Symbolic Data Analysis: a Mathematical Framework and Tool for Data Mining

Abstract

Knowledge extraction from large data bases is called “Data Mining”. In Data Bases the descriptions of the units are more complex than the standard ones due to the fact that they can contain internal variation and be structured. Moreover, symbolic data happen from many sources in order to summarise huge sets of data. They need more complex data tables called “symbolic data tables” because a cell of such data table does not necessarily contain as usual, a single quantitative or categorical values. For instance, a cell can contain several values linked by a taxonomy. The need to extend standard data analysis methods (exploratory, clustering, factorial analysis, discrimination,…) to symbolic data table is increasing in order to get more accurate information and summarise extensive data sets contained in Data Bases. We define “Symbolic Data Analysis” (SDA) the extension of standard Data Analysis to such tables; “Symbolic objects” are defined, in order to describe in an explanatory way classes of such units. They constitute an explanatory output of a SDA and they can be used as queries of the Data Base. A symbolic object is “complete” if its “extent” covers exactly the class that it describes. The set of complete symbolic objects constitutes a Galois lattice. The SDA tools developed in the European Community project “Sodas ” are finally mentioned.