Concept Lattices

  • Octavian Iordache
Part of the Understanding Complex Systems book series (UCS)


Formal concept analysis for multi-dimensional data analysis is highlighted by examples.

Polyadic and temporal formal concept analyses are presented in general PSM framework.

The relation between OLAP (On-Line Analytical Processing) and lattices is outlined.

Computational biochemistry case studies are based on entropy criteria.

Emergent computing capabilities for Physarum systems are evaluated.

Multivariate analysis is correlated to hierarchical classes and formal concept analysis.


Edit Distance Concept Lattice Data Cube Gene Expression Dataset Formal Context 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adamatzky, A.: Physarum machine: implementation of a Kolmogorov-Uspensky machine on a biological substrate. Parallel Processing Letters 17, 455–467 (2007)MathSciNetCrossRefGoogle Scholar
  2. Alqadah, F.: Clustering of Multi-Domain Information Networks. PhD. Thesis. University of Cincinnati, Engineering: Computer Science and Engineering (2010)Google Scholar
  3. Alqadah, F., Bhatnagar, R.: An effective algorithm for mining 3-clusters in vertically partitioned data. In: CIKM 2008: Proceeding of the 17th ACM Conference on Information and Knowledge Management, CIKM 2008, New York, NY, USA, pp. 1103–1112 (2008)Google Scholar
  4. Backhouse, R., Bijsterveld, M.: Category Theory as Coherently Constructive Lattice Theory: An Illustration. Techical Report. Eindhoven University of Technology (1994)Google Scholar
  5. Belohlavek, R., Vychodil, V.: Discovery of optimal factors in binary data via a novel method of matrix decomposition. J. Computer and System Sciences 76, 3–20 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  6. Berson, A., Smith, S.J.: Data Warehousing, Data Mining, and OLAP. McGraw-Hill (1997)Google Scholar
  7. Cerf, L.: Constraint-Based Mining of Closed Patterns in Noisy n-ary Relations. PhD. Thesis. INSA-Lyon (July 2010)Google Scholar
  8. Ceulemans, E., Van Mechelen, I., Leenen, I.: Tucker3 hierarchical classes analysis. Psychometrika 68, 413–433 (2003)MathSciNetCrossRefGoogle Scholar
  9. Chen, Y.H., Yao, Y.Y.: Formal concept analysis based on hierarchical class analysis. In: Proceedings of the 4th IEEE International Conference on Cognitive Informatics, ICCI 2005, pp. 285–292 (2005)Google Scholar
  10. Choi, V., Huang, Y., Lam, V., Potter, D., Laubenbacher, R., Duca, K.: Using Formal Concept Analysis for Microarray Data Comparison. Advances in Bioinformatics and Computational Biology 5, 57–66 (2006)Google Scholar
  11. Dau, F., Wille, R.: On the Modal Understanding of Triadic Contexts. In: Decker, R., Gaul, W. (eds.) Proc. Gesellschaft für Klassifikation, Classification and Information Processing at the Turn of the Milenium (2001)Google Scholar
  12. Dehne, F., Eavis, T., Hambrusch, S., Rau-Chaplin, A.: Parallelizing the data cube. Distributed and Parallel Databases 11(2), 181–201 (2002)zbMATHGoogle Scholar
  13. Deshmukh, M.A.: Concept Based Genomic Data Exploration System. M.Sc. Thesis. University of Cincinnati, Engineering: Computer Science and Engineering (2008)Google Scholar
  14. Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Berlin (1999)zbMATHCrossRefGoogle Scholar
  15. Gunji, Y.-P., Kusunoki, Y., Aono, M.: Interface of global and local semantics in a self-navigating system based on the concept lattice. Chaos, Solitons Fractals 13(2), 261–284 (2002)zbMATHCrossRefGoogle Scholar
  16. Huyn, N.: Scientific OLAP for the Biotech Domain. In: Proceedings of the 27th VLDB Conference, Roma, Italy (2001)Google Scholar
  17. Hwang, S.-H., Kang, Y.-K.: Applying Hierachical Classes Analysis to Triadic context for Folksonomy Mining. In: International Conference on Convergence Information Technology, ICCIT 2006, pp. 103–109 (2007)Google Scholar
