Next Priority Concept: A new and generic algorithm computing concepts from complex and heterogeneous data

In this article, we present a new data type agnostic algorithm calculating a concept lattice from heterogeneous and complex data. Our NextPriorityConcept algorithm is first introduced and proved in the binary case as an extension of Bordat's algorithm with the notion of strategies to select only some predecessors of each concept, avoiding the generation of unreasonably large lattices. The algorithm is then extended to any type of data in a generic way. It is inspired from pattern structure theory, where data are locally described by predicates independent of their types, allowing the management of heterogeneous data.Comment: 28 pages, 8 figures, 7 algorithm

Décomposition sous-directe d'un treillis en facteurs irréductibles

National audienceLa taille d'un treillis de concepts peut augmenter de façon exponentielle avec la taille du contexte. Lorsque le nombre de noeuds devient important, l'´ etude et la génération d'un tel treillis devient impossible. Décomposer le treillis en petit sous-treillis est un moyen de contourner ceprobì eme. Dans la décomposition sous-directe, les petits sous-treillis générés sont des quotients qui ont une interprétation intéressante dans le cadre de l'Analyse de Concepts Formels. Dans cet article, nous présentons les etapes pour obtenir une décomposition sous-directe en treillis irréductibles , en partant d'un contexte fini et réduit. Cette décomposition est obtenue en utilisant trois points de vue : les treillis quotients, les relationsfì eches et les sous-contextes compatibles. Cette approche est essentiellement algébrique car elle repose sur la théorie des treillis, sauf pour le dernier point. Nous donnons un algorithme polynomial permettant de générer cette décomposition a partir d'un contexte initial. Cette méthode peut etré etendue pour permettre l'exploration interactive ou la fouille dans de grands contextes

GALACTIC: GAlois LAttices, Concept Theory, Implicational systems and Closures. A set of python3 packages for studying Formal Concept Analysis

International audienc

On the links between NextPriorityConcept algorithm and generalized convex hulls

International audienceFormal 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

Information Retrieval by On-line Navigation in the Latticial Space-search of a Database, with Limited Objects Access

International audienc

On the links between the NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ algorithm and generalized convex hulls

International audienceFormal 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

GALACTIC: a python framework for Formal Concept Analysis

A tutorial on the GALACTIC python framewor

Interval-based sequence mining using FCA and the NextPriorityConcept algorithm

International audienc

Sequence Mining Using FCA and the NextPriorityConcept Algorithm

International audienc