Advertisement

Formal Concept Analysis

  • Gerd Stumme
Chapter
Part of the International Handbooks on Information Systems book series (INFOSYS)

Summary

Formal concept analysis (FCA) is a mathematical theory about concepts and concept hierarchies. Based on lattice theory, it allows to derive concept hierarchies from datasets. In this survey, we recall the basic notions of FCA, including its relationship to folksonomies. The survey is concluded by a list of FCA based knowledge engineering solutions.

Keywords

Association Rule Description Logic Frequent Itemsets Concept Lattice 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.

References

  1. 1.
    R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large databases. In Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data (SIGMOD’93), pages 207–216. ACM, New York, 1993.Google Scholar
  2. 2.
    A. Arnauld and P. Nicole. La logique ou l’art de penser – Contenant, outre les règles communes, plusieurs observations nouvelles, propres à former le jugement. Ch. Saveux, 1668.Google Scholar
  3. 3.
    F. Baader. Computing a minimal representation of the subsumption lattice of all conjunctions of concepts defined in a terminology. In Proceedings of the International Symposium on Knowledge Retrieval, Use, and Storage for Efficiency, KRUSE 95, pages 168–178, Santa Cruz, USA, 1995.Google Scholar
  4. 4.
    F. Baader, B. Ganter, B. Sertkaya, and U. Sattler. Completing description logic knowledge bases using formal concept analysis. In M. M. Veloso, editor, Proc. IJCAI 2007, pages 230–235, 2007.Google Scholar
  5. 5.
    Y. Bastide, R. Taouil, N. Pasquier, G. Stumme, and L. Lakhal. Mining frequent patterns with counting inference. SIGKDD Explorations, Special Issue on Scalable Algorithms, 2(2):71–80, 2000.zbMATHGoogle Scholar
  6. 6.
    K. Biedermann. How triadic diagrams represent conceptual structures. In D. Lukose, H. S. Delugach, M. Keeler, L. Searle, and J. F. Sowa, editors, Conceptual Structures: Fulfilling Peirce’s Dream, number 1257 in LNAI, pages 304–317. Springer, Heidelberg, 1997.CrossRefGoogle Scholar
  7. 7.
    K. Biedermann. Triadic Galois connections. In K. Denecke and O. Lders, editors, General Algebra and Applications in Discrete Mathematics, pages 23–33. Shaker, Aachen, 1997.Google Scholar
  8. 8.
    J.-F. Boulicaut, A. Bykowski, and C. Rigotti. Approximation of frequency queries by means of free-sets. In PKDD ’00: Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery, pages 75–85. Springer, London, 2000.Google Scholar
  9. 9.
    A. Bykowski and C. Rigotti. A condensed representation to find frequent patterns. In PODS ’01: Proceedings of the Twentieth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pages 267–273. ACM Press, New York, 2001.Google Scholar
  10. 10.
    T. Calders and B. Goethals. Mining all non-derivable frequent itemsets. In PKDD, pages 74–85, 2002.Google Scholar
  11. 11.
    C. Carpineto and G. Romano. Galois : An order-theoretic approach to conceptual clustering. In Proceedings of the 10th International Conference on Machine Learning (ICML’90), pages 33–40, July 1993.Google Scholar
  12. 12.
    C. Carpineto and G. Romano. Concept Data Analysis. Wiley, New York, 2004.CrossRefzbMATHGoogle Scholar
  13. 13.
    L. Chaudron and N. Maille. Generalized formal concept analysis. In B. Ganter and G. W. Mineau, editors, ICCS, volume 1867 of Lecture Notes in Computer Science, pages 357–370. Springer, Berlin, 2000.Google Scholar
  14. 14.
    P. Cimiano, A. Hotho, and S. Staab. Learning concept hierarchies from text corpora using formal concept analysis. Journal on Artificial Intelligence Research, 24:305–339, 2005.zbMATHGoogle Scholar
