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)


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.


Anorexia Nervosa Euclidean Plane Concept Lattice Formal Context Formal Concept Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bokowski, J., Guedes De Oliveira, A., and Richter-Gebert, J. (1991), Algebraic varieties characterizing matroids and oriented matroids, Advances in Mathematics, 87, 160–185.CrossRefGoogle Scholar
  2. Bokowski, J., and Kollewe, W. (1992), On representing contexts in line arrangements, Order, (to appear).Google Scholar
  3. Bokowski, J., and Sturmfels, B. (1989), Computational synthetic geometry, Lecture Notes in Mathematics, 1355.Google Scholar
  4. Cordovil, R. (1983), Oriented matroids of rank three and arrangements of pseudolines, Annals of Discrete Math., 17, 219–223.Google Scholar
  5. Feger, H. (1989), Testdaten als Merkmalsvektoren, Beitrag zur Festschrift für Karl Josef Klauer, ‘Wissenschaft und Verantwortung’, Hogrefe, Göttingen.Google Scholar
  6. Folkman, J., and Lawrence, J. (1978), Oriented matroids, J. Combinatorial Theory, B 25, 199–236.Google Scholar
  7. Gabriel, K. R. (1981), Biplot display of multivariate matrices of data and diagnosis, in: V. Barnett (ed.), Interpreting multivariate data, Wiley, Chichester, 147–173.Google Scholar
  8. Ganter, B., and Wille, R. (1989), Conceptual scaling, in: F. Roberts (ed.), Applications of combinatorics and graph theory to the biological and social sciences, Springer Verlag, New York, 139–167CrossRefGoogle Scholar
  9. Ganter, B., and Wille, R. (1992), Formale Begriffsanalyse, Manuskript 75p.Google Scholar
  10. Grünbaum, B. (1972), Arrangements and spreads, American Math. Soc, Regional Conf. Ser. 10, Rhode Island.Google Scholar
  11. Kollewe, W. (1989), Evaluation of a survey with methods of formal concept analysis, in: O. Opitz (ed.), Conceptual and numerical analysis of data, Springer Verlag, Berlin-Heidelberg, 123–134.CrossRefGoogle Scholar
  12. Ringel, G. (1956), Teilungen der Ebene durch Geraden und topologische Geraden, Math. Zeitschrift, 64, 79–102.CrossRefGoogle Scholar
  13. Slater, P. (1977), The measurement of interpersonal space by grid technique, Vol. I and II, Wiley, New York, 1977.Google Scholar
  14. Spangenberg, N. and Wolff, K.E. (1988), Conceptual grid evaluation, in: H.H. Bock (ed.), Classification and related methods of data analysis, North-Holland, Amsterdam, 577–580Google Scholar
  15. Wille, R. (1984), Liniendiagramme hierarchischer Begriffssysteme, in: H. H. Bock (Hrsg.), Anwendungen der Klassifikation: Datenanalyse und numerische Klassifikation, Indeks-Verlag, Frankfurt, 32–51.Google Scholar
  16. Wille, R. (1987), Bedeutungen von Begriffsverbänden, in: B. Ganter, R. Wille, E. Wolff (Hrsg.), Beiträge zur Begriffsanalyse, B.I.-Wissenschaftsverlag, Mannheim-Wien-Zürich, 161–211Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1993

Authors and Affiliations

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

Personalised recommendations