Fast algorithms for implication bases and attribute exploration using proper premises

Ryssel, Uwe; Distel, Felix; Borchmann, Daniel

doi:10.1007/s10472-013-9355-9

Cited by 22 publications

(21 citation statements)

References 18 publications

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“…As far as the goal of the current paper, theoretical results of the D-basis recovery are supported by the practical evidence tested in [32] and initial testing presented in section 9, that the recovery of the implicational basis based on the hypergraph dualization algorithm will bring a considerable cut in run-times when dealing with tabled data. This will make the new approach critical for analysis of large data sets.…”

Section: Further Theoretical Work and Implementationsupporting

confidence: 54%

“…Recently, U. Russel et al [32] proposed a method of retrieval of the canonical direct unit basis that would employ the hypergraph dualization algorithm. While the actual coding applied some back-tracking and simple heuristics instead of actual implementation of dualization, the computer test results showed considerably shorter running times when compared to existing FCA implementations: on a particular data table of size 26 × 79 the new algorithm would return the basis of 86 1 We mention that some efforts were spent on parallelization of algorithms building a Galois lattice from the binary table, such as in P. Krajca et al [27], but possible utilization of these approaches for computation of pseudo-closed sets has not yet been developed.…”

Section: 2mentioning

confidence: 99%

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

Adaricheva¹,

Nation²

2017

Theoretical Computer Science

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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

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Section: Further Theoretical Work and Implementationsupporting

confidence: 54%

Section: 2mentioning

confidence: 99%

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

Adaricheva¹,

Nation²

2017

Theoretical Computer Science

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“…C (k,k) being a simple 2-context, results on the implication bases of 2-contexts apply to those of n-contexts. Most importantly, implication bases of C (k,k) can be computed using known algorithms [11,1]. .…”

Section: A Type Of Implication Basementioning

confidence: 99%

On implication bases in n-lattices

Bazin

2020

Discrete Applied Mathematics

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“…Implication rules can be obtained through formal concepts [22], formal contexts [17] and concept lattice [23]. In our study, the implication rules extraction is based on formal contexts.…”

Section: Formal Concept Analysismentioning

confidence: 99%

“…Applying different properties to a I set, we can generate implication sets with certain constraints for specific domains. One of these specific sets is the proper implications set, in which for each implication the premise is minimal and the conclusion is a singleton (unit set) [17].…”

Section: Introductionmentioning

confidence: 99%

ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram †

et al. 2018

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Formal concept analysis (FCA) is largely applied in different areas. However, in some FCA applications the volume of information that needs to be processed can become unfeasible. Thus, the demand for new approaches and algorithms that enable processing large amounts of information is increasing substantially. This article presents a new algorithm for extracting proper implications from high-dimensional contexts. The proposed algorithm, called ImplicPBDD, was based on the PropIm algorithm, and uses a data structure called binary decision diagram (BDD) to simplify the representation of the formal context and enhance the extraction of proper implications. In order to analyze the performance of the ImplicPBDD algorithm, we performed tests using synthetic contexts varying the number of objects, attributes and context density. The experiments show that ImplicPBDD has a better performance—up to 80% faster—than its original algorithm, regardless of the number of attributes, objects and densities.

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Fast algorithms for implication bases and attribute exploration using proper premises

Cited by 22 publications

References 18 publications

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

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

On implication bases in n-lattices

ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram †

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