Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach

Formal concept analysis (FCA) is a mathematical theory that is typically used as a knowledge representation method. The approach starts with an input binary relation specifying a set of objects and attributes, finds the natural groupings (formal concepts) described in the data, and then organizes th...

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Autores principales:	Amira Mouakher, Axel Ragobert, Sébastien Gerin, Andrea Ko
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	formal concept analysis essential formal concept full/partial conceptual coverage interestingness measures Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0a050152b4314905a4e08542cd08fa30
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spelling	oai:doaj.org-article:0a050152b4314905a4e08542cd08fa302021-11-11T18:15:34ZConceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach10.3390/math92126942227-7390https://doaj.org/article/0a050152b4314905a4e08542cd08fa302021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2694https://doaj.org/toc/2227-7390Formal concept analysis (FCA) is a mathematical theory that is typically used as a knowledge representation method. The approach starts with an input binary relation specifying a set of objects and attributes, finds the natural groupings (formal concepts) described in the data, and then organizes the concepts in a partial order structure or concept (Galois) lattice. Unfortunately, the total number of concepts in this structure tends to grow exponentially as the size of the data increases. Therefore, there are numerous approaches for selecting a subset of concepts to provide full or partial coverage. In this paper, we rely on the battery of mathematical models offered by FCA to introduce a new greedy algorithm, called <span style="font-variant: small-caps;">Concise</span>, to compute minimal and meaningful subsets of concepts. Thanks to its theoretical properties, the <span style="font-variant: small-caps;">Concise</span> algorithm is shown to avoid the sluggishness of its competitors while offering the ability to mine both partial and full conceptual coverage of formal contexts. Furthermore, experiments on massive datasets also underscore the preservation of the quality of the mined formal concepts through interestingness measures agreed upon by the community.Amira MouakherAxel RagobertSébastien GerinAndrea KoMDPI AGarticleformal concept analysisessential formal conceptfull/partial conceptual coverageinterestingness measuresMathematicsQA1-939ENMathematics, Vol 9, Iss 2694, p 2694 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	formal concept analysis essential formal concept full/partial conceptual coverage interestingness measures Mathematics QA1-939
spellingShingle	formal concept analysis essential formal concept full/partial conceptual coverage interestingness measures Mathematics QA1-939 Amira Mouakher Axel Ragobert Sébastien Gerin Andrea Ko Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach
description	Formal concept analysis (FCA) is a mathematical theory that is typically used as a knowledge representation method. The approach starts with an input binary relation specifying a set of objects and attributes, finds the natural groupings (formal concepts) described in the data, and then organizes the concepts in a partial order structure or concept (Galois) lattice. Unfortunately, the total number of concepts in this structure tends to grow exponentially as the size of the data increases. Therefore, there are numerous approaches for selecting a subset of concepts to provide full or partial coverage. In this paper, we rely on the battery of mathematical models offered by FCA to introduce a new greedy algorithm, called <span style="font-variant: small-caps;">Concise</span>, to compute minimal and meaningful subsets of concepts. Thanks to its theoretical properties, the <span style="font-variant: small-caps;">Concise</span> algorithm is shown to avoid the sluggishness of its competitors while offering the ability to mine both partial and full conceptual coverage of formal contexts. Furthermore, experiments on massive datasets also underscore the preservation of the quality of the mined formal concepts through interestingness measures agreed upon by the community.
format	article
author	Amira Mouakher Axel Ragobert Sébastien Gerin Andrea Ko
author_facet	Amira Mouakher Axel Ragobert Sébastien Gerin Andrea Ko
author_sort	Amira Mouakher
title	Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach
title_short	Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach
title_full	Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach
title_fullStr	Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach
title_full_unstemmed	Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach
title_sort	conceptual coverage driven by essential concepts: a formal concept analysis approach
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0a050152b4314905a4e08542cd08fa30
work_keys_str_mv	AT amiramouakher conceptualcoveragedrivenbyessentialconceptsaformalconceptanalysisapproach AT axelragobert conceptualcoveragedrivenbyessentialconceptsaformalconceptanalysisapproach AT sebastiengerin conceptualcoveragedrivenbyessentialconceptsaformalconceptanalysisapproach AT andreako conceptualcoveragedrivenbyessentialconceptsaformalconceptanalysisapproach
_version_	1718431864158420992

Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach

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