Finding all closed sets: A general approach

Ganter, Bernhard; Reuter, Klaus

doi:10.1007/bf00383449

Cited by 68 publications

(34 citation statements)

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“…Guigues and Duquenne [18] described a minimal set of implications (exact rules) from which all rules can be derived, the Duquenne Guigues base or stem base. In 1984, Ganter developed the Next Closure algorithm ( [20], see also [21]) for its computation. Luxenburger was working on bases for partial implications (approximative rules) [30,31].…”

Section: History and State Of The Art In Fca-based Association Rule Mmentioning

confidence: 99%

Efficient Mining of Association Rules Based on Formal Concept Analysis

Lakhal

Stumme

2005

Formal Concept Analysis

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Abstract. Association rules are a popular knowledge discovery technique for warehouse basket analysis. They indicate which items of the warehouse are frequently bought together. The problem of association rule mining has first been stated in 1993. Five years later, several research groups discovered that this problem has a strong connection to Formal Concept Analysis (FCA). In this survey, we will first introduce some basic ideas of this connection along a specific algorithm, Titanic, and show how FCA helps in reducing the number of resulting rules without loss of information, before giving a general overview over the history and state of the art of applying FCA for association rule mining.

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Section: History and State Of The Art In Fca-based Association Rule Mmentioning

confidence: 99%

Efficient Mining of Association Rules Based on Formal Concept Analysis

Lakhal

Stumme

2005

Formal Concept Analysis

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“…Even then the naïve algorithm enumerating each set S ∈ F and testing whether S is ρ-closed is inefficient because |F | can be exponential in |ρ(F )|. There are several results on efficient enumeration of ρ-closed sets for the case that the underlying set system is finite and closed under intersection (see, e.g., [2,3]). Among others, formal concept analysis [7] and closed frequent itemset mining (see, e.g., [6]) provide some representative applications of this case.…”

Section: The General Problemmentioning

confidence: 99%

Efficient Closed Pattern Mining in Strongly Accessible Set Systems (Extended Abstract)

Boley

Horváth

Poigné

et al.

Knowledge Discovery in Databases: PKDD 2007

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Abstract. Many problems in data mining can be viewed as a special case of the problem of enumerating the closed elements of an independence system with respect to some specific closure operator. Motivated by real-world applications, e.g., in track mining, we consider a generalization of this problem to strongly accessible set systems and arbitrary closure operators. For this more general problem setting, the closed sets can be enumerated with polynomial delay if deciding membership in the set system and computing the closure operator can be solved in polynomial time. We discuss potential applications in graph mining.

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“…the input. Moreover, some important operations, such as finding a concept, are performed for some representations (spanning trees [2,10], ordered lists [7], CbO trees [16], 2-3 trees, see [1] for the definition) in polynomial time, but for some other representations (unordered lists) they can be performed only in exponential time. A representation of a concept lattice can be considered reasonable if its size cannot be exponentially compressed w.r.t.…”

Section: On Principles Of Comparisonmentioning

confidence: 99%

Comparing performance of algorithms for generating concept lattices

Kuznetsov¹,

Obiedkov²

2002

Journal of Experimental & Theoretical Artificial Intelligen

398

186

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Abstract. Several algorithms that generate the set of all formal concepts and diagram graphs of concept lattices are considered. Some modifications of wellknown algorithms are proposed. Algorithmic complexity of the algorithms is studied both theoretically (in the worst case) and experimentally. Conditions of preferable use of some algorithms are given in terms of density/sparseness of underlying formal contexts. Principles of comparing practical performance of algorithms are discussed.

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Finding all closed sets: A general approach

Cited by 68 publications

References 1 publication

Efficient Mining of Association Rules Based on Formal Concept Analysis

Efficient Mining of Association Rules Based on Formal Concept Analysis

Efficient Closed Pattern Mining in Strongly Accessible Set Systems (Extended Abstract)

Comparing performance of algorithms for generating concept lattices

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