symbolic Data = 3
• 1.2.3 Symbolic Objects = 5
• 1.3 Tools and Operations for Symbolic Objects = 8
• 1.4 History and Evolution of SDA = 11
• 1.5 The Content of the SODAS Project = 14
• 1.5.1 SDA Methods Realized in SODAS = 14
• 1.5.2 An Illustrative Example = 15
• 1.5.3 Overview on the SODAS Software = 17
• 1.5.4 Examples for the SODAS Strategy in Applications = 17
• 1.6 Philosophical Background : Concepts and Symbolic Objects = 18
• 1.6.1 First－ and Second－Order Individuals = 18
• 1.6.2 Intent and Extent, the Two Kinds of Concepts = 19
• 1.6.3 Concepts : The Four Traditions and ‘Symbolic Objects’ = 20
• 1.7 Advantages of Using Symbolic Data Analysis = 21
• 1.8 The Future Development of SODAS = 22
• 2. The Classical Data Situation / H. H. Bock = 24
• 2.1 Introduction = 24
• 2.2 Variables as Input Data = 24
• 2.3 Quantitative Variables = 25
• 2.4 Qualitative Variables = 26
• 2.4.1 Nominal Variables = 26
• 2.4.2 Ordinal Variables and Generalized Ordinal Variables = 27
• 2.5 Data Vectors and the Data Matrix = 31
• 2.6 Dependent Variables = 32
• 2.6.1 Logical Dependence = 33
• 2.6.2 Hierarchical Dependence （Mother－Daughter） = 34
• 2.6.3 Stochastic Dependence = 36
• 2.7 Missing Values = 37
• 3. Symbolic Data / H. H. Bock = 39
• 3.1 Three Introductory Examples = 39
• 3.2 Multi－Valued and Interval Variables = 42
• 3.3 Modal Variables = 45
• 3.4 A Synthesis of Symbolic Data Types = 49
• 3.5 The Symbolic Data Array = 49
• 4. Symbolic Objects / H. H. Bock ; E. Diday = 54
• 4.1 Introduction and Examples = 54
• 4.2 Relations and Descriptions = 60
• 4.2.1 Relations = 61
• 4.2.2 Descriptions, Description Vectors and Description Sets = 62
• 4.2.3 Product Relation = 63
• 4.3 Events and Assertion Objects = 64
• 4.4 Boolean Symbolic Objects as Triples = 69
• 4.5 Modal Symbolic Objects = 75
• 5. Generation of Symbolic Objects from Relational Databases / V. St$$\acute e$$phan ; G. H$$\acute e$$brail ; Y. Lechevallier = 78
• 5.1 Introduction to Relational Databases = 78
• 5.2 Principles of Symbolic Object Acquisition from Relational Databases = 80
• 5.3 Interaction with the Database = 85
• 5.3.1 Interpretation of SQL Queries = 85
• 5.3.2 Sampling Individuals = 91
• 5.3.3 Dependent Variables and Missing Values = 92
• 5.4 A Generalization Operator = 93
• 5.4.1 Basic Generalization Operator = 93
• 5.4.2 Problem of Over－Generalization = 95
• 5.4.3 A Quality Criterion to Evaluate a Generalized Description = 97
• 5.4.4 Coding by Testing for a Uniform Distribution Among Intervals = 98
• 5.4.5 A Reduction Algorithm = 100
• 5.4.6 A Numerical Example = 102
• 5.5 Further Operations on Generated Assertions = 103
• 5.5.1 Joining Two Arrays of Assertions = 103
• 5.5.2 Validation of Generated Assertions = 105
• 6. Descriptive Statistics for Symbolic Data / P. Bertrand ; F. Goupil = 106
• 6.1 Descriptive Statistics for a Classical Numerical Variable = 106
• 6.2 The Observed Symbolic Data Set = 108
• 6.2.1 The Data Table = 109
• 6.2.2 Logical Dependencies = 110
• 6.2.3 The Virtual Extension of a Description Vector = 111
• 6.3 The Case of Multi－Valued Variables = 112
• 6.3.1 Frequency Distribution for a Categorical or Quantitative Multi－Valued Variable = 113
• 6.3.2 Summary Measures for a Numerical Multi－Valued Variable = 117
• 6.4 The Case of an Interval－Valued Variable = 119
• 7. Visualizing and Editing Symbolic Objects / M. Norihomme－Fraiture ; M. Rouard = 125
• 7.1 The Zoom Star Representation = 125
• 7.1.1 Existing Solutions = 125
• 7.1.2 Our Graphical Representation = 126
• 7.1.3 Use of Zoom Star = 130
• 7.1.4 Conclusion = 136
• 7.2 Editing Symbolic Objects = 136
• 7.2.1 Modification of an Existing Symbolic Object = 137
