Classification trees in a box extent lattice

Abstract

In this paper we show that, during an elementary extension of a context, each of the classi cation trees of the newly created box extent lattice can be obtained by modifying the classi cation trees of the box extent lattice of the original, smaller context. We also devise an algorithm which, starting from a classi cation tree of the box extent lattice of the smaller context (H;M; I \H M); gives a classi cation tree of the extended context (G;M; I) which contains the new elements inserted. The e ciency of the method is given by the fact that it is su cient to know the original context, the classi cation tree of the box extent lattice and its box extents while the knowledge of a new box extension of the extended context mesh elements is not required (except for one, which is the new element box extension).