Affiliations: Laboratoire d’Informatique Fondamentale de Marseille, Aix-Marseille Université, 13625 Aix-en-Provence Cedex, France
Correspondence:
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Corresponding author: Lotfi Lakhal, Laboratoire d’Informatique Fondamentale de Marseille (LIF), CNRS UMR 7279, Aix-Marseille Université, IUT d’Aix-en-Provence, Avenue Gaston Berger, 13625 Aix-en-Provence Cedex, France. E-mail: Lotfi.Lakhal@lif.univ-mrs.fr
Note: [1] RowId is an attribute used as an identifier for the relation tuples. ti is the tuple provided with i as its RowId.
Note: [10] π′(E) is said rougher than π(E).
Note: [11] Tid(r)={Rowid(t)∣t∈r}.
Abstract: The Skyline concept has been introduced in order to exhibit the best objects according to all the criterion combinations and makes it possible to analyze the relationships between Skyline objects. Like the data cube, the Skycube groups all the multidimensional Skylines and it is so voluminous that reduction approaches are a necessity. In this paper, we define an approach which partially materializes the Skycube. The underlying idea is to discard from the representation the Skycuboids which can be computed again easily. To meet this reduction objective, we characterize a formal framework: the Agree Concept Lattice. It provides a formal framework which makes it possible to improve computation time, reduce representation and easily navigate through the Hasse diagram in order to focus on the most relevant skycuboids. This structure is generic, applies to various database analysis problems and combines both formal concept analysis and database theory. It makes use of the concepts of agree set and database partition. They are associated to define the Agree Concept of a database relation. The set of all the Agree Concepts is organized within the Agree Concept Lattice. From this structure, we derive the Skyline concept lattice which is one of its constrained instances for efficient multidimensional Skyline analysis. The strong points of our approach are: (i) it is attribute oriented; (ii) it provides a boundary for the number of lattice nodes; (iii) it facilitates the navigation within the Skycuboids.
Keywords: Concept lattices, databases, data cube, Skyline, Olap-mining
