ICFCA 2017: Formal Concept Analysis pp 56-71 | Cite as

Making Use of Empty Intersections to Improve the Performance of CbO-Type Algorithms

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10308)

Abstract

This paper describes how improvements in the performance of Close-by-One type algorithms can be achieved by making use of empty intersections in the computation of formal concepts. During the computation, if the intersection between the current concept extent and the next attribute-extent is empty, this fact can be simply inherited by subsequent children of the current concept. Thus subsequent intersections with the same attribute-extent can be skipped. Because these intersections require the testing of each object in the current extent, significant time savings can be made by avoiding them. The paper also shows how further time savings can be made by forgoing the traditional canonicity test for new extents, if the intersection is empty. Finally, the paper describes how, because of typical optimizations made in the implementation of CbO-type algorithms, even more time can be saved by amalgamating inherited attributes with inherited empty intersections into a single, simple test.

Keywords

Formal Concept Analysis FCA FCA algorithms Computing formal concepts Canonicity test Close-by-One CbO In-Close 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Stumme, G., Taouil, R., Bastide, Y., Lakhal, L.: Conceptual clustering with iceberg concept lattices. In: Proceedings of GI-Fachgruppentreffen Maschinelles Lernen (FGML01) (2001)Google Scholar
  2. 2.
    Valtchev, P., Grosser, D., Roume, C., Hacene, M.R.: Galicia: an open platform for lattices. In: de Moor, A., Ganter, B. (eds.) Using Conceptual Structures: Contributions to 11th International Conference on Conceptual Structures, pp. 241–254 (2003)Google Scholar
  3. 3.
    Andrews, S., Orphanides, C.: Knowledge discovery through creating formal contexts. In: IEEE Computer Society, pp. 455–460 (2010)Google Scholar
  4. 4.
    Pensa, R.G., Boulicaut, J.-F.: Towards fault-tolerant formal concept analysis. In: Bandini, S., Manzoni, S. (eds.) AI*IA 2005. LNCS, vol. 3673, pp. 212–223. Springer, Heidelberg (2005). doi: 10.1007/11558590_22 CrossRefGoogle Scholar
  5. 5.
    Dau, F.: An implementation for fault tolerance and experimental results. In: CUBIST Workshop, pp. 21–30 (2013)Google Scholar
  6. 6.
    Andrews, S., Hirsch, L.: A tool for creating and visualising formal concept trees. In: CEUR Workshop Proceedings: Proceedings of the Fifth Conceptual Structures Tools and Interoperability Workshop (CSTIW 2016), vol. 1637, pp. 1–9 (2016)Google Scholar
  7. 7.
    Liu, M., Shao, M., Zhang, W., Wu, C.: Reduction method for concept lattices based on rough set theory and its application. Comput. Math. Appl. 53, 1390–1410 (2007)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Gaume, B., Navarro, E., Prade, H.: Clustering bipartite graphs in terms of approximate formal concepts and sub-contexts. Int. J. Comput. Intell. Syst. 6, 1125–1142 (2013)CrossRefGoogle Scholar
  9. 9.
    ATHENA: The European ATHENA Project - use of new smart devices and social media in crisis situations. http://www.projectathena.eu/. Accessed September 2016
  10. 10.
    Andrews, S., Yates, S., Akhgar, B., Fortune, D.: Strategic intelligence management: national security imperatives and information and communication technologies. In: The ATHENA Project: Using Formal Concept Analysis to Facilitate the Actions of Responders in a Crisis Situation, pp. 167–180. Butterworth-Heinemann, Elsevier (2013)Google Scholar
  11. 11.
    Andrews, S., Brewster, B., Day, T.: Organised crime and social media: detecting and corroborating weak signals of human trafficking online. In: Haemmerlé, O., Stapleton, G., Faron Zucker, C. (eds.) ICCS 2016. LNCS, vol. 9717, pp. 137–150. Springer, Cham (2016). doi: 10.1007/978-3-319-40985-6_11 Google Scholar
  12. 12.
    Kuznetsov, S.O.: Mathematical aspects of concept analysis. Math. Sci. 80, 1654–1698 (1996)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Krajca, P., Outrata, J., Vychodil, V.: Parallel recursive algorithm for FCA. In: Belohavlek, R., Kuznetsov, S. (eds.) Proceedings of Concept Lattices and their Applications (2008)Google Scholar
  14. 14.
    Krajca, P., Vychodil, V., Outrata, J.: Advances in algorithms based on CbO. In: Kryszkiewicz, M., Obiedkov, S. (eds.) CLA 2010. University of Sevilla, pp. 325–337 (2010)Google Scholar
  15. 15.
    Outrata, J., Vychodil, V.: Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. Inf. Sci. 185, 114–127 (2012)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Andrews, S.: In-close2, a high performance formal concept miner. In: Andrews, S., Polovina, S., Hill, R., Akhgar, B. (eds.) ICCS 2011. LNCS (LNAI), vol. 6828, pp. 50–62. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-22688-5_4 CrossRefGoogle Scholar
  17. 17.
    Andrews, S.: A ‘Best-of-Breed’ approach for designing a fast algorithm for computing fixpoints of Galois connections. Inf. Sci. 295, 633–649 (2015)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Andrews, S.: A partial-closure canonicity test to increase the efficiency of CbO-type algorithms. In: Hernandez, N., Jäschke, R., Croitoru, M. (eds.) ICCS 2014. LNCS, vol. 8577, pp. 37–50. Springer, Cham (2014). doi: 10.1007/978-3-319-08389-6_5 Google Scholar
  19. 19.
    Andrews, S.: In-close, a fast algorithm for computing formal concepts. In: Rudolph, S., Dau, F., Kuznetsov, S.O. (eds.) ICCS 2009, CEUR WS, vol. 483 (2009). http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-483/
  20. 20.
    Frank, A., Asuncion, A.: UCI machine learning repository (2010). http://archive.ics.uci.edu/ml

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Conceptual Structures Research Group, Communication and Computing Research Centre, Department of Computing, Faculty of Arts, Computing, Engineering and SciencesSheffield Hallam UniversitySheffieldUK

Personalised recommendations