Incremental Construction of Alpha Lattices and Association Rules

Abstract

In this paper we discuss Alpha Galois lattices (Alpha lattices for short) and the corresponding association rules. An alpha lattice is coarser than the related concept lattice and so contains fewer nodes, so fewer closed patterns, and a smaller basis of association rules. Coarseness depends on a a priori classification, i.e. a cover ${\mathcal C}$ of the powerset of the instance set I, and on a granularity parameter α. In this paper, we define and experiment a Merge operator that when applied to two Alpha lattices $G({\mathcal C}_1,\alpha)$ and $G({\mathcal C}_2,\alpha)$ generates the Alpha lattice $G({\mathcal C}_1 \cup {\mathcal C}_2,\alpha)$, so leading to a class-incremental construction of Alpha lattices. We then briefly discuss the implementation of the incremental process and describe the min-max bases of association rules extracted from Alpha lattices.