On the links between the NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ algorithm and generalized convex hulls - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2022

On the links between the NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ algorithm and generalized convex hulls

Résumé

Formal Concept Analysis is a mathematical formalism offering many methods that can be used in various fields of computer science. FCA highlights the structure of lattice or "concept lattice", defined for binary or categorical data, where a concept is a pair composed of a maximal subset of objects together with their shared data. The whole set of concepts is naturally organized in a hierarchical graph, called the concept lattice. The fundamental theorem in FCA establishes a bijection between lattices and « reduced » binary datasets [BM70] via concept lattice generation, called the “Galois” connection. A nice result establishes that the composition of the two operators of a Galois connection is a closure operator. The notion of closure operator is central in lattice theory. From the original binary formalism of FCA, different extensions to non-binary data have been proposed [FR00] [GK01], by establishing that the Galois connection between a data space and a description space is maintained, as long as the description space verifies the lattice property. We recently introduced in [DBFVK20] a new algorithm, NextPriorityConcept, that is capable of generating concepts from complex and heterogeneous data with a generic description to provide predicates describing a subgroup of objects. We have observed that the generic use of predicates describing subgroups correspond to generalized convex hulls. In this talk, we will present some links between our algorithm and the theory of convex structures.
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Dates et versions

hal-03639401 , version 1 (12-04-2022)

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  • HAL Id : hal-03639401 , version 1

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Karell Bertet, Christophe Demko. On the links between the NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ algorithm and generalized convex hulls. Joint Mathematics Meetings, American Mathematical Society (AMS), Apr 2022, Virtual, United States. ⟨hal-03639401⟩

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