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Iceberg Query Lattices for Datalog

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Conceptual Structures at Work (ICCS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3127))

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Abstract

In this paper we study two orthogonal extensions of the classical data mining problem of mining association rules, and show how they naturally interact. The first is the extension from a propositional representation to datalog, and the second is the condensed representation of frequent itemsets by means of Formal Concept Analysis (FCA). We combine the notion of frequent datalog queries with iceberg concept lattices (also called closed itemsets) of FCA and introduce two kinds of iceberg query lattices as condensed representations of frequent datalog queries. We demonstrate that iceberg query lattices provide a natural way to visualize relational association rules in a non-redundant way.

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References

  1. Agrawal, R., Imielinski, T., Swami, A.: Mining association rules between sets of items in large databases. In: Proc. SIGMOD Conf., pp. 207–216 (1993)

    Google Scholar 

  2. Agrawal, R., Srikant, R.: Fast algorithms for mining association rules. In: Proc. VLDB Conf. 1994, pp. 478–499 (1994) (Expanded version in IBM Report RJ9839)

    Google Scholar 

  3. Agrawal, R., Srikant, R.: Mining Sequential Patterns. In: Proc. 11th Intl. Conference on Data Engineering (ICDE 1995), Taipeh, Taiwan, March 1995, pp. 3–14 (1995)

    Google Scholar 

  4. Bastide, Y., Pasquier, N., Taouil, R., Stumme, G., Lakhal, L.: Mining minimal non-redundant association rules using frequent closed itemsets. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 972–986. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Bastide, Y., Taouil, R., Pasquier, N., Stumme, G., Lakhal, L.: Mining Frequent Patterns with Counting Inference. SIGKDD Explorations 2(2), 66–75 (2000) (Special Issue on Scalable Algorithms)

    Google Scholar 

  6. Bayardo, R.J.: Efficiently mining long patterns from databases. In: Proc. SIGMOD Conf., pp. 85–93 (1998)

    Google Scholar 

  7. Bayardo, R.J., Agrawal, R., Gunopulos, D.: Constraint-based rule mining in large, dense databases. In: Proc. ICDE Conf., pp. 188–197 (1999)

    Google Scholar 

  8. Brin, S., Motwani, R., Ullman, J.D., Tsur, S.: Dynamic itemset counting and implication rules for market basket data. In: Proc. SIGMOD Conf., pp. 255–264 (1997)

    Google Scholar 

  9. Carpineto, C., Romano, G.: GALOIS:An Order-Theoretic Approach to Conceptual Clustering. In: Machine Learning. Proc. ICML 1993, pp. 33–40. Morgan Kaufmann Prublishers, San Francisco (1993)

    Google Scholar 

  10. Dehaspe, L., Toivonen, H.: Discovery of frequent datalog patterns. Data Mining and Knowledge Discovery 3, 7–36 (1999)

    Article  Google Scholar 

  11. Dehaspe, L., Toivonen, H.: Discovery of Relational Association Rules. In: Džeroski, S., Lavrač, N. (eds.) Relational Data Mining, pp. 189–212. Springer, Heidelberg (2001)

    Google Scholar 

  12. Dicky, H., Dony, C., Huchard, M., Libourel, T.: On automatic class insertion with overloading. In: OOPSLA, pp. 251–267 (1996)

    Google Scholar 

  13. Fayyad, U.M., Piatetsky–Shapiro, G., Smyth, P., Uthurusamy, R. (eds.): Advances in knowledge discovery and data mining. AAAI Press, Cambridge (1996)

    Google Scholar 

  14. Ganter, B., Reuter, K.: Finding all closed sets: A general approach. Order, pp. 283–290. Kluwer Academic Publishers, Dordrecht (1991)

    Google Scholar 

  15. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  16. Godin, R., Mili, H., Mineau, G., Missaoui, R., Arfi, A., Chau, T.: Design of class hierarchies based on concept (Galois) lattices. TAPOS 4(2), 117–134 (1998)

    Google Scholar 

  17. Guigues, J.-L., Duquenne, V.: Famille minimale d’implication informatives résultant d’un tableau de données binaires. Mathématiques et Sciences Humaines 24(95), 5–18 (1986)

    MathSciNet  Google Scholar 

  18. Luxenburger, M.: Implications partielles dans un contexte. Mathématiques, Informatique et Sciences Humaines 29(113), 35–55 (1991)

    MathSciNet  Google Scholar 

  19. Luxenburger, M.: Partial implications. Part I of Implikationen, Abhängigkeiten und Galois Abbildungen. PhD thesis, TU Darmstadt. Shaker, Aachen (1993)

    Google Scholar 

  20. Mineau, G., Godin, G.R.: Automatic Structuring of Knowledge Bases by Conceptual Clustering. IEEE Transactions on Knowledge and Data Engineering 7(5), 824–829 (1995)

    Article  Google Scholar 

  21. Missikoff, M., Scholl, M.: An algorithm for insertion into a lattice: application to type classification. In: Litwin, W., Schek, H.-J. (eds.) FODO 1989. LNCS, vol. 367, pp. 64–82. Springer, Heidelberg (1989)

