Polyadic Concept Analysis

Polyadic concept analysis is the multidimensional generalisation of formal concept analysis. At its core, it establishes relations between n-ary relations (n-context), the structure formed by the so-called concepts found in the relation (concept n-lattice), and rules representing the regularities in the relation (implications or extension relations). This provides the means to study the information found in data under three different but complementary points of view: the factual, conceptual and logical points of view. Can the differences in these points of view be leveraged to learn something new about what is observed?

My work

Theory

  • Polyadic Relational Concept Analysis. Alexandre Bazin, Jessie Galasso-Carbonnel, Giacomo Kahn. International Journal of Approximate Reasoning 2024. (Abstract) (pdf)
  • Bounding the Number of Minimal Transversals in Tripartite 3-Uniform Hypergraphs. Alexandre Bazin, Laurent Beaudou, Giacomo Kahn, Kaveh Khoshkhah. Discrete Mathematics & Theoretical Computer Science, 2023. (Abstract) (pdf)
  • A Triadic Generalisation of the Boolean Concept Lattice. Alexandre Bazin. ICFCA 2023. (Abstract) (pdf)
  • Condensed Representations of Association Rules in n-ary Relations. Alexandre Bazin, Nicolas Gros, Aurélie Bertaux, Christophe Nicolle. IEEE Transactions on Knowledge and Data Engineering 2022. (Abstract) (pdf)
  • On Implication Bases in n-Lattices. Alexandre Bazin. Discrete Applied Mathematics 2020. (Abstract) (pdf)
  • Reduction and Introducers in d-contexts. Alexandre Bazin and Giacomo Kahn. ICFCA 2019. (Abstract) (pdf)
  • k-Partite Graphs as Contexts. Alexandre Bazin and Aurélie Bertaux. CLA 2018. (Abstract) (pdf)

Applications

  • Variability-Driven User-Story Generation using LLM and Triadic Concept Analysis. Alexandre Bazin, Alain Gutierrez, Marianne Huchard, Pierre Martin and Yulin (Huaxi) Zhang. ENASE 2025. (Abstract) (pdf)
  • Exploring the 3-Dimensional Variability of Websites’ User-Stories using Triadic Concept Analysis. Alexandre Bazin, Thomas Georges, Marianne Huchard, Pierre Martin and Chouki Tibermacine. International Journal of Approximate Reasoning 2024. (Abstract) (pdf)
  • Towards Analyzing Variability in Space and Time of Products from a Product Line using Triadic Concept Analysis. Alexandre Bazin, Marianne Huchard, Pierre Martin. Varivolution@SPLC2023. (Abstract) (pdf)

Tools

  • PCA : Python module for computing n-concepts, association rules and implications in the polyadic concept analysis framework, including its extensions to graph contexts and relational contexts

Other people’s work

Under construction ! If your work isn’t featured here and you want it to be, please send me an e-mail or talk to me in front of the croissants at the next conference.

  • Pattern discovery in triadic contexts. Rokia Missaoui, Pedro HB Ruas, Léonard Kwuida and Mark AJ Song. ICCS 2020. (link)
  • Mining triadic association rules from ternary relations. Rokia Missaoui and Léonard Kwuida, ICFCA 2011. (link)
  • Multidimensional Association Rules in Boolean Tensors. Kim-Ngan Nguyen, Loïc Cerf, Marc Plantevit, and Jean-François Boulicaut. ICDM 2011. (link)
  • Data-peeler: Constraint-based closed pattern mining in n-ary relations. L. Cerf, J. Besson, C. Robardet and J.F. Boulicaut. ICDM 2008. (link)
  • Polyadic concept analysis. George Voutsadakis. Order 19, 2002. (link)
  • The basic theorem of triadic concept analysis. Rudolf Wille, Order 12, 1995. (link)
  • A triadic approach to formal concept analysis. Fritz Lehmann, Fritz and Rudolf Wille. ICCS’95, 1995. (link)