Abstract
Concept lattices are well-known conceptual structures that organise interesting patterns – the concepts – extracted from data. In some applications, the size of the lattice can be a problem, as it is often too large to be efficiently computed and too complex to be browsed. In others, redundant information produces noise that makes understanding the data difficult. In classical FCA, those two problems can be attenuated by, respectively, computing a substructure of the lattice – such as the AOC-poset – and reducing the context. These solutions have not been studied in d-dimensional contexts for \(d > 3\). In this paper, we generalise the notions of AOC-poset and reduction to d-lattices, the structures that are obtained from multidimensional data in the same way that concept lattices are obtained from binary relations.
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Notes
- 1.
I was unable to put my hands on those two books in order to learn more about that. If you have a copy, I am most interested.
- 2.
Stirling number of the second kind, or number of ways of arranging d dimensions into k slots.
- 3.
Not that well known, but it is said in this paper [11].
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Bazin, A., Kahn, G. (2019). Reduction and Introducers in d-contexts. In: Cristea, D., Le Ber, F., Sertkaya, B. (eds) Formal Concept Analysis. ICFCA 2019. Lecture Notes in Computer Science(), vol 11511. Springer, Cham. https://doi.org/10.1007/978-3-030-21462-3_6
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