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Distances Between Formal Concept Analysis Structures

Authors Alexandre Bazin , Giacomo Kahn

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TGDK.3.2.2.pdf
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ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
Keywords
  • Formal Concept Analysis
  • Implication Base
  • Concept Lattice
  • Pattern Mining
  • Ordinal Data Science

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Abstract

In this paper, we study the notion of distance between the most important structures of formal concept analysis: formal contexts, concept lattices, and implication bases. We first define three families of Minkowski-like distances between these three structures. We then present experiments showing that the correlations of these distances are low and depend on the distance between formal contexts.

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Alexandre Bazin and Giacomo Kahn. Distances Between Formal Concept Analysis Structures. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 2, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/TGDK.3.2.2

Author Details

Alexandre Bazin
  • LIRMM, CNRS, Université de Montpellier, Montpellier, France
Giacomo Kahn
  • Université Lumière Lyon 2, INSA Lyon, Université Claude Bernard Lyon 1, France
  • Université Jean Monnet Saint-Etienne, DISP UR4570, Bron, France

Funding

This work was partially supported by the ANR SmartFCA project Grant ANR-21-CE23-0023 of the French National Research Agency.

Acknowledgements

The authors thank the members of the SmartFCA project for their advice.

Supplementary Materials

References

  1. Alexandre Bazin, Jessie Carbonnel, and Giacomo Kahn. On-demand generation of aoc-posets: Reducing the complexity of conceptual navigation. In Foundations of Intelligent Systems: 23rd International Symposium, ISMIS 2017, Warsaw, Poland, June 26-29, 2017, Proceedings 23, pages 611-621. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-60438-1_60.
  2. Alexandre Bazin, Jessie Galasso, and Giacomo Kahn. Polyadic relational concept analysis. International Journal of Approximate Reasoning, 164:109067, 2024. URL: https://doi.org/10.1016/j.ijar.2023.109067.
  3. Alexandre Bazin, Marianne Huchard, and Pierre Martin. Towards analyzing variability in space and time of products from a product line using triadic concept analysis. In Proceedings of the 27th ACM International Systems and Software Product Line Conference-Volume B, pages 85-89, 2023. URL: https://doi.org/10.1145/3579028.3609019.
  4. Karell Bertet, Christophe Demko, Jean-François Viaud, and Clément Guérin. Lattices, closures systems and implication bases: A survey of structural aspects and algorithms. Theoretical Computer Science, 743:93-109, 2018. URL: https://doi.org/10.1016/j.tcs.2016.11.021.
  5. Karell Bertet and Bernard Monjardet. The multiple facets of the canonical direct unit implicational basis. Theoretical Computer Science, 411(22-24):2155-2166, 2010. URL: https://doi.org/10.1016/j.tcs.2009.12.021.
  6. Daniel Borchmann and Tom Hanika. Some experimental results on randomly generating formal contexts. In CLA, volume 1624, pages 57-69, 2016. URL: https://ceur-ws.org/Vol-1624/paper5.pdf.
  7. Victor Codocedo and Amedeo Napoli. Formal concept analysis and information retrieval-a survey. In International Conference on Formal Concept Analysis, pages 61-77. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-19545-2_4.
  8. Elena Deza, Michel Marie Deza, Michel Marie Deza, and Elena Deza. Encyclopedia of distances. Springer, 2009. Google Scholar
  9. Florent Domenach. Similarity measures of concept lattices. In Data Science, Learning by Latent Structures, and Knowledge Discovery, pages 89-99. Springer, 2015. URL: https://doi.org/10.1007/978-3-662-44983-7_8.
  10. Florent Domenach and Bruno Leclerc. Closure systems, implicational systems, overhanging relations and the case of hierarchical classification. Mathematical Social Sciences, 47(3):349-366, 2004. URL: https://doi.org/10.1016/j.mathsocsci.2003.09.008.
  11. Bernhard Ganter, Sergei Obiedkov, Bernhard Ganter, and Sergei Obiedkov. Attribute exploration. Conceptual exploration, pages 125-185, 2016. URL: https://doi.org/10.1007/978-3-662-49291-8_4.
  12. Bernhard Ganter and Rudolf Wille. Formal Concept Analysis: Mathematical Foundations. Springer Science & Business Media, 1999. Google Scholar
  13. Kathy J Horadam and Michael A Nyblom. Distances between sets based on set commonality. Discrete Applied Mathematics, 167:310-314, 2014. URL: https://doi.org/10.1016/j.dam.2013.10.037.
  14. Marianne Huchard, Pierre Martin, Emile Muller, Pascal Poncelet, Vincent Raveneau, and Arnaud Sallaberry. Rcaviz: Exploratory search in multi-relational datasets represented using relational concept analysis. International Journal of Approximate Reasoning, page 109123, 2024. URL: https://doi.org/10.1016/j.ijar.2024.109123.
  15. Priscilla Keip, Alain Gutierrez, Marianne Huchard, Florence Le Ber, Samira Sarter, Pierre Silvie, and Pierre Martin. Effects of input data formalisation in relational concept analysis for a data model with a ternary relation. In International Conference on Formal Concept Analysis, pages 191-207. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-21462-3_13.
  16. Claudio L Lucchesi and Sylvia L Osborn. Candidate keys for relations. Journal of Computer and System Sciences, 17(2):270-279, 1978. URL: https://doi.org/10.1016/0022-0000(78)90009-0.
  17. Jonas Poelmans, Dmitry I Ignatov, Sergei O Kuznetsov, and Guido Dedene. Formal concept analysis in knowledge processing: A survey on applications. Expert systems with applications, 40(16):6538-6560, 2013. URL: https://doi.org/10.1016/j.eswa.2013.05.009.
  18. Jonas Poelmans, Dmitry I Ignatov, Sergei O Kuznetsov, and Guido Dedene. Fuzzy and rough formal concept analysis: a survey. International Journal of General Systems, 43(2):105-134, 2014. URL: https://doi.org/10.1080/03081079.2013.862377.
  19. Jonas Poelmans, Sergei O Kuznetsov, Dmitry I Ignatov, and Guido Dedene. Formal concept analysis in knowledge processing: A survey on models and techniques. Expert systems with applications, 40(16):6601-6623, 2013. URL: https://doi.org/10.1016/j.eswa.2013.05.007.
  20. UCI Machine Learning Repository. Mushroom. UCI Machine Learning Repository, 1981. DOI: https://doi.org/10.24432/C5959T. Google Scholar
  21. Mohamed Rouane-Hacene, Marianne Huchard, Amedeo Napoli, and Petko Valtchev. Relational concept analysis: mining concept lattices from multi-relational data. Annals of Mathematics and Artificial Intelligence, 67:81-108, 2013. URL: https://doi.org/10.1007/s10472-012-9329-3.
  22. Sebastian Rudolph, Christian Săcărea, and Diana Troancă. Conceptual navigation for polyadic formal concept analysis. In IFIP International Workshop on Artificial Intelligence for Knowledge Management, pages 50-70. Springer, 2016. URL: https://doi.org/10.1007/978-3-319-92928-6_4.
  23. Gerd Stumme, Dominik Dürrschnabel, and Tom Hanika. Towards ordinal data science. Transactions on Graph Data and Knowledge (TGDK), 2023. URL: https://doi.org/10.4230/TGDK.1.1.6.
  24. George Voutsadakis. Polyadic concept analysis. Order, 19:295-304, 2002. URL: https://doi.org/10.1023/A:1021252203599.
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