Maintaining Class Membership Information

Galois lattices (or concept lattices), which are lattices built on a binary relation, are now used in many fields, such as Data Mining and hierarchy organization, but may be of exponential size. In this paper, we propose a decomposition of a Galois sub-hierarchy which is of small size but contains useful inheritance information. We show how to efficiently maintain this information when an element is added to or removed from the relation, using a dynamic domination table which describes the underlying graph with which we encode the lattice

Maintaining class membership information

Abstract. Galois lattices (or concept lattices), which are lattices built on a binary relation, are now used in many fields, such as Data Mining and hierarchy organization, but may be of exponential size. In this paper, we propose a decomposition of a Galois sub-hierarchy which is of small size but contains useful inheritance information. We show how to efficiently maintain this information when an element is added to or removed from the relation, using a dynamic domination table which describes the underlying graph with which we encode the lattice. 1 Introduction Galois lattices (also called concept lattices), are an emerging tool in research areas such as Data Mining, Database Managing and Object Hierarchy Organization (see [5], [10], [11], [13], [14], [15]). A lattice has the advantage over a tree that it allows a much more complex structure, as every pair of elements not only has a greatest lower bound, but also has a lowest upper bound. In particular, this structure has been shown to be well adapted to representing multiple inheritance (a car can be both a wheeled vehicle and water-faring)