  15. 15.
    P. Cimiano, A. Hotho, G. Stumme, and J. Tane. Conceptual knowledge processing with formal concept analysis and ontologies. In P. Eklund, editor, Concept Lattices, volume 2961 of LNAI, pages 189–207, Heidelberg, 2004. Second International Conference on Formal Concept Analysis, ICFCA 2004, Springer, Berlin, 2004.Google Scholar
  16. 16.
    R. J. Cole, P. W. Eklund, and G. Stumme. Document retrieval for email search and discovery using formal concept analysis. Journal of Applied Artificial Intelligence (AAI), 17(3):257–280, 2003.CrossRefGoogle Scholar
  17. 17.
    F. Dau and R. Wille. On the modal understanding of triadic contexts. In R. Decker and W. Gaul, editors, Classification and Information Processing at the Turn of the Millennium, Proc. Gesellschaft für Klassifikation, 2001.Google Scholar
  18. 18.
    Deutsches Institut für Normung. DIN 2331: Begriffssysteme und ihre Darstellung, 1980.Google Scholar
  19. 19.
    Deutsches Institut für Normung. DIN 2330: Begriffe und Benennungen - Allgemeine Grundsätze, 1993.Google Scholar
  20. 20.
    J. Ducrou, B. Vormbrock, and P. W. Eklund. FCA-based browsing and searching of a collection of images. In Proc. of the 14th Int. Conference on Conceptual Structures. Springer, Berlin, 2006.Google Scholar
  21. 21.
    V. Duquenne and J.-L. Guigues. Famille minimale d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines, 24(95):5–18, 1986.Google Scholar
  22. 22.
    S. Ferré and O. Ridoux. A file system based on concept analysis. In J. W. Lloyd, V. Dahl, U. Furbach, M. Kerber, K.-K. Lau, C. Palamidessi, L. M. Pereira, Y. Sagiv, and P. J. Stuckey, editors, Computational Logic, volume 1861 of Lecture Notes in Computer Science, pages 1033–1047. Springer, Berlin, 2000.Google Scholar
  23. 23.
    S. Ferré and O. Ridoux. A logical generalization of formal concept analysis. In G. Mineau and B. Ganter, editors, Int. Conf. Conceptual Structures, LNCS 1867, pages 371–384. Springer, Berlin, 2000.Google Scholar
  24. 24.
    B. Ganter. Algorithmen zur Formalen Begriffsanalyse. In B. Ganter, R. Wille, and K. E. Wolff, editors, Beiträge zur Begriffsanalyse, pages 241–254. BI-Wissenschaftsverlag, Mannheim, 1987.Google Scholar
  25. 25.
    B. Ganter and S. A. Obiedkov. Implications in triadic contexts. In Conceptual Structures at Work: 12th International Conference on Conceptual Structures, volume 3127 of Lecture Notes in Computer Science, pages 186–195. Springer, Berlin, 2004.Google Scholar
  26. 26.
    B. Ganter, J. Stahl, and R. Wille. Conceptual measurement and many-valued contexts. In W. Gaul and M. Schader, editors, Classification as a Tool of Research, pages 169–176. North-Holland, Amsterdam, 1986.Google Scholar
  27. 27.
    B. Ganter and G. Stumme. Creation and merging of ontology top-levels. In A. de Moor, W. Lex, and B. Ganter, editors, Conceptual Structures for Knowledge Creation and Communication, volume 2746 of LNAI, pages 131–145. Springer, Heidelberg, 2003.CrossRefGoogle Scholar
  28. 28.
    B. Ganter, G. Stumme, and R. Wille, editors. Formal Concept Analysis – Foundations and Applications, volume 3626 of LNAI. Springer, Heidelberg, 2005.zbMATHGoogle Scholar
  29. 29.
    B. Ganter and R. Wille. Contextual attribute logic. In W. M. Tepfenhart and W. R. Cyre, editors, ICCS, volume 1640 of Lecture Notes in Computer Science, pages 377–388. Springer, Berlin, 1999.Google Scholar
  30. 30.
    B. Ganter and R. Wille. Formal Concept Analysis: Mathematical Foundations. Springer, 1999. Translation of: Formale Begriffs analyse: Mathematische Grundlagen. Springer, Heidelberg, 1996.Google Scholar
