Sondess Ben Tekaya ; Sadok Ben Yahia ; Yahia Slimani - An Algorithm for the Construction of a Formal Concept Lattice and for the Extraction of Minimal Generators

arima:1835 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, August 10, 2005, Volume 3, Special Issue CARI'04, november 2005 - https://doi.org/10.46298/arima.1835
An Algorithm for the Construction of a Formal Concept Lattice and for the Extraction of Minimal Generators

Authors: Sondess Ben Tekaya ; Sadok Ben Yahia ; Yahia Slimani

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.


Volume: Volume 3, Special Issue CARI'04, november 2005
Published on: August 10, 2005
Submitted on: January 24, 2005
Keywords: Data Mining, Formal Concept Analysis, Galois lattice, Generic association rules, Minimal generator,Fouille de données,Analyse de Concepts Formels,Treillis de Galois,Règles d'associations génériques,Générateur minimal.,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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