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Dynamic Visualization of Generalized One-Sided Concept Lattices and Their Reductions

  • Miroslav SmatanaEmail author
  • Peter Butka
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 521)

Abstract

One of the approaches applied in data analysis is related to the theory of concept lattices, also known as Formal Concept Analysis (FCA), which is suitable for processing and analysis of object-attribute input data models. Concept lattice represents hierarchically organized structure of clusters of objects (concepts) based on the presence of their shared attributes. While basic FCA framework works only with binary input data tables, several approaches were introduced in order to process fuzzy attributes. The model of Generalized One-Sided Concept Lattices (GOSCL) is suitable to work with different types of attributes used in input data tables, which helped in understanding and interpretation of analysis. One of the main issues which remains is large number of concepts for visualization to user. The solution is to provide user with the reduction methods and advanced dynamic visualization of concept lattices and their reductions. In this paper we introduce and compare some of the implemented visualizations and reductions applied to concept lattices generated from input data.

Keywords

Formal concept analysis One-sided concept lattices Dynamic visualization Reductions 

Notes

Acknowledgments

The work presented in this paper was supported by the Slovak VEGA grant 1/0493/16 and Slovak KEGA grant 025TUKE-4/2015.

References

  1. 1.
    Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer Verlag, Berlin (1999)CrossRefzbMATHGoogle Scholar
  2. 2.
    Krajci, S.: A generalized concept lattice. Logic Journal of IGPL 13(5), 543–550 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Medina, J., Ojeda-Aciego, M., Ruiz-Calvino, J.: Formal concept analysis via multi-adjoint concept lattices. Fuzzy Set. Syst. 160, 130–144 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Pocs, J.: Note on generating fuzzy concept lattices via Galois connections. Inform. Sci. 185(1), 128–136 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Antoni, L., Krajci, S., Kridlo, O., Macek, B., Piskova, L.: On heterogeneous formal contexts. Fuzzy Set. Syst. 234, 22–33 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Krajci, S.: Cluster based efficient generation of fuzzy concepts. Neural Netw. World 13(5), 521–530 (2003)MathSciNetGoogle Scholar
  7. 7.
    Butka, P., Pocs, J.: Generalization of one-sided concept lattices. Comput. Inf. 32(2), 355–370 (2013)MathSciNetGoogle Scholar
  8. 8.
    Butka, P., Pocs, J., Pocsova, J.: Use of concept lattices for data tables with different types of attributes. J. Inf. Organ. Sci. 36(1), 1–12 (2012)Google Scholar
  9. 9.
    Butka, P., Pocs, J., Pocsova, J.: On equivalence of conceptual scaling and generalized one-sided concept lattices. Inform. Sci. 259, 57–70 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Butka, P., Pocsova, J., Pocs, J.: Design and implementation of incremental algorithm for creation of generalized one-sided concept lattices. In: Proceedings of CINTI 2012, Budapest, Hungary, pp. 373–378 (2011)Google Scholar
  11. 11.
    Butka, P., Pocs, J., Pocsová, J.: Reduction of concepts from generalized one-sided concept lattice based on subsets quality measure. Adv. Intell. Syst. Comput. 314, 101–111 (2015)CrossRefGoogle Scholar
  12. 12.
    Antoni, L., Krajci, S., Kridlo, O.: Randomized fuzzy formal contexts and relevance of one-sided concepts. LNAI (Subseries of LNCS) 9113, 183–199 (2014)zbMATHGoogle Scholar
  13. 13.
    Melo, C., Le-Grand, B., Aufaure, A.: Browsing large concept lattices through tree extraction and reduction methods. Int. J. Intell. Inf. Technol. (IJIIT) 9(4), 16–34 (2013)CrossRefGoogle Scholar
  14. 14.
    Gajdos, P., Moravec, P., Snasel, V.: Concept lattice generation by singular value decomposition. In: Proceedings of CLA 2004, pp. 13–22 (2004)Google Scholar
  15. 15.
    Snasel, V., Polovincak, M., Abdulla, H.: Concept lattice reduction by singular value decomposition. In: Proceedings of the SYRCoDIS 2007, Moscow, Russia (2007)Google Scholar
  16. 16.
    Kumar, ChA, Srinivas, S.: Concept lattice reduction using fuzzy K-Means clustering. Expert Syst. Appl. 37(3), 2696–2704 (2010)CrossRefGoogle Scholar
  17. 17.
    Dias, S., Vieira, N.: Reducing the size of concept lattices: the JBOS approach. In: Proceedings of CLA 2010, pp. 80–91 (2010)Google Scholar
  18. 18.
    Quan, T., Hui, S., Cao, T.: A fuzzy FCA-based approach to conceptual clustering for automatic generation of concept hierarchy on uncertainty data. In: Proceedings of CLA 2004, pp. 1–12 (2004)Google Scholar
  19. 19.
    Lengler, R., Eppler, M.: Towards a periodic table of visualization methods for management. In: Proceedings of the International Conference on Graphic and Visualization in Engineering (GVE 2007), Clearwater, Florida, pp. 83–88 (2007)Google Scholar
  20. 20.
    Wills, G.: Visualizing hierarchical data. In: Encyclopedia of Database Systems, pp. 3425–3432 (2009)Google Scholar
  21. 21.
    Theron, R.: Hierarchical-temporal data visualization using a tree-ring metaphor. In: Smart Graphics. Springer, Berlin, pp. 70–81 (2006)Google Scholar
  22. 22.
    Itoh, T., Yamaguchi, Y., Ikehata, Y., Kajinaga, Y.: Hierarchical data visualization using a fast rectangle-packing algorithm. IEEE Trans. Visual Comput. Graphics 10(3), 302–313 (2004)CrossRefGoogle Scholar
  23. 23.
    Neumann, P., Schlechtweg, S., Carpendale, S.: ArcTrees: Visualizing relations in hierarchical data. In: Proceedings of EuroVis 2005, pp. 53–60 (2005)Google Scholar
  24. 24.
    Jadeja, M., Shah, K.: Tree-map: A visualization tool for large data. In: Proceedings of 1st International Workshop on Graph Search and Beyond (GSB 2015), pp. 9–13 (2015)Google Scholar
  25. 25.
    Gotz, D.: Dynamic Voronoi Treemaps: a visualization technique for time-varying hierarchical data. IBM Research Technical Report, RC25132 (2011)Google Scholar
  26. 26.
    Crampes, M., Oliveira-Kumar, J., Ranwez, S., Villerd, J.: Visualizing social photos on a hasse diagram for eliciting relations and indexing new photos. IEEE Trans. Visual Comput. Graphics 15(6), 985–992 (2009)CrossRefGoogle Scholar
  27. 27.
    Fattore, M., Arcagni, A., Barberis, S.: Visualizing partially ordered sets for socioeconomic analysis. Revista Colombiana de Estadística 37(2), 437–450 (2014)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Holten, D.: Hierarchical edge bundles: visualization of adjacency relations in hierarchical data. IEEE Trans. Visual Comput. Graphics 12(5), 741–748 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Cybernetics and Artificial Intelligence, Faculty of Electrical Engineering and InformaticsTechnical University of KosiceKosiceSlovakia

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