Basic Level Concepts as a Means to Better Interpretability of Boolean Matrix Factors and Their Application to Clustering

  • Petr Krajča
  • Martin Trnecka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11144)


We present an initial study linking in cognitive psychology well known phenomenon of basic level concepts and a general Boolean matrix factorization method. The result of this fusion is a new algorithm producing factors that explain a large portion of the input data and that are easy to interpret. Moreover, the link with the cognitive psychology allowed us to design a new clustering algorithm that groups objects into clusters that are close to human perception. In addition we present experiments that provide insight to the relationship between basic level concepts and Boolean factors.


  1. 1.
    Andrews, S.: Making use of empty intersections to improve the performance of CbO-type algorithms. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds.) ICFCA 2017. LNCS (LNAI), vol. 10308, pp. 56–71. Springer, Cham (2017). Scholar
  2. 2.
    Belohlavek, R., Outrata, J., Trnecka, M.: How to assess quality of BMF algorithms? In: Yager, R.R., Sgurev, V.S., Hadjiski, M., Jotsov, V.S. (eds.) Proceeding of International Conference on Intelligent Systems, IS 2016. pp. 227–233 (2016)Google Scholar
  3. 3.
    Belohlavek, R., Trnecka, M.: Basic Level of Concepts in Formal Concept Analysis. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds.) ICFCA 2012. LNCS (LNAI), vol. 7278, pp. 28–44. Springer, Heidelberg (2012). Scholar
  4. 4.
    Belohlavek, R., Trnecka, M.: Basic level in formal concept analysis: Interesting concepts and psychological ramifications. In: Rossi, F. (ed.) Proceedings of the 23rd International Joint Conference on Artificial Intelligence, IJCAI 2013. pp. 1233–1239 (2013)Google Scholar
  5. 5.
    Belohlavek, R., Trnecka, M.: From-below approximations in boolean matrix factorization: Geometry and new algorithm. J. Comput. Syst. Sci. 81(8), 1678–1697 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Belohlavek, R., Vychodil, V.: Discovery of optimal factors in binary data via a novel method of matrix decomposition. J. Comput. Syst. Sci. 76(1), 3–20 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Dheeru, D., Karra Taniskidou, E.: UCI machine learning repository (2017),
  8. 8.
    Farhadi, A., Endres, I., Hoiem, D., Forsyth, D.A.: Describing objects by their attributes. In: Proceedings of Conference on Computer Vision and Pattern Recognition (CVPR 2009). pp. 1778–1785 (2009)Google Scholar
  9. 9.
    Ganter, B., Wille, R.: Formal concept analysis - mathematical foundations. Springer (1999)Google Scholar
  10. 10.
    Gottwald, S.: A Treatise on Many-Valued Logics, vol. 3. research studies press Baldock (2001)Google Scholar
  11. 11.
    Krajca, P., Outrata, J., Vychodil, V.: Computing formal concepts by attribute sorting. Fundam. Inform. 115(4), 395–417 (2012)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Krajča, P.: Rank-aware clustering of relational data: Organizing search results. In: USB Proceedings The 13th International Conference on Modeling Decisions for Artificial Intelligence, pp. 61–72. (2016)Google Scholar
  13. 13.
    Lucchese, C., Orlando, S., Perego, R.: Mining top-\(k\) patterns from binary datasets in presence of noise. Proceedings of the International Conference on Data Mining, SDM 2010, 165–176 (2010)Google Scholar
  14. 14.
    Lucchese, C., Orlando, S., Perego, R.: A unifying framework for mining approximate top-\(k\) binary patterns. IEEE Trans. Knowl. Data Eng. 26(12), 2900–2913 (2014)CrossRefGoogle Scholar
  15. 15.
    Miettinen, P.: Matrix decomposition methods for data mining: Computational complexity and algorithms. Ph.D. thesis (2009)Google Scholar
  16. 16.
    Outrata, J., Vychodil, V.: Fast algorithm for computing fixpoints of galois connections induced by object-attribute relational data. Inf. Sci. 185(1), 114–127 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Computer SciencePalacky University OlomoucOlomoucCzech Republic

Personalised recommendations