Abstract not found

The data descriptions of the units are called "symbolic" when they are more complex than the standard ones due to the fact that they contain internal variation and are structured. Symbolic data happen from many sources, for instance in order to summarise huge Relational Data Bases by their underlying concepts. "Extracting knowledge" means getting explanatory results, that why, "symbolic objects" are introduced and studied in this paper. They model concepts and constitute an explanatory output for data analysis. Moreover they can be used in order to define queries of a Relational Data Base and propagate concepts between Data Bases. We define "Symbolic Data Analysis" (SDA) as the extension of standard Data Analysis to symbolic data tables as input in order to find symbolic objects as output. In this paper we give an overview on recent development on SDA. We present some tools and methods of SDA and introduce the SODAS software prototype (issued from the work of 17 teams of nine countries involved in an European project of EUROSTAT). 1

Numerical induction from data is one of the statistical data analysis tasks, which uses a tabular model, with almost exclusively numerical features, as data representation formalism. The output representations are different: from functions to probability distributions, from surface equations to tables of indexes. One approach to extend the classical data analysis techniques to symbolic objects is the Symbolic Data Analysis: the input and the output of classical techniques are expressed in a symbolic way, so guaranteeing the comprehensibility of both the observations and the results, while the processing techniques, although appropriately adapted, maintain the efficiency of the classical statistical inferential models. Also in the field of Machine Learning several methods have been proposed to extend some inductive approaches from statistical data analysis to data represented as attribute-value couples. Sometimes these approaches transform ideas and principles coming from numerical induction to handle propositional calculus descriptions, otherwise they combine different techniques in order to treat numericalcontinuous data and algebraic-symbolic data differently. The aim here is to improve the efficiency and to preserve the expressive power of the representations during the learning process, and to save the accuracy and flexibility of the numerical techniques during the recognition phase. This kind of integration is more and more complex when using first-order computational learning models, which are useful for handling object descriptions in structured domains, when not only the properties of objects but also the relations between different objects must be considered. The necessity arises from integrating different computational strategies, different knowledge represe...

In this paper we address the problem of organising probabilistic data by Galois concept lattices. Two lattices are proposed, the union lattice and the intersection lattice, corresponding to two distinct semantics, by choosing accordingly the join and meet operators. A new algorithm is proposed to construct the concept lattice. Two real data examples illustrate the presented approach.