Generating a Condensed Representation for Association Rules

Pasquier, Nicolas; Taouil, Rafik; Bastide, Yves; Stumme, Gerd; Lakhal, Lotfi

doi:10.1007/s10844-005-0266-z

Cited by 155 publications

(162 citation statements)

References 21 publications

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“…This is especially important when the database is too large for main memory, as each disk access significantly increases computation time. A theoretical and experimental analysis of this behavior is given in [45], further experimental results are provided in [40].…”

Section: Computing the Iceberg Concept Lattice With Titanicmentioning

confidence: 99%

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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: Computing the Iceberg Concept Lattice With Titanicmentioning

confidence: 99%

“…The min-max basis [35,40] is an alternative to the couple of Duquenne/Guigues and Luxenburger base. It is based both on free and on closed itemsets.…”

Section: Bases Of Association Rulesmentioning

confidence: 99%

Efficient Mining of Association Rules Based on Formal Concept Analysis

Lakhal

Stumme

2005

Formal Concept Analysis

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“…the greatest element of the class, and therefore we have p ≤ q. As an example the min-max basis is made of the implications p → q where p = q and p is a minimal element of the class of q [13]. Whenever F is a confluence*, we have seen that each such equivalence class is associated to several closed patterns q 1 ...q m each being the greatest element of a subclass.…”

Section: Discussionmentioning

confidence: 99%

Closed Patterns and Abstraction Beyond Lattices

Soldano¹

2014

Formal Concept Analysis

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Abstract. Recently pattern mining has investigated closure operators in families of subsets of an attribute set that are not lattices. In particular, various authors have investigated closure operators starting from a context, in the Formal Concept Analysis (FCA) sense, in which objects are described as usual according to their relation to attributes, and in which a closed element is a maximal element of the equivalence class of elements sharing the same support, i.e. occurring in the same objects. The purpose of this paper is twofold. First we thoroughly investigate this framework and relate it to FCA, defining in particular a structure called a preconfluence, weaker than a lattice, in which we can define a closure operator with respect to a set of objects. Second, we show that the requirements allowing us to define abstract concept lattices also allow us to define corresponding abstract Galois pre-confluences.

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“…We obtain then the two implication rules HasHairs → {HasHairs, HasTeats} and {HasTeats} → {HasHairs, HasTeats} that are rewritten as {HasHairs} → {HasTeats} and {HasTeats} → {HasHairs}. This set is further extended to association rules, whose confidences are smaller than 1 and whose right part are intents of more specific nodes [8]. The resulting set produces the so called minmax basis of association rules.…”

Section: Class Incrementality Of Alpha Latticesmentioning

confidence: 99%

“…This means that a fraction of the language (the set of intents) represents all the distinguishable subsets of instances. Such an intent is also denoted as a closed term, and as a frequent closed term when only closed terms, whose extents are large enough according to a bound minsupp * |I|, are considered [8]. In Data Mining the problem of finding frequent itemsets, an essential part of the process of extracting association rules, is therefore reduced to finding closed frequent itemsets.…”

Section: Introductionmentioning

confidence: 99%

Incremental Construction of Alpha Lattices and Association Rules

Soldano

Ventos

Champesme

et al. 2010

Knowledge-Based and Intelligent Information and Engineering Systems

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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.

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Generating a Condensed Representation for Association Rules

Cited by 155 publications

References 21 publications

Efficient Mining of Association Rules Based on Formal Concept Analysis

Efficient Mining of Association Rules Based on Formal Concept Analysis

Closed Patterns and Abstraction Beyond Lattices

Incremental Construction of Alpha Lattices and Association Rules

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