  18. Lambek, J.: A fixpoint theorem for complete categories. Mathematische Zeitschrift 103, 151–161 (1968)MathSciNetzbMATHCrossRefGoogle Scholar
  19. Lehmann, F., Wille, R.: A Triadic Approach to Formal Concepts Analysis. In: Ellis, G., Rich, W., Levinson, R., Sowa, J.F. (eds.) ICCS 1995. LNCS, vol. 954, pp. 32–43. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  20. Potter, D.P.: A combinatorial approach to scientific exploration of gene expression data: An integrative method using Formal Concept Analysis for the comparative analysis of microarray data. Thesis dissertation. Department of Mathematics. Virginia Tech. (August 2005)Google Scholar
  21. Stumme, G.: Exploring Conceptual Similarities of Objects for Analyzing Inconsistences in Relational Databases. In: Proc. Workshop on Knowledge Discovery and Data Mining, 5th Pacific Rim Intl. Conf. on Artificial Intelligence, Singapore, November 22-27, pp. 41–50 (1998)Google Scholar
  22. Stumme, G.: A Finite State Model for On-Line Analytical Processing in Triadic Contexts. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 315–328. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  23. Tsuda, S., Aono, M., Gunji, Y.P.: Robust and emergent Physarum logical-computing. Biosystems 73(1), 45–55 (2004)CrossRefGoogle Scholar
  24. Van Mechelen, I., Lombardi, L., Ceulemans, E.: Hierarchical classes modeling of rating data. Psychometrika 72, 475–488 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  25. Voutsadakis, G.: Polyadic Concept Analysis. Order 19, 295–304 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  26. Wille, R.: The basic theorem of triadic concept analysis. Order 12, 149–158 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  27. Wille, R.: Restructuring mathematical logic: an approach based on Peirce’s pragmatism. In: Ursini, A., Agliano, P. (eds.) Logic and Algebra, pp. 267–281. Marcel Dekker, New York (1996a)Google Scholar
  28. Wille, R.: Conceptual structures of multicontexts. In: Eklund, P.W., Ellis, G., Mann, G. (eds.) Conceptual Structures: Knowledge Representation of Interlingua, pp. 23–39. Springer, Heidelberg (1996b)CrossRefGoogle Scholar
  29. Wollbold, J.: Attribute Exploration of Discrete Temporal Transitions. In: Kuznetsov, S.O., Schmidt, S. (eds.) ICFCA 2007. LNCS (LNAI), vol. 4390, pp. 121–130. Springer, Heidelberg (2007)Google Scholar
  30. Wollbold, J., Guthke, R., Ganter, B.: Constructing a Knowledge Base for Gene Regulatory Dynamics by Formal Concept Analysis Methods. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds.) AB 2008. LNCS, vol. 5147, pp. 230–244. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  31. Wollbold, J., Huber, R., Kinne, R., Wolff, K.E.: Conceptual Representation of Gene Expression Processes. In: Wolff, K.E., Palchunov, D.E., Zagoruiko, N.G., Andelfinger, U. (eds.) KONT 2007 and KPP 2007. LNCS, vol. 6581, pp. 79–100. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  32. Wolff, K.E.: Temporal Concept Analysis. In: Mephu Nguifo, E., et al. (eds.) ICCS 2001 International Workshop on Concept Lattices-Based Theory, Methods and Tools for Knowledge Discovery in Databases, pp. 91–107. Stanford University, Palo Alto, CA (2001)Google Scholar
  33. Wolff, K.E.: States, Transitions, and Life Tracks in Temporal Concept Analysis. In: Ganter, B., Stumme, G., Wille, R. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3626, pp. 127–148. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  34. Wolff, K.E.: Applications of Temporal Conceptual Semantic Systems. In: Wolff, K.E., Palchunov, D.E., Zagoruiko, N.G., Andelfinger, U. (eds.) KONT 2007 and KPP 2007. LNCS, vol. 6581, pp. 59–78. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.PolystochasticMontrealCanada

Personalised recommendations