Analysis of Symbolic Data

Transcription

1 Hans-Hermann Bock Edwin Diday (Eds.) Analysis of Symbolic Data Exploratory Methods for Extracting Statistical Information from Complex Data Springer

2 Contents Preface of the Scientific Editors Preface of the Project Managers v viii 1 Symbolic Data Analysis and the SODAS Project: Purpose, History, Perspective 1 E.Diday 1.1 Introduction Symbolic Data Tables and Symbolic Objects The Input of SDA: Symbolic Data Tables, Rules and Taxonomies Sources of Symbolic Data Symbolic Objects Tools and Operations for Symbolic Objects History and Evolution of SDA The Content of the SODAS Project SDA Methods Realized in SODAS An Illustrative Example Overview on the SODAS Software Examples for the SODAS Strategy in Applications Philosophical Background: Concepts and Symbolic Objects First- and Second-Order Individuais Intent and Extent, the Two Kinds of Concepts Concepts: The Four Traditions and 'Symbolic Objects' Advantages of Using Symbolic Data Analysis The Future Development of SODAS 22 2 The Classical Data Situation 24 H.H. Bock 2.1 Introduction Variables as Input Data Quantitative Variables Qualitative Variables 26

3 XU Contents Nominal Variables Ordinal Variables and Generalized Ordinal Variables Data Vectors and the Data Matrix Dependent Variables Logical Dependence Hierarchical Dependence (Mother-Daughter) Stochastic Dependence Missing Values 37 3 Symbolic Data 39 H.H. Bock 3.1 Three Introductory Examples Multi-Valued and Interval Variables Modal Variables ' A Synthesis of Symbolic Data Types The Symbolic Data Array 49 4 Symbolic Objects 54 H.H. Bock, E. Diday 4.1 Introduction and Examples Relations and Descriptions Relations Descriptions, Description Vectors and Description Sets Product Relations Events and Assertion Objects Boolean Symbolic Objects as Triples Modal Symbolic Objects 75 5 Generation of Symbolic Objects from Relational Databases 78 V. Stephan, G. Hebrail, Y. Lechevallier 5.1 Introduction to Relational Databases Principles of Symbolic Object Acquisition from Relational Databases Interaction with the Database Interpretation of SQL Queries 85

4 Contents xiii Sampling Individuais Dependent Variables and Missing Values A Generalization Operator Basic Generalization Operator Problem of Over-Generalization A Quality Criterion to Evaluate a Generalized Description Coding by Testing for a Uniform Distribution Among Intervals A Reduction Algorithm A Numerical Example Further Operations on Generated Assertions Joining Two Arrays of Assertions Validation of Generated Assertions Descriptive Statistics for Symbolic Data 106 P. Bertrand, F. Goupil 6.1 Descriptive Statistics for a Classical Numerical Variable The Observed Symbolic Data Set The Data Table Logical Dependencies The Virtual Extension of a Description Vector The Case of Multi-Valued Variables Frequency Distribution for a Categorical or Quantitative Multi-Valued Variable Summary Measures for a Numerical Multi-Valued Variable The Case of an Interval-Valued Variable Visualizing and Editing Symbolic Objects 125 M. Noirhomme-Fraiture, M. Rouard 7.1 The Zoom Star Representation Existing Solutions Our Graphical Representation Use of Zoom Star Conclusion Editing Symbolic Objects Modification of an Existing Symbolic Object Modification of Labels 138

5 xiv Contents 8 Similarity and Dissimilarity Classical Resemblance Measures 139 F. Esposito, D. Malerba, V. Tamma, H.H. Bock Resemblance Measures Dissimilarity and Distance: Special Cases Distance Measures from a Classical Data Matrix Similarity Measures from a Categorical Data Matrix Dissimilarity Measures for Probability Distributions 153 H.H. Bock Divergence Measures: The General Case Divergence Measures: Special Cases The Affinity Coefficient (H Bacelar-Nicolau) Dissimilarity Measures for Symbolic Objects 165 F. Esposito, D. Malerba, V. Tamma Gowda and Diday's Dissimilarity Measure The Approach by Ichino and Yaguchi Dissimilarity Measures of De Carvalho De Carvalho's Dissimilarity: Constrained Case The Dissimilarity Options in the SODAS Package Matching Symbolic Objects 186 F. Esposito, D. Malerba, F.A. Lisi Canonical Matching of Boolean Symbolic Objects Flexible Matching of Boolean Symbolic Objects An Application Symbolic Factor Analysis Classical Principal Component Analysis 198 H.H. Bock 9.2 Symbolic Principal Component Analysis 200 A. Chouakria, P. Cazes, E. Diday Introduction: Interval Data The Purpose of the Method The VERTICES Method The CENTERS Method Representation by Rectangles Example of Oils and Fats Conclusions 212

