Advertisement

A New Concise and Exact Representation of Data Cubes

  • Hanen Brahmi
  • Tarek Hamrouni
  • Riadh Ben Messaoud
  • Sadok Ben Yahia
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 398)

Abstract

To efficiently answer OLAP queries on data warehouses, pre-computed data cubes provide an interesting solution. Nevertheless, the amount of generated aggregated data is huge and requires large amounts of storage space and mining time. To address this issue, various research works highlighted the added-value of compact representations of data cubes from which the remaining redundant patterns can be derived. In this respect, we introduce in this chapter a new concise and exact representation called closed non derivable data cubes (CND-Cube), which is based on the concept of non derivable minimal generators. We also propose a novel algorithm dedicated to the mining of CND-Cube from multidimensional databases. Our experiment results show the effectiveness of our approach in comparison with those fitting in the same trend. In this comparison, we focus on the efficiency of our algorithm and the compactness of the storage space terms.

Keywords

Association Rule Minimal Generator Concise Representation Data Cube Exact Representation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Agrawal et al., 1993]
    Agrawal, R., Imielinski, T., Swami, A.: Mining Association Rules between Sets of Items in Large Databases. In: Proceedings of the ACM-SIGMOD International Conference on Management of Data, Washington, USA, pp. 207–216 (1993)Google Scholar
  2. [Agrawal and Srikant, 1994]
    Agrawal, R., Srikant, R.: Fast Algorithms for Mining Association Rules. In: Proceedings of the 20th International Conference on Very Large Data Bases (VLDB 1994), Santiago, Chile, pp. 478–499 (1994)Google Scholar
  3. [Bastide et al., 2000]
    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)CrossRefGoogle Scholar
  4. [Ben Messaoud et al., 2006]
    Ben Messaoud, R., Rabaséda, S.L., Boussaid, O., Missaoui, R.: Enhanced Mining of Association Rules from Data Cubes. In: Proceedings of the 9th ACM International Workshop on Data Warehousing and OLAP, Arlington, Virginia, USA, pp. 11–18 (2006)Google Scholar
  5. [Ben Yahia et al., 2009]
    Ben Yahia, S., Gasmi, G., Mephu Nguifo, E.: A New Generic Basis of Factual and Implicative Association Rules. Intelligent Data Analysis (IDA) 13(4), 633–656 (2009)Google Scholar
  6. [Beyer and Ramakrishnan, 1999]
    Beyer, K., Ramakrishnan, R.: Bottom-Up Computation of Sparse and Iceberg CUBEs. In: Proceedings of the 1999 ACM-SIGMOD International Conference on Management of Data (SIGMOD 1999), Philadelphia, Pennsylvania, USA, pp. 359–370 (1999)Google Scholar
  7. [Brahmi et al., 2009]
    Brahmi, H., Hamrouni, T., Ben Messaoud, R., Ben Yahia, S.: Closed Non Derivable Data Cubes Based on Non Derivable Minimal Generators. In: Huang, R., Yang, Q., Pei, J., Gama, J., Meng, X., Li, X. (eds.) ADMA 2009. LNCS, vol. 5678, pp. 55–66. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. [Brahmi et al., 2010]
    Brahmi, H., Hamrouni, T., Messaoud, R.B., Yahia, S.B.: CND-Cube: Nouvelle Représentation Concise Sans Perte d’Information d’un Cube de Données. In: Proceedings of the French-Speaking Conference on Knowledge Extraction and Management (EGC 2010), Hammamet, Tunisia, pp. 261–272 (2010)Google Scholar
  9. [Calders and Goethals, 2007]
    Calders, T., Goethals, B.: Non-Derivable Itemset Mining. Data Mining and Knowledge Discovery 14(1), 171–206 (2007)MathSciNetCrossRefGoogle Scholar
  10. [Casali et al., 2003a]
    Casali, A., Cicchetti, R., Lakhal, L.: Cube Lattices: A Framework for Multidimensional Data Mining. In: Proceedings of the 3rd SIAM International Conference on Data Mining, San Francisco, USA, pp. 304–308 (2003a)Google Scholar
  11. [Casali et al., 2003b]
    Casali, A., Cicchetti, R., Lakhal, L.: Extracting Semantics from Data Cubes using Cube Transversals and Closures. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, USA, pp. 69–78 (2003b)Google Scholar
  12. [Casali et al., 2009a]
    Casali, A., Cicchetti, R., Lakhal, L.: Closed Cubes Lattices. Annals of Information Systems 3, 145–165 (2009a); Special Issue on New Trends in Data Warehousing and Data AnalysisCrossRefGoogle Scholar
  13. [Casali et al., 2009b]
    Casali, A., Nedjar, S., Cicchetti, R., Lakhal, L., Novelli, N.: Lossless Reduction of Datacubes Using Partitions. International Journal of Data Warehousing and Mining (IJDWM) 4(1), 18–35 (2009b)CrossRefGoogle Scholar
  14. [Chaudhuri and Dayal, 1997]
    Chaudhuri, S., Dayal, U.: An Overview of Data Warehousing and OLAP Technology. SIGMOD Record 26(1), 65–74 (1997)CrossRefGoogle Scholar
