Raymond Bisdorff CRP-GL, Luxembourg The development of the SODAS software based on symbolic data analysis was extensively described in the previous chapters of this book. It was accompanied by a series of benchmark activities involving some official statistical institutes throughout Europe. Partners in these benchmark activities were the National Statistical Institute (INE) of Portugal, the Instituto Vasco de Estadistica Euskal (EUSTAT) from Spain, the Office For National Statistics (ONS) from the United Kingdom, the Inspection Generale de la Securite Sociale (IGSS) from Luxembourg 1 and marginally the University of Athens . The principal goal of these benchmark activities was to demonstrate the usefulness of symbolic data analysis for practical statistical exploitation and analysis of official statistical data. This chapter aims to report briefly on these activities by presenting some signifi cant insights into practical results obtained by the benchmark partners in using the SODAS software package as described in chapter 14 below.
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Preface of the Scientific Editors v Preface of the Project Managers viii Symbolic Data Analysis and the SODAS Project: Purpose, History, Perspective 1(23) E. Diday Introduction 1(1) Symbolic Data Tables and Symbolic Objects 2(6) The Input of SDA: Symbolic Data Tables, Rules and Taxonomies 2(1) Sources of Symbolic Data 3(2) Symbolic Objects 5(3) Tools and Operations for Symbolic Objects 8(3) History and Evolution of SDA 11(3) The Content of the SODAS Project 14(4) SDA Methods Realized in SODAS 14(1) An Illustrative Example 15(2) Overview on the SODAS Software 17(1) Examples for the SODAS Strategy in Applications 17(1) Philosophical Background: Concepts and Symbolic Objects 18(3) First- and Second-Order Individuals 18(1) Intent and Extent, the Two Kinds of Concepts 19(1) Concepts: The Four Traditions and Symbolic Objects 20(1) Advantages of Using Symbolic Data Analysis 21(1) The Future Development of SODAS 22(2) The Classical Data Situation 24(15) H.H. Bock Introduction 24(1) Variables as Input Data 24(1) Quantitative Variables 25(1) Qualitative Variables 26(5) Nominal Variables 26(1) Ordinal Variables and Generalized Ordinal Variables 27(4) Data Vectors and the Data Matrix 31(1) Dependent Variables 32(5) Logical Dependence 33(1) Hierarchical Dependence (Mother-Daughter) 34(2) Stochastic Dependence 36(1) Missing Values 37(2) Symbolic Data 39(15) H.H. Bock Three Introductory Examples 39(3) Multi-Valued and Interval Variables 42(3) Modal Variables 45(4) A Synthesis of Symbolic Data Types 49(1) The Symbolic Data Array 49(5) Symbolic Objects 54(24) H.H. Bock E. Diday Introduction and Examples 54(6) Relations and Descriptions 60(4) Relations 61(1) Descriptions, Description Vectors and Description Sets 62(1) Product Relations 63(1) Events and Assertion Objects 64(5) Boolean Symbolic Objects as Triples 69(6) Modal Symbolic Objects 75(3) Generation of Symbolic Objects from Relational Databases 78(28) V. Stephan G. Hebrail Y. Lechevallier Introduction to Relational Databases 78(2) Principles of Symbolic Object Acquisition from Relational Databases 80(5) Interaction with the Database 85(8) Interpretation of SQL Queries 85(6) Sampling Individuals 91(1) Dependent Variables and Missing Values 92(1) A Generalization Operator 93(10) Basic Generalization Operator 93(2) Problem of Over-Generalization 95(2) A Quality Criterion to Evaluate a Generalized Description 97(1) Coding by Testing for a Uniform Distribution Among Intervals 98(2) A Reduction Algorithm 