Advertisement

Empirically Evaluating the Similarity Model of Geist, Lengnink and Wille

  • Moritz Schubert
  • Dominik Endres
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10872)

Abstract

In applications of formal concept analysis to real-world data, it is often necessary to model a reduced set of attributes to keep the resulting concept lattices from growing unmanageably big. If the results of the modeling are to be used by humans, e.g. in search engines, then it is important that the similarity assessment matches human expectations. We therefore investigated experimentally if the set-theoretic reformulation of Tversky’s contrast model by Geist, Lengnink and Wille provides such a match. Predicted comparability and its direction was reflected in the human data. However, the model rated a much larger proportion of pairs as incomparable than human participants did, indicating a need for a refined similarity model.

Notes

Acknowledgements

The authors were supported by the DFG-CRC-TRR 135 ‘Cardinal Mechanisms of Perception’, project C6.

References

  1. 1.
    von Ahn, L., Dabbish, L.: Labeling images with a computer game. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. CHI 2004, pp. 319–326. ACM, New York (2004).  https://doi.org/10.1145/985692.985733
  2. 2.
    Ganter, B., Wille, R.: Formal Concept Analysis Mathematical Foundations. Springer, Heidelberg (1999).  https://doi.org/10.1007/978-3-642-59830-2CrossRefzbMATHGoogle Scholar
  3. 3.
    Geist, S., Lengnink, K., Wille, R.: An order-theoretic foundation for similarity measures. In: Lengnink, K. (ed.) Formalisierungen von Ähnlichkeit aus Sicht der Formalen Begriffsanalyse, pp. 75–87. Shaker Verlag (1996)Google Scholar
  4. 4.
    Kuznetsov, S.O.: On stability of a formal concept. Ann. Math. Artif. Intell. 49(1–4), 101–115 (2007)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Murphy, G.L.: The Big Book of Concepts 1. MIT Press, Cambridge (2004). MIT Press paperback ed. A Bradford bookGoogle Scholar
  6. 6.
    Schubert, M.: Empirische Überprüfung des generalisierten Kontrastmodells nach Lengnink. Geist und Wille, Marburg (2017)Google Scholar
  7. 7.
    Shepard, R.N.: The analysis of proximities: multidimensional scaling with an unknown distance function. I. Psychometrika 27(2), 125–140 (1962)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Shepard, R.N.: The analysis of proximities: multidimensional scaling with an unknown distance function. II. Psychometrica 27(3), 219–246 (1962)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Stumme, G., et al.: Conceptual clustering with iceberg concept lattices. In: Proceedings of GI-Fachgruppentreffen Maschinelles Lernen 2001. Universität DortmundGoogle Scholar
  10. 10.
    Tversky, A.: Features of similarity. 84(4), 327–352 (1977).  https://doi.org/10.1037/0033-295X.84.4.327

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Philipps University MarburgMarburgGermany

Personalised recommendations