Treillis des concepts skylines : Analyse multidimensionnelle des skylines fond\'ee sur les ensembles en accord

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 analyse the relationships between skyline objects. Like the data cube, the skycube is so voluminous that reduction approaches are really necessary. 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 the most easily. To meet this reduction objective, we characterize a formal framework: the agree concept lattice. From this structure, we derive the skyline concept lattice which is one of its constrained instances. 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.