  31. 31.
    R. Godin and P. Valtchev. Formal Concept Analysis-Based Class Hierarchy Design in Object-Oriented Software Development, volume 3626 of LNAI, pages 304–323. Springer, Berlin, 2005.zbMATHGoogle Scholar
  32. 32.
    W. Hesse and T. A. Tilley. Formal Concept Analysis used for Software Analysis and Modelling, volume 3626 of LNAI, pages 288–303. Springer, Berlin, 2005.Google Scholar
  33. 33.
    A. Hotho, R. Jäschke, C. Schmitz, and G. Stumme. BibSonomy: A social bookmark and publication sharing system. In Proc. of the ICCS 2006 Conceptual Structures Tool Interoperability Workshop, 2006.Google Scholar
  34. 34.
    A. Hotho, R. Jäschke, C. Schmitz, and G. Stumme. Information retrieval in folksonomies: Search and ranking. In Proceedings of the 3rd European Semantic Web Conference, Lecture Notes in Computer Science. Springer, Berlin, 2006.Google Scholar
  35. 35.
    R. Jäschke, A. Hotho, C. Schmitz, B. Ganter, and G. Stumme. Trias – An algorithm for mining iceberg tri-lattices. In Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06), pages 907–911. IEEE Computer Society, Hong Kong, December 2006.Google Scholar
  36. 36.
    R. Jäschke, A. Hotho, C. Schmitz, B. Ganter, and G. Stumme. Discovering shared conceptualizations in folksonomies. Journal of Web Semantics, 6(1):38–53, 2008.CrossRefGoogle Scholar
  37. 37.
    W. Kollewe, M. Skorsky, F. Vogt, and R. Wille. TOSCANA – ein Werkzeug zur begrifflichen Analyse und Erkundung von Daten. In R. Wille and M. Zickwolff, editors, Begriffliche Wissensverarbeitung-Grundfragen und Aufgaben, pages 267–288. BI-Wissenschaftsverlag, Mannheim, 1994.Google Scholar
  38. 38.
    F. Lehmann and R. Wille. A triadic approach to formal concept analysis. In G. Ellis, R. Levinson, W. Rich, and J. F. Sowa, editors, Conceptual Structures: Applications, Implementation and Theory, volume 954 of Lecture Notes in Artificial Intelligence, pages 32–43. Springer, Berlin, 1995.CrossRefGoogle Scholar
  39. 39.
    M. Luxenburger. Implications partielles dans un contexte. Mathématiques, Informatique et Sciences Humaines, 29(113):35–55, 1991.MathSciNetzbMATHGoogle Scholar
  40. 40.
    G. Mineau and R. Godin. Automatic structuring of knowledge bases by conceptual clustering. IEEE Transactions on Knowledge and Data Engineering, 7(5):824–829, 1985.CrossRefGoogle Scholar
  41. 41.
    I. O. of Standardization. ISO 704. Terminology Work – Principles and Methods, 2000.Google Scholar
  42. 42.
    N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Pruning closed itemset lattices for association rules. In Actes des 14\grave{e}mes journées Bases de Donnes Avancées (BDA’98), pages 177–196, Octobre 1998.Google Scholar
  43. 43.
    N. Pasquier, R. Taouil, Y. Bastide, G. Stumme, and L. Lakhal. Generating a condensed representation for association rules. Journal of Intelligent Information Systems, 24(1):29–60, 2005.CrossRefzbMATHGoogle Scholar
  44. 44.
    C. S. Peirce. Collected Papers of Charles Sanders Peirce. Harvard University Press, Cambridge, 1931–1935, 1958.Google Scholar
  45. 45.
    S. Prediger. Logical scaling in formal concept analysis. In D. Lukose, H. Delugach, M. Keeler, L. Searle, and J. F. Sowa, editors, Conceptual Structures: Fulfilling Peirce’s Dream, number 1257 in Lecture Notes in Artificial Intelligence. Springer, Berlin, 1997.Google Scholar
  46. 46.
    S. Prediger and G. Stumme. Theory-driven logical scaling. In E. F. et al. editors, Proc. 6th Intl. Workshop Knowledge Representation Meets Databases (KRDB’99), volume CEUR Workshop Proc. 21, 1999. Also in P. Lambrix et al. editors, Proc. Intl. Workshop on Description Logics (DL’99). CEUR Workshop Proc. 22, 1999 http://ceur-ws.org/Vol-21.
