Analysis of Symbolic Data

Symbolic Data Analysis and the SODAS Project: Purpose, History, Perspective.- 1.1 Introduction.- 1.2 Symbolic Data Tables and Symbolic Objects.- 1.3 Tools and Operations for Symbolic Objects.- 1.4 History and Evolution of SDA.- 1.5 The Content of the SODAS Project.- 1.6 Philosophical Background: Concepts and Symbolic Objects.- 1.7 Advantages of Using Symbolic Data Analysis.- 1.8 The Future Development of SODAS.- 2 The Classical Data Situation.- 2.1 Introduction.- 2.2 Variables as Input Data.- 2.3 Quantitative Variables.- 2.4 Qualitative Variables.- 2.5 Data Vectors and the Data Matrix.- 2.6 Dependent Variables.- 2.7 Missing Values.- 3 Symbolic Data.- 3.1 Three Introductory Examples.- 3.2 Multi-Valued and Interval Variables.- 3.3 Modal Variables.- 3.4 A Synthesis of Symbolic Data Types.- 3.5 The Symbolic Data Array.- 4 Symbolic Objects.- 4.1 Introduction and Examples.- 4.2 Relations and Descriptions.- 4.3 Events and Assertion Objects.- 4.4 Boolean Symbolic Objects as Triples.- 4.5 Modal Symbolic Objects.- 5 Generation of Symbolic Objects from Relational Databases.- 5.1 Introduction to Relational Databases.- 5.2 Principles of Symbolic Object Acquisition from Relational Databases.- 5.3 Interaction with the Database.- 5.4 A Generalization Operator.- 5.5 Further Operations on Generated Assertions.- 6 Descriptive Statistics for Symbolic Data.- 6.1 Descriptive Statistics for a Classical Numerical Variable.- 6.2 The Observed Symbolic Data Set.- 6.3 The Case of Multi-Valued Variables.- 6.4 The Case of an Interval-Valued Variable.- 7 Visualizing and Editing Symbolic Objects.- 7.1 The Zoom Star Representation.- 7.2 Editing Symbolic Objects.- 8 Similarity and Dissimilarity.- 8.1 Classical Resemblance Measures.- 8.2 Dissimilarity Measures for Probability Distributions.- 8.3 Dissimilarity Measures for Symbolic Objects.- 8.4 Matching Symbolic Objects.- 9 Symbolic Factor Analysis.- 9.1 Classical Principal Component Analysis.- 9.2 Symbolic Principal Component Analysis.- 9.3 Factorial Discriminant Analysis on Symbolic Objects.- 10 Discrimination: Assigning Symbolic Objects to Classes.- 10.1 Classical Methods of Discrimination.- 10.2 Symbolic Kernel Discriminant Analysis.- 10.3 Symbolic Discrimination Rules.- 10.4 Segmentation Trees for Stratified Data.- 11 Clustering Methods for Symbolic Objects.- 11.1 Clustering Problem, Clustering Methods for Classical Data.- 11.2 Criterion-Based Divisive Clustering for Symbolic Data.- 11.3 Hierarchical and Pyramidal Clustering with Complete Symbolic Objects.- 11.4 Pyramidal Classification for Interval Data Using Galois Lattice Reduction.- 12 Symbolic Approaches for Three-way Data.- 12.1 Introduction.- 12.2 The Input and Output Data.- 12.3 Processing Temporal Data.- 12.4 Interpretation of Outcomes from Processing of Temporal Changes.- 12.5 Real-Case Examples.- 13 Illustrative Benchmark Analyses.- 13.1. Introduction.- 13.2 Professional Careers of Retired Working Persons.- 13.3 Comparing European Labour Force Survey Results from the Basque Country and Portugal.- 13.4 Processing Census Data from ONS.- 13.5 General Conclusion.- 14 The SODAS Software Package.- 14.1 Short Introduction to the SODAS Software.- 14.2 Short Processing of a Chaining.- 14.3 Short List of Methods in SODAS Software.- Notations and Abbreviations.- Addresses of Contributors to this Volume.