• 7.2.2 Modification of Labels = 138
• 8. Similarity and Dissimilarity = 139
• 8.1 Classical Resemblance Measures / F. Esposito ; D. Malerba ; V. Tamma ; H. H. Bock = 139
• 8.1.1 Resemblance Measures = 140
• 8.1.2 Dissimilarity and Distance : Special Cases = 142
• 8.1.3 Distance Measures from a Classical Data Matrix = 145
• 8.1.4 Similarity Measures from a Categorical Data Matrix = 148
• 8.2 Dissimilarity Measures for Probability Distributions / H. H. Bock = 153
• 8.2.1 Divergence Measures : The General Case = 154
• 8.2.2 Divergence Measures : Special Cases = 155
• 8.2.3 The Affinity Coefficient （H. Bacelar－Nicolau） = 160
• 8.3 Dissimilarity Measures for Symbolic Objects / F. Esposito ; D. Malerba ; V. Tamma = 165
• 8.3.1 Gowda and Diday's Dissimilarity Measure = 166
• 8.3.2 The Approach by Ichino and Yaguchi = 170
• 8.3.3 Dissimilarity Measures of De Carvalho = 173
• 8.3.4 De Carvalho's Dissimilarity : Constrained Case = 177
• 8.3.5 The Dissimilarity Options in the SODAS Package = 183
• 8.4 Matching Symbolic Objects / F. Esposito ; D. Malerba ; F. A. Lisi = 186
• 8.4.1 Canonical Matching of Boolean Symbolic Objects = 186
• 8.4.2 Flexible Matching of Boolean Symbolic Objects = 188
• 8.4.3 An Application = 196
• 9. Symbolic Factor Analysis = 198
• 9.1 Classical Principal Component Analysis / H. H. Dock = 198
• 9.2 Symbolic Principal Component Analysis / A. Chouakria ; P. Cazes ; E. Diday = 200
• 9.2.1 Introduction : Interval Data = 200
• 9.2.2 The Purpose of the Method = 201
• 9.2.3 The VERTICES Method = 202
• 9.2.4 The CENTERS Method = 205
• 9.2.5 Representation by Rectangles = 206
• 9.2.6 Example of Oils and Fats = 207
• 9.2.7 Conclusions = 212
• 9.3 Factorial Discriminant Analysis on Symbolic Objects / N. C. Lauro ; R. Verde ; F. Palumbo = 212
• 9.3.1 Introduction = 212
• 9.3.2 A Reminder of Factorial Discriminant Analysis = 214
• 9.3.3 FDA on Symbolic Data = 219
• 9.3.4 Illustrative Application to a Data Set = 231
• 10. Discrimination : Assigning Symbolic Objects to Classes = 234
• 10.1 Classical Methods of Discrimination / J. P. Rasson, ; S. Lissoir = 234
• 10.1.1 Introduction = 234
• 10.1.2 The Problem = 234
• 10.1.3 The Decision Rule = 235
• 10.1.4 The Classical Probabilistic Framework = 236
• 10.1.5 Density Estimation = 238
• 10.2 Symbolic Kernel Discriminant Analysis / J. P. Rasson ; S. Lissoir = 240
• 10.2.1 Kernel Intensity Measures for Symbolic Data = 240
• 10.2.2 Determining the Prior Probabilities = 242
• 10.2.3 The Output Data = 243
• 10.3 Symbolic Discrimination Rules / E. P$$\acute e$$rinel ; Y. Lechevallier = 244
• 10.3.1 Introduction = 244
• 10.3.2 The Underlying Population and the Variables = 244
• 10.3.3 The Set of Binary Questions and the Construction of a New Data Table from Binary Variables = 247
• 10.3.4 The Recursive Partition Algorithm = 250
• 10.3.5 Detailed Description of the Different Steps = 253
• 10.3.6 Decisional Considerations = 259
• 10.3.7 Example = 261
• 10.4 Segmentation Trees for Stratified Data / M. C. Bravo Llatas ; J. M. Garc$$\acute i$$a－Santesmases = 266
• 10.4.1 Introduction = 266
• 10.4.2 Input and Output Data = 267
• 10.4.3 An Example : Distinction from Classical Decision Trees = 271
• 10.4.4 Main Steps of the Algorithm = 274
• 10.4.5 Detailed Description of the Algorithm = 277
• 10.4.6 Choices in the Algorithm for Classical Data = 280
• 10.4.7 Choices in the Algorithm for Probabilistic Data = 285
• 10.4.8 Symbolic Object Description of Strata = 289
• 10.4.9 The Example 10.4.3 Revisited = 291
• 10.4.10 Conclusion = 293
• 11. Clustering Methods for Symbolic Objects = 294
