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Knowledge Discovery From Symbolic Data And The Sodas Software
 Conf. on Principles and Practice of Knowledge Discovery in Databases, PPKDD2000
, 2000
"... 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 under ..."
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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
Pyramidal Clustering Algorithms in ISO3D Project
, 2000
"... Pyramidal clustering method generalizes hierarchies by allowing nondisjoint classes at a given level instead of a partition. Moreover, the clusters of the pyramid are intervals of a total order on the set being clustered. [Diday 1984], [Bertrand, Diday 1990] and [Mfoumoune 1998] proposed algorithms ..."
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Pyramidal clustering method generalizes hierarchies by allowing nondisjoint classes at a given level instead of a partition. Moreover, the clusters of the pyramid are intervals of a total order on the set being clustered. [Diday 1984], [Bertrand, Diday 1990] and [Mfoumoune 1998] proposed algorithms to build a pyramid starting with an arbitrary order of the individual. In this paper we present two new algorithms name CAPS and CAPSO. CAPSO builds a pyramid starting with an order given on the set of the individuals (or symbolic objects) while CAPS finds this order. These two algorithms allows moreover to cluster more complex data than the tabular model allows to process, by considering variation on the values taken by the variables, in this way, our method produces a symbolic pyramid. Each cluster thus formed is defined not only by the set of its elements (i.e. its extent) but also by a symbolic object, which describes its properties (i.e. its intent). These two algorithms were implemented in C++ and Java to the ISO3D project. 1 Definitions Diday in [5, Diday (1984)] proposes the algorithm CAP to build numeric pyramids. Algorithms are also presented with this purpose in [2, Bertrand y Diday (1990)], [10, Gil (1998)] and [11, Mfoumoune (1998)]. Paula Brito in [3, Brito (1991)] proposes a macroalgorithm that generalizes the algorithm to build numeric pyramids proposed by Bertrand to the symbolic case. In this article we propose two algorithm designed to build symbolic pyramids (CAPS and CAPSO), that is to say, a pyramid in which each node is again a symbolic object. These algorithms also calculate the extension of each one of these symbolic objects and verifie its completeness. Notation:  # the set of individuals.  O j the description space for the variable j....
Recognition of Robinsonian dissimilarities
, 1996
"... We present an O(n 3 )time, O(n 2 )space algorithm to test whether a dissimilarity d on an nobject 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 ..."
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We present an O(n 3 )time, O(n 2 )space algorithm to test whether a dissimilarity d on an nobject 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; Divideandconquer algorithm. 1.
Seriation in the Presence of Errors: A Factor 16 Approximation Algorithm for l∞Fitting Robinson Structures to Distances
 ALGORITHMICA
, 2007
"... 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 ..."
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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 NPhard fitting problem: given a finite set X and a dissimilarity d on X, wewish to find a Robinsonian dissimilarity dR on X minimizing the lâerror âd â dRâ â = maxx,yâX{d(x,y) â dR(x, y)} between d and dR.