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

We present an O(n 3 )--time, O(n 2 )--space algorithm to test whether a dissimilarity d on an n--object set X is Robinsonian, i.e., X admits an ordering such that i j k implies that d(x i ; xk ) maxfd(x i ; x j ); d(x j ; xk )g: R'esum'e: Nous pr'esentons un algorithme de complexit'e O(n 3 ) pour le temps et O(n 2 ) pour l'espace m'emoire, afin de tester si une dissimilarit'e d sur un ensemble X de n objets est de Robinson, i.e., si X admet un ordre tel que i j k entraine d(x i ; xk ) maxfd(x i ; x j ); d(x j ; xk )g: Keywords: Robinsonian dissimilarities; Order compatible with a dissimilarity; Divide--and--conquer algorithm. 1.

The classical seriation problem consists in finding a permutation of the rows and the columns of the distance (or, more generally, dissimilarity) matrix d on a finite set X so that small values should be concentrated around the main diagonal as close as possible, whereas large values should fall as far from it as possible. This goal is best achieved by considering the Robinson property: a distance dR on X is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonal along any row or column. If the distance d fails to satisfy the Robinson property, then we are lead to the problem of finding a reordering of d which is as close as possible to a Robinsonian distance. In this paper, we present a factor 16 approximation algorithm for the following NP-hard fitting problem: given a finite set X and a dissimilarity d on X, wewish to find a Robinsonian dissimilarity dR on X minimizing the l∞-error ‖d − dR‖ ∞ = maxx,y∈X{|d(x,y) − dR(x, y)|} between d and dR.