Representation of Data by Pseudoline Arrangements

  • Wolfgang Kollewe
Conference paper
Part of the Studies in Classification, Data Analysis and Knowledge Organization book series (STUDIES CLASS)

Abstract

Formal contexts are under certain conditions representable by oriented pseudoline arrangements. Oriented pseudoline arrangements respect the hierarchical order of concept lattices. The formal context is reconstructable out of an oriented pseudoline arrangement. The representation of oriented pseudoline arrangements are quite easy to understand. In general there is no sufficient condition to decide if a context is representable (pictorial) or not. There is an infinite class of minor-minimal non-pictorial contexts. This tells us that excluding a finite number of examples is never sufficient to guarantee that a formal context is pictorial. Oriented pseudoline arrangements are isomorphic to oriented matroids of rank 3. We can therefore use an algorithmic approach which is generating oriented matroids of rank 3 and decide wether a context is representable by an oriented pseudoline arrangement.

Keywords

Manifold 

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1993

Authors and Affiliations

  • Wolfgang Kollewe
    • 1
  1. 1.Forschungsgruppe Begriffsanalyse, Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtGermany

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