  47. 47.
    F. Rioult. Extraction de connaissances dans les bases de données comportant des valeurs manquantes ou un grand nombre d’attributs. PhD thesis, Université de Caen Basse-Normandie, 2005.Google Scholar
  48. 48.
    S. Rudolph. Relational Exploration – Combining Description Logics and Formal Concept Analysis for Knowledge Specification. Universitätsverlag Karlsruhe, 2006. Dissertation.Google Scholar
  49. 49.
    C. Schmitz, A. Hotho, R. Jäschke, and G. Stumme. Mining association rules in folksonomies. In Proceedings of the IFCS 2006 Conference, Lecture Notes in Computer Science. Springer, July 2006.Google Scholar
  50. 50.
    G. Snelting. Reengineering of configurations based on mathematical concept analysis. ACM Trans. Softw. Eng. Methodol., 5(2):146–189, 1996.CrossRefGoogle Scholar
  51. 51.
    G. Snelting. Concept Lattices in Software Analysis, volume 3626 of LNAI, pages 272–287. Springer, Berlin, 2005.Google Scholar
  52. 52.
    G. Snelting and F. Tip. Understanding class hierarchies using concept analysis. ACM Trans. Program. Lang. Syst., 22(3):540–582, 2000.CrossRefGoogle Scholar
  53. 53.
    J. F. Sowa. Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley, Reading, MA, 1984.zbMATHGoogle Scholar
  54. 54.
    S. Staab, S. Santini, F. Nack, L. Steels, and A. Maedche. Emergent semantics. Intelligent Systems, IEEE [see also IEEE Expert], 17(1):78–86, 2002.Google Scholar
  55. 55.
    L. Steels. The origins of ontologies and communication conventions in multi-agent systems. Autonomous Agents and Multi-agent Systems, 1(2):169–194, October 1998.CrossRefGoogle Scholar
  56. 56.
    S. Strahringer and R. Wille. Conceptual clustering via convex-ordinal structures. In O. Opitz, B. Lausen, and R. Klar, editors, Information and Classification, pages 85–98. Springer, Berlin, 1993.CrossRefGoogle Scholar
  57. 57.
    G. Stumme. Knowledge acquisition by distributive concept exploration. In G. Ellis, R. Levinson, W. Rich, and J. F. Sowa, editors, Conceptual Structures: Applications, Implementation and Theory, number 954 in Lecture Notes in Artificial Intelligence. Springer, Berlin, 1995.Google Scholar
  58. 58.
    G. Stumme. The concept classification of a terminology extended by conjunction and disjunction. In N. Foo and R. Goebel, editors, PRICAI’96: Topics in Artificial Intelligence. Proc. PRICAI’96, volume 1114 of LNAI, pages 121–131. Springer, Heidelberg, 1996.Google Scholar
  59. 59.
    G. Stumme. Exploration tools in formal concept analysis. In E. Diday, Y. Lechevallier, and O. Opitz, editors, Ordinal and Symbolic Data Analysis. Proc. OSDA’95. Studies in Classification, Data Analysis, and Knowledge Organization 8, pages 31–44. Springer, Heidelberg, 1996.Google Scholar
  60. 60.
    G. Stumme. Concept exploration – A tool for creating and exploring conceptual hierarchies. In D. Lukose, H. Delugach, M. Keeler, L. Searle, and J. F. Sowa, editors, Conceptual Structures: Fulfilling Peirce’s Dream, Lecture Notes in Artificial Intelligence, volume 1257, pages 318–331. Springer, Berlin, 1997.CrossRefGoogle Scholar
  61. 61.
    G. Stumme. Conceptual knowledge discovery with frequent concept lattices. FB4-Preprint 2043, TU Darmstadt, 1999.Google Scholar
  62. 62.
    G. Stumme. A finite state model for on-line analytical processing in triadic contexts. In B. Ganter and R. Godin, editors, Proc. 3rd Intl. Conf. on Formal Concept Analysis, volume 3403 of LNCS, pages 315–328. Springer, Berlin, 2005.Google Scholar