• 11.1 Clustering Problem, Clustering Methods for Classical Data / M. Chavent ; H. H. Bock = 294
• 11.2 Criterion－Based Divisive Clustering for Symbolic Data / M. Chavent = 299
• 11.2.1 The Symbolic Data Matrix = 299
• 11.2.2 Two Distance Measures = 301
• 11.2.3 Extension of the Within－Class Variance Criterion = 304
• 11.2.4 Bipartitioning a Cluster = 305
• 11.2.5 Choice of the Cluster to be Split. = 307
• 11.2.6 The Stopping Rule and the Output = 307
• 11.2.7 Example of a Classical Dataset = 308
• 11.2.8 Example of a Symbolic Data Set = 309
• 11.3 Hierarchical and Pyramidal Clustering with Complete Symbolic Objects / P. Brito = 312
• 11.3.1 Pyramidal Clustering = 312
• 11.3.2 Complete Symbolic Objects = 314
• 11.3.3 A Hierarchical－Pyramidal Clustering Algorithm for Symbolic Data = 315
• 11.3.4 Extension to More Complex Symbolic Data Types = 317
• 11.3.5 A Numerical Example = 322
• 11.4 Pyramidal Classification for Interval Data Using Galois Lattice Reduction / G. Polaillon = 324
• 11.4.1 Definition and Construction of Galois Lattices = 325
• 11.4.2 Reduction of a Galois Lattice into a Pyramid = 334
• 11.4.3 A Real－case Application = 337
• 12. Symbolic Approaches for Three－way Data / M. Gettler－Sumrna ; C. Pardoux = 342
• 12.1 Introduction = 342
• 12.2 The Input and Output Data = 343
• 12.3 Processing Temporal Data = 343
• 12.3.1 Two Approaches for Analysis = 343
• 12.3.2 Data Compression by Time Clustering = 344
• 12.3.3 Adapted Data Analysis Methods = 345
• 12.4 Interpretation of Outcomes from Processing of Temporal Changes = 346
• 12.4.1 Outcomes from a Factorial Analysis = 346
• 12.4.2 Symbolic Interpretation of Clustering Results = 347
• 12.5 Real－Case Examples = 347
• 12.5.1 Behavioural Data Resulting in Rule Objects = 347
• 12.5.2 On－site Telecommunication : Fuzzy Coding and Compression = 348
• 12.5.3 Fishery Study : Temporal Changes of Nominal Variables = 350
• 12.5.4 Fishing Tactics : Using Time Lines for Markings = 352
• 13. Illustrative Benchmark Analyses = 355
• 13.1 Introduction / R. Bisdorff = 355
• 13.2 Professional Careers of Retired Working Persons / R. Bisdorff = 356
• 13.2.1 Basic Statistical Data Matrix = 356
• 13.2.2 Divisive Clustering of Professional Careers = 359
• 13.2.3 About the Discrimination of the Retiring Age from the Professional Careers = 369
• 13.3 Comparing European Labour Force Survey Results from the Basque Country and Portugal / A. Iztueta ; P. Calvo = 374
• 13.3.1 The European Labour Force Survey Data = 374
• 13.3.2 Building Symbolic Objects = 376
• 13.4 Processing Census Data from ONS / F. Goupil ; M. Touati ; E. Diday ; R. Moult = 382
• 13.4.1 Data Description = 382
• 13.4.2 Analysis of Census Data = 382
• 13.5 General Conclusion = 385
• 14 The SODAS Software Package / A. Morineau = 386
• 14.1 Short Introduction to the SODAS Software = 386
• 14.2 Short Processing of a Chaining = 386
• 14.3 Short List of Methods in SODAS Software = 388
• 14.3.1 DB2SO : From Data Base to Symbolic Objects = 388
• 14.3.2 DI : Computing a Distance Matrix for Symbolic Objects = 388
• 14.3.3 DIV : Divisive Classification of Symbolic Data = 388
• 14.3.4 DKS : Symbolic Kernel Discriminant Analysis = 389
• 14.3.5 DSD : Symbolic Description of Groups = 389
• 14.3.6 FDA : Factorial Discriminant Analysis = 389
• 14.3.7 PCM : Principal Component Analysis = 390
• 14.3.8 SOE : Symbolic Object Editor = 390
• 14.3.9 STAT : Histograms and Elementary Statistics = 390
• 14.3.10 STD : Segmentation Tree for Stratified Data = 390
• 14.3.11 TREE : Decision Tree = 391
• Notations and Abbreviations = 392
• Bibliography = 394
• Addresses of Contributors to this Volume = 414
• Subject Index = 417