    Google Scholar 

  22. Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Pruning closed itemset lattices for association rules. In: Proc. 14ièmes Journées Bases de Données Avancées (BDA 1998), Hammamet, Tunisie, pp. 177–196 (1998)

    Google Scholar 

  23. Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Discovering frequent closed itemsets for association rules. In: Proc. ICDT Conf., pp. 398–416 (1999)

    Google Scholar 

  24. Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Efficient mining of association rules using closed itemset lattices. Journal of Information Systems 24(1), 25–46 (1999)

    Article  Google Scholar 

  25. Pasquier, N., Taouil, R., Bastide, Y., Stumme, G., Lakhal, L.: Generating a Condensed Representation for Association Rules. J. Intelligent Information Systems (JIIS) (accepted)

    Google Scholar 

  26. Pei, J., Han, J., Mao, R.: CLOSET: An efficient algorithm for mining frequent closed itemsets. In: Proc. ACMSIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery, pp. 21–30 (2000)

    Google Scholar 

  27. Schmitt, I., Saake, G.: Merging inheritance hierarchies for database integration. In: Proc. 3rd IFCIS Intl. Conf. on Cooperative Information Systems, NewYork City, Nework, USA, pp. 122–131 (August 20-22, 1998)

    Google Scholar 

  28. Srikant, R., Agrawal, R.: Mining generalized association rules. In: Proc. VLDB Conf. 1995, pp. 407–419 (1995)

    Google Scholar 

  29. Srikant, R., Vu, Q., Agrawal, R.: Mining association rules with item constraints. In: Proc. KDD Conf. 1997, pp. 67–73 (1997)

    Google Scholar 

  30. Strahringer, S., Wille, R.: Conceptual clustering via convex-ordinal structures. In: Opitz, O., Lausen, B., Klar, R. (eds.) Information and Classification, pp. 85–98. Springer, Heidelberg (1993)

    Google Scholar 

  31. Stumme, G.: Conceptual Knowledge Discovery with Frequent Concept Lattices. FB4-Preprint 2043, TU Darmstadt (1999)

    Google Scholar 

  32. Stumme, G.: Off to New Shores — Conceptual Knowledge Discovery and Processing. Intl. J. Human–Comuter Studies (IJHCS) 59(3), 287–325 ( 2003)

    Article  Google Scholar 

  33. Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L.: Fast Computation of Concept Lattices Using Data Mining Techniques In: Proc. 7th Intl. Workshop on Knowledge Representation Meets Databases, Berlin (August 21-22, 2000),CEUR workshop proceeding http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/

  34. Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L.: Intelligent Structuring and Reducing of Association Rules with Formal Concept Analysis. In: Baader, F., Brewka, G., Eiter, T. (eds.) KI 2001. LNCS (LNAI), vol. 2174, pp. 335–350. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  35. Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L.: Computing Iceberg Concept Lattices with Titanic. J. on Knowledge and Data Engineering (KDE) 42(2), 189–222 (2002)

    Article  MATH  Google Scholar 

  36. Waiyamai, K., Taouil, R., Lakhal, L.: Towards an object database approach for managing concept lattices. In: Embley, D.W. (ed.) ER 1997. LNCS, vol. 1331, pp. 299–312. Springer, Heidelberg (1997)

    Google Scholar 

  37. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered sets, Reidel, Dordrecht–Boston, pp. 445–470 (1982)

    Google Scholar 

  38. Yahia, A., Lakhal, L., Bordat, J.P., Cicchetti, R.: iO2: An algorithmic method for building inheritance graphs in object database design. In: Thalheim, B. (ed.) ER 1996. LNCS, vol. 1157, pp. 422–437. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  39. Zaki, M.J., Ogihara, M.: Theoretical Foundations of Association Rules. In: 3rd SIGMOD 1998 Workshop on Research Issues in Data Mining and Knowledge Discovery (DMKD), Seattle, WA, pp. 7:1–7:8 (June 1998)

    Google Scholar 

  40. Zaki, M.J., Hsiao, C.-J.: ChARM: An efficient algorithm for closed association rule mining. Technical Report 99–10, Computer Science Dept., Rensselaer Polytechnic Institute (October 1999)

    Google Scholar 

  41. Zaki, M.J.: Generating non-redundant association rules. In: Proc. KDD 2000, pp. 34–43 (2000)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Knowledge & Data Engineering Group, Department of Mathematics & Computer Science, University of Kassel, D–34121, Kassel, Germany

    Gerd Stumme

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  1. Gerd Stumme
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Editors and Affiliations

  1. Mathematics and Science Faculty, Darmstadt University of Applied Sciences, Schoefferstr. 3, D-64295, Darmstadt, Germany

    Karl Erich Wolff

  2. New Mexico State University,  

    Heather D. Pfeiffer

  3. Computer Science Department, Univ. of Alabama in Huntsville, AL 35899, Huntsville

    Harry S. Delugach

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Stumme, G. (2004). Iceberg Query Lattices for Datalog. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds) Conceptual Structures at Work. ICCS 2004. Lecture Notes in Computer Science(), vol 3127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27769-9_7

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  • DOI: https://doi.org/10.1007/978-3-540-27769-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22392-4

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