Advertisement

Probabilistic Concepts in Formal Contexts

  • Alexander Demin
  • Denis Ponomaryov
  • Evgeny Vityaev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7162)

Abstract

We generalize the main notions of Formal Concept Analysis with the ideas of the semantic probabilistic inference. We demonstrate that under standard restrictions, our definitions completely correspond to the original notions of Formal Concept Analysis. From the point of view of applications, we propose a method of recovering concepts in formal contexts in presence of noise on data.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Deogun, J., Jiang, L., Xie, Y., Raghavan, V.: Probability Logic Modeling of Knowledge Discovery in Databases. In: Zhong, N., Raś, Z.W., Tsumoto, S., Suzuki, E. (eds.) ISMIS 2003. LNCS (LNAI), vol. 2871, pp. 402–407. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)zbMATHCrossRefGoogle Scholar
  3. 3.
    Ganter, B., Stumme, G., Wille, R. (eds.): Formal Concept Analysis: Foundations and Applications. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  4. 4.
    Guigues, J.– L., Duquenne, V.: Families minimales d’implications informatives resultant d’un tableau de données binaires. Math. Sci. Humaines 95, 5–18 (1986)MathSciNetGoogle Scholar
  5. 5.
    Kovalerchuk, B., Vityaev, E.: Data Mining in Finance: Advances in Relational and Hybrid methods. Kluwer (2000)Google Scholar
  6. 6.
    Kuznetsov, S.: On the intractability of computing the Duquenne–Guigues base. J. UCS 10(8), 927–933 (2004)MathSciNetGoogle Scholar
  7. 7.
    Kuznetsov, S., Obiedkov, S.: Comparing performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. 14(2-3), 189–216 (2002)zbMATHCrossRefGoogle Scholar
  8. 8.
    van der Merwe, D., Obiedkov, S., Kourie, D.: AddIntent: A New Incremental Algorithm for Constructing Concept Lattices. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 372–385. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Smerdov, S., Vityaev, E.: Synthesis of logic, probability, and learning: Formalizing the concept of prediction. Siberian Electronic Mathematical Reports 6, 340–365 (2009) (in Russian, with english abstract)MathSciNetGoogle Scholar
  10. 10.
    Vityaev, E.: Knowledge Discovery. Computational Cognition. Models of Cognitive Processes, p. 293. Novosibirsk State University (2006) (in Russian)Google Scholar
  11. 11.
    Vityaev, E.: The logic of prediction. In: Proc. 9th Asian Logic Conference, pp. 263–276 (2006)Google Scholar
  12. 12.
    Vityaev, E., Kovalerchuk, B.: Empirical theories discovery based on the Measurement Theory. Mind and Machine 14(4), 551–573 (2005)CrossRefGoogle Scholar
  13. 13.
    Vityaev, E., Lapardin, K., Khomicheva, I., Proskura, A.: Transcription factor binding site recognition by regularity matrices based on the natural classification method. Intelligent Data Analysis 12(5), 495–512 (2008); Vityaev, E., Kolchanov, N. (eds.) Special Issue New Methods in BioinformaticsGoogle Scholar
  14. 14.
    Vityaev, E., Smerdov, S.: New definition of prediction without logical inference. In: Kovalerchuk, B. (ed.) Proc. IASTED Int. Conf. on Computational Intelligence (CI 2009), pp. 48–54 (2009)Google Scholar
  15. 15.
    Scientific Discovery website, http://math.nsc.ru/AP/ScientificDiscovery/

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander Demin
    • 1
  • Denis Ponomaryov
    • 1
  • Evgeny Vityaev
    • 2
  1. 1.Institute of Informatics SystemsNovosibirskRussia
  2. 2.Institute of MathematicsNovosibirskRussia

Personalised recommendations