TAILIEUCHUNG - Báo cáo " Concept lattice and adjacency matrix "

In this paper, we introduce a new encoding for a given binary relation, by using adjacency matrix constructed on the relation. Therefore, a coatom of a concept lattice can be characterized by supports of row vectors of adjacency matrix. Moreover, we are able to compute a poly-sized sub-relation resulting in a sublattice of the original lattice for a given binary relation. | VNU Journal of Science Mathematics - Physics 24 2008 11-15 Concept lattice and adjacency matrix Nguyen Duc Dat1 Hoang Le Truong2 1 Department of Mathematics Mechanics Informatics College of Science VNU 334 Nguyen Trai Hanoi Vietnam Institute of Mathematics 18 Hoang Quoc Viet CauGiay 10307 Hanoi Vietnam Received 26 October 2007 received in revised form 7 January 2008 Abstract. In this paper we introduce a new encoding for a given binary relation by using adjacency matrix constructed on the relation. Therefore a coatom of a concept lattice can be characterized by supports of row vectors of adjacency matrix. Moreover we are able to compute a poly-sized sub-relation resulting in a sublattice of the original lattice for a given binary relation. 1. Introduction Lattices have given rise to much interest for the past years first as a powerful mathematical structure see . Birkhoff s work from 1967 then as useful in applications such as exploiting questionnaires is Social Sciences see . Barbet and Monjardet s work from 1970 1 . Galois lattices were later widely publicized and studied by the large body of work done by Wille and Granter and the many researchers who worked with them under the name of concept lattices in a much more general context see . 2 . Nowadays concept lattices are well-studied as a classification tool see 2 are used in several areas related to Artifical Intelligence and Data Mining such as Data Base Management Machine Learning and Frequent Set Generation see . 3-5 . The main drawback of concept lattices is that they may be of exponential size. This makes it impossible in practice to compute and span the entire structure they describe. It is thus of primeval importance to be able to navigate the lattice efficiently or to be able to define a polynomial sized sub-lattice which contains the right information. In this paper we introduce a new encoding for a given binary relation by using adjacency matrix constructed on the relation. Therefore a .

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