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Attribute Selection Using Contranominal Scales

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 12879)

Abstract

Formal Concept Analysis (FCA) allows to analyze binary data by deriving concepts and ordering them in lattices. One of the main goals of FCA is to enable humans to comprehend the information that is encapsulated in the data; however, the large size of concept lattices is a limiting factor for the feasibility of understanding the underlying structural properties. The size of such a lattice depends on the number of subcontexts in the corresponding formal context that are isomorphic to a contranominal scale of high dimension. In this work, we propose the algorithm ContraFinder that enables the computation of all contranominal scales of a given formal context. Leveraging this algorithm, we introduce \(\delta \)-adjusting, a novel approach in order to decrease the number of contranominal scales in a formal context by the selection of an appropriate attribute subset. We demonstrate that \(\delta \)-adjusting a context reduces the size of the hereby emerging sub-semilattice and that the implication set is restricted to meaningful implications. This is evaluated with respect to its associated knowledge by means of a classification task. Hence, our proposed technique strongly improves understandability while preserving important conceptual structures.

Keywords

  • Formal Concept Analysis
  • Contranominal scales
  • Concept lattices
  • Attribute selection
  • Feature selection
  • Implications

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Notes

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    https://arxiv.org/abs/2106.10978.

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Correspondence to Dominik Dürrschnabel or Maren Koyda .

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Dürrschnabel, D., Koyda, M., Stumme, G. (2021). Attribute Selection Using Contranominal Scales. In: Braun, T., Gehrke, M., Hanika, T., Hernandez, N. (eds) Graph-Based Representation and Reasoning. ICCS 2021. Lecture Notes in Computer Science(), vol 12879. Springer, Cham. https://doi.org/10.1007/978-3-030-86982-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-86982-3_10

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