## Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical Information from Complex DataHans-Hermann Bock, Edwin Diday 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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### Contents

The Classical Data Situation | 24 |

Symbolic Data | 39 |

Symbolic Objects | 54 |

Generation of Symbolic Objects from Relational Databases | 78 |

Descriptive Statistics for Symbolic Data | 106 |

Visualizing and Editing Symbolic Objects | 125 |

Similarity and Dissimilarity | 139 |

Symbolic Factor Analysis | 198 |

Assigning Symbolic Objects to Classes | 234 |

Clustering Methods for Symbolic Objects | 294 |

Symbolic Approaches for Threeway Data | 342 |

Illustrative Benchmark Analyses | 355 |

The SODAS Software Package | 386 |

Notations and Abbreviations | 392 |

Addresses of Contributors to this Volume | 414 |

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### Common terms and phrases

algorithm assertion objects binary questions Boolean symbolic objects Cartesian product characterized classes classes C1 coding coefficient column compute concept consider corresponding criterion data matrix data units data vector database decision tree decisional node defined definition dendrogram denoted described description set descriptors Diday discriminant dissimilarity measure domain elements empirical distribution function Euclidean distance example extension factorial plane Figure frequency distribution Galois lattices given graphical histogram hypercube interval variables logical dependence modal variables multi-valued variable nominal variable observed obtained ordinal variables pairs partition predictors principal component analysis principal components probabilistic probability distribution proposed pyramid quantitative variables recursive partition relation representation rows Section set Q similarity SODAS project SODAS software split SQL query statistical strata stratum subsets symbolic data analysis symbolic data array symbolic data matrix symbolic data table symbolic description symbolic variables terminal nodes variables Y1 weight Zoom Star