Skip to main content

Attribute Selection Using Contranominal Scales

  • 261 Accesses

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


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.


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

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-86982-3_10
  • Chapter length: 15 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
USD   64.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-86982-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   84.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.


  1. 1.


  1. Albano, A., Chornomaz, B.: Why concept lattices are large - extremal theory for the number of minimal generators and formal concepts. In: 12th International Conference on Concept Lattices and Their Applications (CLA 2016). CEUR Workshop Proceedings, vol. 1466, pp. 73–86. (2015)

    Google Scholar 

  2. Boley, M., Gärtner, T., Grosskreutz, H.: Formal concept sampling for counting and threshold-free local pattern mining. In: SIAM International Conference on Data Mining (SDM 2010), pp. 177–188. SIAM (2010)

    Google Scholar 

  3. Bron, C., Kerbosch, J.: Finding all cliques of an undirected graph (algorithm 457). Commun. ACM 16(9), 575–576 (1973)

    CrossRef  Google Scholar 

  4. Czerniak, J., Zarzycki, H.: Application of rough sets in the presumptive diagnosis of urinary system diseases. In: Sołdek, J., Drobiazgiewicz, L. (eds.) Artificial Intelligence and Security in Computing Systems. The Springer International Series in Engineering and Computer Science, vol. 752, pp. 41–51. Springer, Boston (2002).

    CrossRef  Google Scholar 

  5. Dias, S., Vieira, N.: Reducing the size of concept lattices: the JBOS approach. In: 7th International Conference on Concept Lattices and Their Applications (CLA 2010). CEUR Workshop Proceedings, vol. 672, pp. 80–91. (2010)

    Google Scholar 

  6. Dua, D., Graff, C.: UCI machine learning repository (2017).

  7. Duffus, D., Rival, I.: Crowns in dismantlable partially ordered sets. In: 5th Hungarian Combinatorial Colloquium, vol. I, pp. 271–292 (1978)

    Google Scholar 

  8. Dürrschnabel, D., Hanika, T., Stumme, G.: Drawing order diagrams through two-dimension extension. CoRR arXiv:1906.06208 (2019)

  9. Dürrschnabel, D., Koyda, M., Stumme, G.: Attribute selection using contranominal scales [dataset], April 2021.

  10. Ganter, B., Wille, R.: Formal Concept Analysis - Mathematical Foundations. Springer, Heidelberg (1999).

    CrossRef  MATH  Google Scholar 

  11. Hanika, T., Hirth, J.: Knowledge cores in large formal contexts. CoRR arXiv:2002.11776 (2020)

  12. Hanika, T., Koyda, M., Stumme, G.: Relevant attributes in formal contexts. In: Endres, D., Alam, M., Şotropa, D. (eds.) ICCS 2019. LNCS (LNAI), vol. 11530, pp. 102–116. Springer, Cham (2019).

    CrossRef  Google Scholar 

  13. Hanika, T., Marx, M., Stumme, G.: Discovering implicational knowledge in wikidata. In: Cristea, D., Le Ber, F., Sertkaya, B. (eds.) ICFCA 2019. LNCS (LNAI), vol. 11511, pp. 315–323. Springer, Cham (2019).

    CrossRef  Google Scholar 

  14. Ho, V.T., Stepanova, D., Gad-Elrab, M.H., Kharlamov, E., Weikum, G.: Rule learning from knowledge graphs guided by embedding models. In: Vrandečić, D., et al. (eds.) ISWC 2018. LNCS, vol. 11136, pp. 72–90. Springer, Cham (2018).

    CrossRef  Google Scholar 

  15. Karp, R.: Reducibility among combinatorial problems. In: Proceedings of a Symposium on the Complexity of Computer Computations. The IBM Research Symposia Series, pp. 85–103. Plenum Press, New York (1972)

    Google Scholar 

  16. Koyda, M., Stumme, G.: Boolean substructures in formal concept analysis. CoRR arXiv:2104.07159 (2021)

  17. Kuitché, R., Temgoua, R., Kwuida, L.: A similarity measure to generalize attributes. In: 14th International Conference on Concept Lattices and Their Applications (CLA 2018). CEUR Workshop Proceedings, vol. 2123, pp. 141–152. (2018)

    Google Scholar 

  18. Kumar, C.: Knowledge discovery in data using formal concept analysis and random projections. Int. J. Appl. Math. Comput. Sci. 21(4), 745–756 (2011)

    CrossRef  Google Scholar 

  19. Kunegis, J.: KONECT: the Koblenz network collection. In: Proceedings of the 22nd International Conference on World Wide Web, pp. 1343–1350 (2013)

    Google Scholar 

  20. Kuznetsov, S.: Stability as an estimate of the degree of substantiation of hypotheses derived on the basis of operational similarity. Nauchno-Tekhnicheskaya Informatsiya, Seriya 2 24, 21–29 (1990)

    Google Scholar 

  21. Lozin, V.: On maximum induced matchings in bipartite graphs. Inf. Process. Lett. 81(1), 7–11 (2002)

    CrossRef  MathSciNet  Google Scholar 

  22. Rowley, D.: PC/BEAGLE. Expert. Syst. 7(1), 58–62 (1990)

    CrossRef  Google Scholar 

  23. Schlimmer, J.: Mushroom Records Drawn from the Audubon Society Field Guide to North American Mushrooms. GH Lincoff (Pres), New York (1981)

    Google Scholar 

  24. Seshapanpu, J.: Students performance in exams, November 2018.

  25. Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L.: Computing iceberg concept lattices with titanic. Data Knowl. Eng. 42(2), 189–222 (2002)

    CrossRef  Google Scholar 

  26. Wille, R.: Lattices in data analysis: how to draw them with a computer. In: Rival, I. (ed.) Algorithms and Order. NATO ASI Series (Series C: Mathematical and Physical Sciences), vol. 255, pp. 33–58. Springer, Dordrecht (1989).

    CrossRef  Google Scholar 

  27. Xiao, M., Tan, H.: Exact algorithms for maximum induced matching. Inf. Comput. 256, 196–211 (2017)

    CrossRef  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding authors

Correspondence to Dominik Dürrschnabel or Maren Koyda .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

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.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86981-6

  • Online ISBN: 978-3-030-86982-3

  • eBook Packages: Computer ScienceComputer Science (R0)