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Algorithme de construction d'un treillis des concepts formels et de détermination des générateurs minimaux

Abstract : The extremely large number of association rules that can be drawn from ―even reasonably sized datasets―, bootstrapped the development of more acute techniques or methods to reduce the size of the reported rule sets. In this context, the battery of results provided by the Formal Concept Analysis (FCA) allowed to define "irreducible" nuclei of association rule subset better known as generic basis. However, a thorough overview of the literature shows that all the algorithms dedicated neglected an essential component: the relation of order, or the extraction of the minimal generators. In this paper, we introduce the GenAll algorithm to build a formal concept lattice, in which each formal concept is "decorated" by its minimal generators. The GenAll algorithm aims to extract generic bases of association rules. The main novelty in this algorithm is the use of refinement process to compute immediate successor lists to simultaneously determine the set of formal concepts, their underlying partial order and the set of minimal generators associated with each formal concept. Carried out experiments showed that the GenAll algorithm is especially efficient for dense extraction contexts compared to that of Nourine et al. Response times obtained from the GenAll algorithm largely outperform those of Nourine et al.
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Sondess Ben Tekaya, Sadok Ben Yahia, Yahia Slimani. Algorithme de construction d'un treillis des concepts formels et de détermination des générateurs minimaux. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2005, Volume 3, Special Issue CARI'04, november 2005, pp.171-193. ⟨10.46298/arima.1835⟩. ⟨hal-01261707⟩



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