100(2) A Numerical Example 102(1) Further Operations on Generated Assertions 103(3) Joining Two Arrays of Assertions 103(2) Validation of Generated Assertions 105(1) Descriptive Statistics for Symbolic Data 106(19) P. Bertrand F. Goupil Descriptive Statistics for a Classical Numerical Variable 106(2) The Observed Symbolic Data Set 108(4) The Data Table 109(1) Logical Dependencies 110(1) The Virtual Extension of a Description Vector 111(1) The Case of Multi-Valued Variables 112(7) Frequency Distribution for a Categorical or Quantitative Multi-Valued Variable 113(4) Summary Measures for a Numerical Multi-Valued Variable 117(2) The Case of an Interval-Valued Variable 119(6) Visualizing and Editing Symbolic Objects 125(14) M. Noirhomme-Fraiture M. Rouard The Zoom Star Representation 125(11) Existing Solutions 125(1) Our Graphical Representation 126(4) Use of Zoom Star 130(6) Conclusion 136(1) Editing Symbolic Objects 136(3) Modification of an Existing Symbolic Object 137(1) Modification of Labels 138(1) Similarity and Dissimilarity 139(59) Classical Resemblance Measures 139(14) F. Esposito D. Malerba V. Tamma H.H. Bock Resemblance Measures 140(2) Dissimilarity and Distance: Special Cases 142(3) Distance Measures from a Classical Data Matrix 145(3) Similarity Measures from a Categorical Data Matrix 148(5) Dissimilarity Measures for Probability Distributions 153(12) H.H. Bock Divergence Measures: The General Case 154(1) Divergence Measures: Special Cases 155(5) The Affinity Coefficient (H. Bacelar-Nicolau) 160(5) Dissimilarity Measures for Symbolic Objects 165(21) F. Esposito D. Malerba V. Tamma Gowda and Didays Dissimilarity Measure 166(4) The Approach by Ichino and Yaguchi 170(3) Dissimilarity Measures of De Carvalho 173(4) De Carvalhos Dissimilarity: Constrained Case 177(6) The Dissimilarity Options in the SODAS Package 183(3) Matching Symbolic Objects 186(12) F. Esposito D. Malerba F.A. Lisi Canonical Matching of Boolean Symbolic Objects 186(2) Flexible Matching of Boolean Symbolic Objects 188(8) An Application 196(2) Symbolic Factor Analysis 198(36) Classical Principal Component Analysis 198(2) H.H. Bock Symbolic Principal Component Analysis 200(12) A. Chouakria P. Cazes E. Diday Introduction: Interval Data 200(1) The Purpose of the Method 201(1) The VERTICES Method 202(3) The CENTERS Method 205(1) Representation by Rectangles 206(1) Example of Oils and Fats 207(5) Conclusions 212(1) Factorial Discriminant Analysis on Symbolic Objects 212(22) N.C. Lauro R. Verde F. Palumbo Introduction 212(2) A Reminder of Factorial Discriminant Analysis 214(5) FDA on Symbolic Data 219(12) Illustrative Application to a Data Set 231(3) Discrimination: Assigning Symbolic Objects to Classes 234(60) Classical Methods of Discrimination 234(6) J.P. Rasson S. Lissoir Introduction 234(1) The Problem 234(1) The Decision Rule 235(1) The Classical Probabilistic Framework 236(2) Density Estimation 238(2) Symbolic Kernel Discriminant Analysis 240(4) J.P. Rasson S. Lissoir Kernel Intensity Measures for Symbolic Data 240(2) Determining the Prior Probabilities 242(1) The Output Data 243(1) Symbolic Discrimination Rules 244(22) E. Perinel Y. Lechevallier Introduction 244(1) The Underlying Population and the Variables 244(3) The Set of Binary Questions and the Construction of a New Data Table from Binary Variables 247(3) The Recursive Partition Algorithm 250(3) Detailed Description of the Different Steps 253(6) Decisional Considerations 259(2) Example 261(5) Segmentation Trees for Stratified Data 266(28) M.C. Bravo Llatas J.M. Garcia-Santesmases Introduction 