Incremental Construction of Alpha Lattices and Association Rules

Abstract

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 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(C1, α) and G(C2, α) generates the Alpha lattice G(C1∪C2, α), 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.

Survey on attribute and concept reduction methods in formal concept analysis

“…i.e., given two formal concepts (𝐴 1 , 𝐵 1 ), (𝐴 2 , 𝐵 2 ), where (𝐴 1 , 𝐵 1 ) ≤ (𝐴 2 , 𝐵 2 ), sup (𝐵 1 , 𝐺) ≤ sup (𝐵 2 , 𝐺), where 𝐺 is the sets of objects. Stumme et al [35], the authors present the "Titanic algorithm" for the creation of "iceberg concept lattices" and illustrate the functionality of these lattices in a variety of applications, like mining association rules, the visualization of implications as well as the analysis of "large-scale" databases Soldano et al [64], the authors presented a new model of concept lattice that can be considered of as being similar to iceberg concept lattice. The concept lattice that was produced as a result was given the name "alpha concept lattice" by the authors.…”

“…Under the non-essential distinctions elimination category, all of those [32], [33], [43], [59], [60], [82]- [85] reduction methods have formal context as a preliminary step for the reduction process, except for the method in [86], which has both formal context and formal concepts as a point to start the reduction process and the method in [76], which has both formal concepts and concept lattice as a preliminary step for the reduction process. In the concept filtration category, eight methods [65], [71], [79], [82], [87]- [90] use formal context as a preliminary step for the reduction process, four methods [35], [64], [91], [92] use concept lattice as a preliminary step for the reduction process, three reduction methods [61], [69], [73] use both formal concepts and concept lattice as a preliminary step for the reduction process, and two reduction methods [20], [36] use both formal context and formal concepts as a preliminary step for the reduction process. The approach can be enhanced by using domain experts (prior knowledge) about the domain problem to lead the reduction process.…”

Fuzzy formal concept analysis: approaches, applications and issues

“…Selection [58] The authors introduced a type of concept lattice, which are like iceberg concept lattices. Some class restraints are built with attributes in a formal context.…”

A comprehensive overview on the foundations of formal concept analysis

“…one having only frequent formal concepts. Soldano et al (2010) have discussed the construction of alpha lattices. The extent of a term in Alpha lattices is restricted according to constraints based on an apriori categorization of Forge ( 2010) instances in classes, and on a degree α, which results in a smaller lattice.…”