  63. 63.
    G. Stumme and A. Maedche. FCA-Merge: Bottom-up merging of ontologies. In B. Nebel, editor, Proc. 17th Intl. Conf. on Artificial Intelligence (IJCAI ’01), pages 225–230, Seattle, WA, USA, 2001.Google Scholar
  64. 64.
    G. Stumme, R. Taouil, Y. Bastide, N. Pasqier, and L. Lakhal. Computing iceberg concept lattices with Titanic. Journal on Data and Knowledge Engineering, 42(2):189–222, 2002.CrossRefzbMATHGoogle Scholar
  65. 65.
    G. Stumme, R. Taouil, Y. Bastide, N. Pasquier, and L. Lakhal. Intelligent structuring and reducing of association rules with formal concept analysis. In F. Baader, G. Brewker, and T. Eiter, editors, KI 2001: Advances in Artificial Intelligence, volume 2174 of LNAI, pages 335–350. Springer, Heidelberg, 2001.CrossRefGoogle Scholar
  66. 66.
    V. Takcs. Two applications of Galois graphs in pedagogical research. Manuscript of a lecture given at TH Darmstadt, 60 pages, February 1984.Google Scholar
  67. 67.
    J. Tane. Using a query-based multicontext for knowledge base browsing. In Formal Concept Analysis, Third International Conf., ICFCA 2005-Supplementary Volume, pages 62–78. IUT de Lens, Universite d Artois, FEB 2006.Google Scholar
  68. 68.
    J. Tane, P. Cimiano, and P. Hitzler. Query-based multicontexts for knowledge base browsing: An evaluation. In H. Schärfe, P. Hitzler, and P. Øhrstrøm, editors, Proc. 14th Intl. Conf. on Conceptual Structures, volume 4068 of LNCS, pages 413–426. Springer, Berlin, 2006.Google Scholar
  69. 69.
    J. Tane, C. Schmitz, and G. Stumme. Semantic resource management for the Web: An e-learning application. In Proc. 13th International World Wide Web Conference (WWW 2004), pages 1–10, 2004.Google Scholar
  70. 70.
    T. A. Tilley, R. J. Cole, P. Becker, and P. W. Eklund. A Survey of Formal Concept Analysis Support for Software Engineering Activities, volume 3626 of LNAI, pages 250–271. Springer, Berlin, 2005.zbMATHGoogle Scholar
  71. 71.
    R. Wille. Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival, editor, Ordered Sets, pages 445–470. Reidel, Dordrecht, 1982.CrossRefGoogle Scholar
  72. 72.
    R. Wille. The basic theorem of triadic concept analysis. Order, 12:149–158, 1995.MathSciNetCrossRefzbMATHGoogle Scholar
  73. 73.
    R. Wille. Conceptual structures of multicontexts. In P. W. Eklund, G. Ellis, and G. Mann, editors, Conceptual Structures: Representation as Interlingua, pages 23–39. Springer, Berlin, 1996.CrossRefGoogle Scholar
  74. 74.
    R. Wille. Restructuring mathematical logic: An approach based on peirce’s pragmatism. In A. Ursini and P. Agliano, editors, Logic and Algebra, pages 267–281. Marcel Dekker, New York, 1996.Google Scholar
  75. 75.
    R. Wille. Conceptual graphs and formal concept analysis. In D. Lukose, H. Delugach, M. Keeler, L. Searle, and J. F. Sowa, editors, Conceptual Structures: Fulfilling Peirce’s Dream, volume 1257 of Lecture Notes in Artificial Intelligence, pages 290–303. Springer, Heidelberg, 1997.CrossRefGoogle Scholar
  76. 76.
    M. J. Zaki. Generating non-redundant association rules. In Proc. KDD 2000, pages 34–43, 2000.Google Scholar
  77. 77.
    M. J. Zaki and C.-J. Hsiao. Charm: An efficient algorithm for closed association rule mining. technical report 99–10. Technical report, Computer Science Dept., Rensselaer Polytechnic, October 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gerd Stumme
    • 1
    • 2
  1. 1.Hertie Chair for Knowledge & Data EngineeringUniversity of Kassel WilhelmshöherKasselGermany
  2. 2.Research Center L3SAppelstr. 9aHannoverGermany

Personalised recommendations