Alpha Galois Lattices: An Overview

Ventos, Véronique; Soldano, Henry

doi:10.1007/978-3-540-32262-7_21

Cited by 17 publications

(14 citation statements)

References 13 publications

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“…In Alpha lattices the extent of a term is restricted according to constraints depending on a a priori categorization of instances in classes, and on a degree α, so resulting in a smaller lattice [16].…”

Section: Resultsmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

“…Still the number of closed patterns is often too high when dealing with realworld data, and some way to select them has to be found [6]. Recently, Alpha Galois lattices (Alpha lattices for short) have been defined [16]. Each node of an Alpha lattice corresponds to an Alpha closed term i.e.…”

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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“…ext A = p A • ext and the corresponding abstract support closure operator with respect to A is therefore f A = int • p A • ext. Intuitively, as noticed in [7], this is because the corresponding abstract Galois lattice is isomorphic, and as same support closure subset as the Galois lattice associated to the object set O(A) each object a of which is an element of A and described in T as int(a) 4 . It is then straighforward that we obtain that abstract Galois pre-confluences are simply the Galois pre-confluences obtained through this change on object set.…”

Section: Abstract Closed Patterns In Confluences*mentioning

confidence: 96%

“…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. Because of the one-to-one correspondence between projections (dual closures) and abstractions (subsets closed under joins) the corresponding projected Galois lattices are also called abstract Galois lattices [12].…”

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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Knowledge representation and processing with formal concept analysis

Kuznetsov

Poelmans

2013

WIREs Data Min & Knowl

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During the last three decades, formal concept analysis (FCA) became a well‐known formalism in data analysis and knowledge discovery because of its usefulness in important domains of knowledge discovery in databases (KDD) such as ontology engineering, association rule mining, machine learning, as well as relation to other established theories for representing knowledge processing, like description logics, conceptual graphs, and rough sets. In early days, FCA was sometimes misconceived as a static crisp hardly scalable formalism for binary data tables. In this paper, we will try to show that FCA actually provides support for processing large dynamical complex (may be uncertain) data augmented with additional knowledge. © 2013 Wiley Periodicals, Inc. This article is categorized under: Fundamental Concepts of Data and Knowledge > Key Design Issues in Data Mining Fundamental Concepts of Data and Knowledge > Knowledge Representation Technologies > Computational Intelligence

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Alpha Galois Lattices: An Overview

Cited by 17 publications

References 13 publications

Incremental Construction of Alpha Lattices and Association Rules

Incremental Construction of Alpha Lattices and Association Rules

Closed Patterns and Abstraction Beyond Lattices

Knowledge representation and processing with formal concept analysis

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