Discovery of the D-basis in binary tables based on hypergraph dualization

Abstract

Abstract. Discovery of (strong) association rules, or implications, is an important task in data management, and it finds application in artificial intelligence, data mining and the semantic web. We introduce a novel approach for the discovery of a specific set of implications, called the D-basis, that provides a representation for a reduced binary table, based on the structure of its Galois lattice. At the core of the method are the D-relation defined in the lattice theory framework, and the hypergraph dualization algorithm that allows us to effectively produce the set of transversals for a given Sperner hypergraph. The latter algorithm, first developed by specialists from Rutgers Center for Operations Research, has already found numerous applications in solving optimization problems in data base theory, artificial intelligence and game theory. One application of the method is for analysis of gene expression data related to a particular phenotypic variable, and some initial testing is done for the data provided by the

The joy of implications, aka pure Horn formulas: Mainly a survey

“…It is argued that even if the resulting base Σ is considerably larger than Σ GD , this is more than offset by the short time to obtain Σ. A similar approach is taken in [AN2], but instead of Σ cd the D-basis of 4.3 (a subset of Σ cd ) is targeted. Furthermore the likely superior [MU] subroutine for hypergraph dualization is used.…”

“…This particular kind of Query Learning strives to compute the canonical base Σ GD of some hidden closure system F. Unfortunately, as a not always welcome side product, the whole of F gets calculated one by one along the way. Impressive strides to avoid this succeed for the kind of "modern" attribute exploration proposed in [RDB] and [AN2].…”

The Bases of Association Rules of High Confidence

“…Finding association rules is a computationally complex problem [1] and our approach is meant to address this issue using a collection of parallelizable algorithms that are scalable in a distributed processing environment.…”

“…An algorithm in Adaricheva and Nation [1] works to extract the basis of implications of the table, and it is known as the D-basis, which was introduced in Adaricheva, Nation, and Rand [3]. The advantage of this basis is in the possibility to use algorithms for dualization of an associated hypergraph that are known to be sub-exponential in their complexity, see Fredman and Khachiyan [10].…”

“…The algorithm in [1] allows us to retrieve only those implications X → b in the D-basis that have a fixed attribute b as a conclusion. This is called a b-sector of the basis.…”