Abstract
Efficient algorithms exist for constructing the attribute-object concept (AOC) partially-ordered set (poset) from a formal context. The atoms and co-atoms of the corresponding concept lattice can be determined from this AOC poset and horizontally ordered so as to reduce arc crossings in a layered drawing of the AOC poset initially, and ultimately of the concept lattice digraph. The remaining, abstract concepts must then be computed and progressively inserted into the AOC poset to construct the lattice digraph. This paper describes the preparation of a formal context for efficient computation of these abstract concepts, and the consequent localisation in the AOC poset digraph of any resultant insertions. In particular, it provides simple screening tests for identifying bigraph edges, and hence also any attributes and objects, which do not contribute to abstract concepts. Elimination of these bigraph elements reduces the size of the context and paves the way for dividing and conquering the enumeration of the abstract concepts. These screening tests are also used to determine ab initio which arcs in the AOC poset digraph will not be subject to subsequent transitive reduction. These arcs are visually distinguished in the line diagram to focus attention on the remaining digraph arcs where the insertion of additional concepts may yet occur, and where the graphical interpretation of meets and joins is unsafe.
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Pattison, T., Ceglar, A. (2021). Towards Interactive Transition from AOC Poset to Concept Lattice. In: Braud, A., Buzmakov, A., Hanika, T., Le Ber, F. (eds) Formal Concept Analysis. ICFCA 2021. Lecture Notes in Computer Science(), vol 12733. Springer, Cham. https://doi.org/10.1007/978-3-030-77867-5_12
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