6 Contents xv 9.3 Factorial Discriminant Analysis on Symbolic Objects 212 N.C. Lauro, R. Verde, F. Palumbo Introduction A Reminder of Factorial Discriminant Analysis FDA on Symbolic Data Illustrative Application to a Data Set Discrimination: Assigning Symbolic Objects to Classes Classical Methods of Discrimination 234 J.P. Rasson, S. Lissoir Introduction The Problem The Decision Rule The Classical Probabilistic Framework Density Estimation Symbolic Kernel Discriminant Analysis 240 J.P. Rasson, S. Lissoir Kernel Intensity Measures for Symbolic Data Determining the Prior Probabilities The Output Data Symbolic Discrimination Rules 244 E. Perinel, Y. Lechevallier Introduction The Underlying Population and the Variables The Set of Binary Questions and the Construction of a New Data Table from Binary Variables The Recursive Partition Algorithm Detailed Description of the Different Steps Decisional Considerations Example Segmentation Trees for Stratified Data 266 M.C. Bravo Llatas, J.M. Garcia-Santesmases Introduction Input and Output Data An Example; Distinction from Classical Decision Trees.. 271

7 xvi Contents Main Steps of the Algorithm Detailed Description of the Algorithm Choices in the Algorithm for Classical Data Choices in the Algorithm for Probabilistic Data Symbolic Object Description of Strata The Example Revisited Conclusion Clustering Methods for Symbolic Objects Clustering Problem, Clustering Methods for Classical Data M. Chavent, H.H. Bock 11.2 Criterion-Based Divisive Clustering for Symbolic Data 299 M. Chavent The Symbolic Data Matrix Two Distance Measures Extension of the Within-Class Variance Criterion Bipartitioning a Cluster Choice of the Cluster to be Split The Stopping Rule and the Output Example of a Classical Dataset Example of a Symbolic Data Set Hierarchical and Pyramidal Clustering with Complete Symbolic Objects 312 P. Brito Pyramidal Clustering Complete Symbolic Objects A Hierarchical-Pyramidal Clustering Algorithm for Symbolic Data Extension to More Complex Symbolic Data Types A Numerical Example Pyramidal Classification for Interval Data Using Galois Lattice Reduction 324 G. Polaillon Definition and Construction of Galois Lattices Reduction of a Galois Lattice into a Pyramid A Real-case Application 337

8 Contents xvn 12 Symbolic Approaches for Three-way Data 342 M. Gettler-Summa, C. Pardoux 12.1 Introduction The Input and Output Data Processing Temporal Data Two Approaches for Analysis Data Compression by Time Clustering Adapted Data Analysis Methods Interpretation of Outcomes from Processing of Temporal Changes Outcomes from a Factorial Analysis Symbolic Interpretation of Clustering Results Real-Case Examples Behavioural Data Resulting in Rule Objects On-site Telecommunication: Fuzzy Coding and Compression Fishery Study: Temporal Changes of Nominal Variables Fishing Tactics: Using Time Lines for Markings Illustrative Benchmark Analyses Introduction 355 R. Bisdorff 13.2 Professional Careers of Retired Working Persons 356 R. Bisdorff Basic Statistical Data Matrix Divisive Clustering of Professional Careers About the Discrimination of the Retiring Age from the Professional Careers Comparing European Labour Force Survey Results from the Basque Country and Portugal 374 A. Iztueta, P. Calvo The European Labour Force Survey Data Building Symbolic Objects Processing Census Data from ONS 382 F. Goupil, M. Touati, E. Diday, R. Moult Data Description Analysis of Census Data General Conclusion 385

9 xviii Contents 14 The SODAS Software Package 386 A. Morineau 14.1 Short Introduction to the SODAS Software Short Processing of a Chaining Short List of Methods in SODAS Software DB2SO: From Data Base to Symbolic Objects DI: Computing a Distance Matrix for Symbolic Objects DIV: Divisive Classification of Symbolic Data DKS: Symbolic Kernel Discriminant Analysis DSD: Symbolic Description of Groups FDA: Factorial Discriminant Analysis PCM: Principal Component Analysis SOE: Symbolic Object Editor STAT: Histograms and Elementary Statistics STD: Segmentation Tree for Stratified Data TREE: Decision Tree 391 Notations and Abbreviations 392 Bibliography 394 Addresses of Contributors to this Volume 414 Subject Index 417