266(1) Input and Output Data 267(4) An Example; Distinction from Classical Decision Trees 271(3) Main Steps of the Algorithm 274(3) Detailed Description of the Algorithm 277(3) Choices in the Algorithm for Classical Data 280(5) Choices in the Algorithm for Probabilistic Data 285(4) Symbolic Object Description of Strata 289(2) The Example 10.4.3 Revisited 291(2) Conclusion 293(1) Clustering Methods for Symbolic Objects 294(48) Clustering Problem, Clustering Methods for Classical Data 294(5) M. Chavent H.H. Bock Criterion-Based Divisive Clustering for Symbolic Data 299(13) M. Chavent The Symbolic Data Matrix 299(2) Two Distance Measures 301(3) Extension of the Within-Class Variance Criterion 304(1) Bipartitioning a Cluster 305(2) Choice of the Cluster to be Split 307(1) The Stopping Rule and the Output 307(1) Example of a Classical Dataset 308(1) Example of a Symbolic Data Set 309(3) Hierarchical and Pyramidal Clustering with Complete Symbolic Objects 312(12) P. Brito Pyramidal Clustering 312(2) Complete Symbolic Objects 314(1) A Hierarchical-Pyramidal Clustering Algorithm for Symbolic Data 315(2) Extension to More Complex Symbolic Data Types 317(5) A Numerical Example 322(2) Pyramidal Classification for Interval Data Using Galois Lattice Reduction 324(18) G. Polaillon Definition and Construction of Galois Lattices 325(9) Reduction of a Galois Lattice into a Pyramid 334(3) A Real-case Application 337(5) Symbolic Approaches for Three-way Data 342(13) M. Gettler-Summa C. Pardoux Introduction 342(1) The Input and Output Data 343(1) Processing Temporal Data 343(3) Two Approaches for Analysis 343(1) Data Compression by Time Clustering 344(1) Adapted Data Analysis Methods 345(1) Interpretation of Outcomes from Processing of Temporal Changes 346(1) Outcomes from a Factorial Analysis 346(1) Symbolic Interpretation of Clustering Results 347(1) Real-Case Examples 347(8) Behavioural Data Resulting in Rule Objects 347(1) On-site Telecommunication: Fuzzy Coding and Compression 348(2) Fishery Study: Temporal Changes of Nominal Variables 350(2) Fishing Tactics: Using Time Lines for Markings 352(3) Illustrative Benchmark Analyses 355(31) Introduction 355(1) R. Bisdorff Professional Careers of Retired Working Persons 356(18) R. Bisdorff Basic Statistical Data Matrix 356(3) Divisive Clustering of Professional Careers 359(10) About the Discrimination of the Retiring Age from the Professional Careers 369(5) Comparing European Labour Force Survey Results from the Basque Country and Portugal 374(8) A. Iztueta P. Calvo The European Labour Force Survey Data 374(2) Building Symbolic Objects 376(6) Processing Census Data from ONS 382(3) F. Goupil M. Touati E. Diday R. Moult Data Description 382(1) Analysis of Census Data 382(3) General Conclusion 385(1) The SODAS Software Package 386(6) A. Morineau Short Introduction to the SODAS Software 386(1) Short Processing of a Chaining 386(2) Short List of Methods in SODAS Software 388(4) DB2SO: From Data Base to Symbolic Objects 388(1) DI: Computing a Distance Matrix for Symbolic Objects 388(1) DIV: Divisive Classification of Symbolic Data 388(1) DKS: Symbolic Kernel Discriminant Analysis 389(1) DSD: Symbolic Description of Groups 389(1) FDA: Factorial Discriminant Analysis 389(1) PCM: Principal Component Analysis 390(1) SOE: Symbolic Object Editor 390(1) STAT: Histograms and Elementary Statistics 390(1) STD: Segmentation Tree for Stratified Data 390(1) TREE: Decision Tree 391(1) Notations and Abbreviations 392(2) Bibliography 394(20) Addresses of Contributors to this Volume 414(3) Subject Index 417
