Dichotomic lattices and local discretization for Galois lattices

Abstract

The present paper deals with supervised classification methods based on Galois lattices and decision trees. Such ordered structures require attributes discretization and it is known that, for decision trees, local discretization improves the classification performance compared with global discretization. While most literature on discretization for Galois lattices relies on global discretization, the presented work introduces a new local discretization algorithm for Galois lattices which hinges on a property of some specific lattices that we introduce as dichotomic lattices. Their properties, co-atomicity and $$\vee $$ź-complementarity are proved along with their links with decision trees. Finally, some quantitative and qualitative evaluations of the local discretization are proposed.