Maximal and stochastic Galois lattices

Diday, Edwin; Emilion, Richard

doi:10.1016/s0166-218x(02)00210-x

Cited by 33 publications

(17 citation statements)

References 3 publications

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“…terms generated by first considering the set of object descriptions, and then closing it under the least general generalization ∧ L . Independently, E. Diday and R. Emilion start from the same assumptions [9]. Proposition 1 directly follows from, for instance, theorem 2 in [9].…”

Section: Extension-intension Latticesmentioning

confidence: 90%

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Abstract Concept Lattices

Soldano

Ventos

2011

Formal Concept Analysis

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Abstract. We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language L of terms and the powerset of a set of instances O. Such a relation is materialized as an extension-intension lattice, namely a concept lattice when L is the powerset of a set P of attributes. We define and characterize an abstraction A as some part of either the language or the powerset of O, defined in such a way that the extension-intension latticial structure is preserved. Such a structure is denoted for short as an abstract lattice. We discuss the extensional abstract lattices obtained by so reducing the powerset of O, together together with the corresponding abstract implications, and discuss alpha lattices as particular abstract lattices. Finally we give formal framework allowing to define a generalized abstract lattice whose language is made of terms mixing abstract and non abstract conjunctions of properties.

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Section: Extension-intension Latticesmentioning

confidence: 90%

“…Independently, E. Diday and R. Emilion start from the same assumptions [9]. Proposition 1 directly follows from, for instance, theorem 2 in [9]. We call extension-intension lattice the Galois lattice G coresponding to this Galois connection.…”

Section: Extension-intension Latticesmentioning

confidence: 96%

Abstract Concept Lattices

Soldano

Ventos

2011

Formal Concept Analysis

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“…Note that, any Galois connection between two lattices may be rewritten as the connection between two powersets and therefore there is no strict gain in expressive power in the more general setting. However, the direct formulation as sets of closed elements of the lattice T is often useful [9,10,3]. Proposition 3 follows from, for instance, theorem 2 in [3].…”

Section: Proposition 4 Intmentioning

confidence: 99%

“…However, the direct formulation as sets of closed elements of the lattice T is often useful [9,10,3]. Proposition 3 follows from, for instance, theorem 2 in [3]. Projected or abstract Galois lattices have been recently defined by noticing that applying an interior (or projection) operator on T [10,11] or 2 O (or both) [11,7] when there exists a Galois connection between them, we obtain again closure operators and lattices of closure subsets.…”

Section: Proposition 4 Intmentioning

confidence: 99%

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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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The State of the Art in Symbolic Data Analysis: Overview and Future

Diday

2007

Symbolic Data Analysis and the SODAS Software

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Maximal and stochastic Galois lattices

Cited by 33 publications

References 3 publications

Abstract Concept Lattices

Abstract Concept Lattices

Closed Patterns and Abstraction Beyond Lattices

The State of the Art in Symbolic Data Analysis: Overview and Future

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