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Simultaneous, Polynomial-Time Layout of Context Bigraph and Lattice Digraph

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Formal Concept Analysis (ICFCA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11511))

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Abstract

Formal Concept Analysis (FCA) takes as input the bipartite context graph and produces a directed acyclic graph representing the lattice of formal concepts. Excepting possibly the supremum and infimum, the set of formal concepts corresponds to the set of proper maximal bicliques in the context bigraph. This paper proposes polynomial-time graph layouts which emphasise maximal bicliques in the context bigraph and facilitate “reading” directed paths in the lattice digraph. These layouts are applied to sub-contexts of the InfoVis 2004 data set which are indivisible by the Carve divide-and-conquer FCA algorithm. The paper also investigates the relationship between vertex proximity in the bigraph layout and co-membership of maximal bicliques, and demonstrates the significant reduction of edge crossings in the digraph layout.

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Notes

  1. 1.

    A sentence containing square brackets is true both when read without the bracketed terms, and when read with each bracketed term substituted for the preceding term.

  2. 2.

    Table 1 demonstrates that this lexicographic permutation of the resistance-assigned ordering of the co-atoms has only a minor effect on edge crossings.

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Authors and Affiliations

  1. Defence Science and Technology Group, Adelaide, Australia

    Tim Pattison & Aaron Ceglar

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  1. Tim Pattison
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  2. Aaron Ceglar
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Correspondence to Tim Pattison .

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Editors and Affiliations

  1. Babeș-Bolyai University, Cluj-Napoca, Romania

    Diana Cristea

  2. University of Strasbourg, ENGEES, Strasbourg, France

    Florence Le Ber

  3. Frankfurt University of Applied Sciences, Frankfurt, Germany

    Baris Sertkaya

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Pattison, T., Ceglar, A. (2019). Simultaneous, Polynomial-Time Layout of Context Bigraph and Lattice Digraph. 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_15

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  • DOI: https://doi.org/10.1007/978-3-030-21462-3_15

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-21462-3

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