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Computing triadic generators and association rules from triadic contexts

  • S706 Conceptual Structures
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Abstract

In this paper, we present a set of algorithms to display a Hasse diagram of triadic concepts in Triadic Concept Analysis and compute triadic generators and association rules, including implications without any need for a preprocessing step to convert the triadic representation into a dyadic one. Our contributions are as follows. First, we adapt the iPred algorithm for precedence link computation in concept lattices to the triadic framework. Then, new algorithms are proposed to compute triadic generators by extending the notion of faces to further calculate association rules. Finally, an empirical study is conducted in order to mainly show the performance of our prototype on triadic contexts and estimate the cost of each one of its components.

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References

  1. Ananias, K.H.A., Missaoui, R., Ruas, P.H.B., Zárate, L. E., Song, M.A.J.: Triadic Formal Concept Analysis and triclustering: searching for optimal patterns. Journal of Information Sciences To appear (2021)

  2. Baixeries, J., Szathmary, L., Valtchev, P., Godin, R.: Yet a faster algorithm for building the Hasse diagram of a concept lattice. In: ICFCA’09, pp. 162–177 (2009)

  3. Balcázar, J. L., Tîrnǎucǎ, C.: Border algorithms for computing hasse diagrams of arbitrary lattices. LNAI 6628, 49–64 (2011)

    MATH  Google Scholar 

  4. Biedermann, K.: How Triadic Diagrams Represent Conceptual Structures. In: ICCS, pp. 304–317 (1997)

  5. Cerf, L., Besson, J., Robardet, C., Boulicaut, J.: Closed patterns meet n-ary relations. ACM Trans. Knowl. Discov. Data 3(1), 3:1–3:36 (2009)

    Article  Google Scholar 

  6. Ganter, B., Obiedkov, S.A.: Implications in Triadic Formal Contexts. In: ICCS, pp. 186–195 (2004)

  7. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, New York (1999). Translator-C. Franzke

    Book  MATH  Google Scholar 

  8. Ignatov, D.I., Gnatyshak, D.V., Kuznetsov, S.O., Mirkin, B.G.: Triadic formal concept analysis and triclustering: searching for optimal patterns. Mach. Learn. 101(1), 271–302 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Jaschke, R., Hotho, A., Schmitz, C., Ganter, B., Stumme, G.: TRIAS - an algorithm for mining iceberg tri-lattices. In: ICDM’06, pp. 907–911 (2006)

  10. Kaytoue, M., Kuznetsov, S.O., Macko, J., Napoli, A.: Biclustering meets triadic concept analysis. Ann. Math. Artif. Intell. 70(1-2), 55–79 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lehmann, F., Wille, R.: A triadic approach to formal concept analysis. In: ICCS, pp. 32–43 (1995)

  12. Missaoui, R., Kwuida, L.: Mining triadic association rules from ternary relations. In: LNAI, vol. 6628, pp 204–218 (2011)

  13. Missaoui, R., Ruas, P.H.B., Kwuida, L., Song, M.A.J.: Pattern discovery in triadic contexts. In: Alam, M., Braun, T., Yun, B. (eds.) Ontologies and concepts in mind and machine - 25th international conference on conceptual structures, ICCS 2020, Bolzano, Italy, September 18-20, 2020, Proceedings, Lecture Notes in Computer Science, vol. 12277, pp 117–131. Springer (2020)

  14. Pfaltz, J.L., Taylor, C.M.: Closed Set Mining of Biological Data. In: BIOKDD’02, pp. 43–48 (2002)

  15. Rudolph, S., Sacarea, C., Troanca, D.: Towards a navigation paradigm for triadic concepts. In: ICFCA’15, pp. 252–267 (2015)

  16. Wille, R.: The basic theorem of triadic concept analysis. Order 12 (2), 149–158 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhao, L., Zaki, M.J.: Tricluster: An effective algorithm for mining coherent clusters in 3d microarray data. In: Özcan, F. (ed.) Proceedings of the ACM SIGMOD international conference on management of data, Baltimore, Maryland, USA, June 14-16, 2005, pp 694–705. ACM (2005). https://doi.org/10.1145/1066157.1066236

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Acknowledgements

The authors acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brazil (CAPES) - Finance Code 001. They thank the anonymous reviewers for their careful reading of the manuscript and their numerous insightful comments and suggestions.

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Authors and Affiliations

  1. Université du Québec en Outaouais, Gatineau, Canada

    Rokia Missaoui & Mohamed Hamza Ibrahim

  2. Pontifical Catholic University of Minas Gerais, Belo Horizonte, Brazil

    Pedro H. B. Ruas & Mark A. J. Song

  3. Bern University of Applied Sciences, Bern, Switzerland

    Léonard Kwuida

  4. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    Mohamed Hamza Ibrahim

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  1. Rokia Missaoui
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  2. Pedro H. B. Ruas
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  3. Léonard Kwuida
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  4. Mark A. J. Song
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  5. Mohamed Hamza Ibrahim
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Correspondence to Rokia Missaoui.

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Missaoui, R., Ruas, P.H.B., Kwuida, L. et al. Computing triadic generators and association rules from triadic contexts. Ann Math Artif Intell 90, 1083–1105 (2022). https://doi.org/10.1007/s10472-022-09784-4

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  • DOI: https://doi.org/10.1007/s10472-022-09784-4

Keywords

Mathematics Subject Classification (2010)