  15. [Galambos and Simonelli, 2000]
    Galambos, J., Simonelli, I.: Bonferroni-type Inequalities with Applications. Springer (2000)Google Scholar
  16. [Ganter and Wille, 1999]
    Ganter, B., Wille, R.: Formal Concept Analysis. Springer (1999)Google Scholar
  17. [Gray et al., 1997]
    Gray, J., Chaudhuri, S., Bosworth, A., Layman, A., Reichart, D., Venkatrao, M.: Data Cube: A Relational Aggregation Operator Generalizing Group-by, Cross-Tab, and Sub Totals. Data Mining and Knowledge Discovery 1(1), 29–53 (1997)CrossRefGoogle Scholar
  18. [Ji et al., 2006]
    Ji, L., Tan, K.-L., Tung, A.K.H.: Mining Frequent Closed Cubes in 3D Datasets. In: Proceedings of the 32nd International Conference on Very Large Data Bases (VLDB 2006), Seoul, Korea, pp. 811–822 (2006)Google Scholar
  19. [Lakshmanan et al., 2002]
    Lakshmanan, L., Pei, J., Han, J.: Quotient Cube: How to Summarize the Semantics of a Data Cube. In: CAiSE 2002 and VLDB 2002, pp. 778–789 (2002)Google Scholar
  20. [Morfonios and Ioannidis, 2006]
    Morfonios, K., Ioannidis, Y.E.: Cure for Cubes: Cubing Using a ROLAP Engine. In: Proceedings of the 32nd International Conference on Very Large Data Bases, Seoul, Korea, pp. 379–390 (2006)Google Scholar
  21. [Muhonen and Toivonen, 2006]
    Muhonen, J., Toivonen, H.: Closed Non-Derivable Itemsets. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) PKDD 2006. LNCS (LNAI), vol. 4213, pp. 601–608. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. [Nedjar et al., 2010]
    Nedjar, S., Casali, A., Cicchetti, R., Lakhal, L.: Cube Fermés/ Quotients Émergents. In: Proceedings of the French-Speaking Conference on Knowledge Extraction and Management (EGC 2010), Hammamet, Tunisia, pp. 285–296 (2010)Google Scholar
  23. [Pasquier et al., 1999]
    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)CrossRefGoogle Scholar
  24. [Pedersen et al., 1999]
    Pedersen, T., Jensen, C., Dyreson, C.: Supporting Imprecision in Multidimensional Databases Using Granularities. In: Proceedings of the 11th International Conference on Scientific and Statistical Database Management (SSDBM 1999), Cleveland, Ohio, USA, pp. 90–101 (1999)Google Scholar
  25. [Ross and Srivastava, 1997]
    Ross, K., Srivastava, D.: Fast Computation of Sparse Data Cubes. In: Proceedings of the 23rd International Conference on Very Large Databases (VLDB 1997), Athens, Greece, pp. 116–125 (1997)Google Scholar
  26. [Shao et al., 2004]
    Shao, Z., Han, J., Xin, D.: MM-Cubing: Computing Iceberg Cubes by Factorizing the Lattice Space. In: Proceedings of the 16th International Conference on Scientific and Statistical Database Management (SSDBM 2004), Washington, DC, USA, pp. 213–222 (2004)Google Scholar
  27. [Sismanis et al., 2002]
    Sismanis, Y., Deligiannakis, A., Roussopoulos, N., Kotidis, Y.: Dwarf: Shrinking the Petacube. In: Proceedings of the 2002 ACM-SIGMOD International Conference on Management of Data (SIGMOD 2002), Madison, USA, pp. 464–475 (2002)Google Scholar
  28. [Stumme et al., 2002]
    Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L.: Computing Iceberg Concept Lattices with Titanic. Journal on Knowledge and Data Engineering (KDE) 2(42), 189–222 (2002)CrossRefGoogle Scholar
  29. [Wang and Iyer, 1997]
    Wang, M., Iyer, B.: Efficient Roll-Up and Drill-Down Analysis in Relational Databases. In: Proceedings of the Workshop on Research Issues on Data Mining and Knowledge Discovery (SIGMOD 1997), Tucson, Arizona, pp. 39–43 (1997)Google Scholar
  30. [Wang et al., 2002]
    Wang, W., Lu, H., Feng, J., Yu, J.: Condensed Cube: An Effective Approach to Reducing Data Cube Size. In: Proceedings of the 18th International Conference on Data Engineering (ICDE 2002), San Jose, USA, pp. 213–222 (2002)Google Scholar
  31. [Xin et al., 2003]
    Xin, D., Han, J., Li, X., Wah, B.: Star-Cubing: Computing Iceberg Cubes by Top-Down and Bottom-Up Integration. In: Proceedings of the 29th International Conference on Very Large Data Bases (VLDB 2003), Berlin, Germany, pp. 476–487 (2003)Google Scholar
  32. [Yannis and Nick, 2004]
    Yannis, S., Nick, R.: The Polynomial Complexity of Fully Materialized Coalesced Cubes. In: Proceedings of the 13th International Conference on Very Large Data Bases, Toronto, Canada, pp. 540–551 (2004)Google Scholar
  33. [Zhao et al., 1997]
    Zhao, Y., Deshpande, P., Naughton, J.: An Array-Based Algorithm for Simultaneous Multidimensional Aggregates. In: Proceedings of the 1997 ACM SIGMOD International Conference on Management of Data (SIGMOD 1997), Tucson, Arizona, United States, pp. 159–170 (1997)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  • Hanen Brahmi
    • 1
  • Tarek Hamrouni
    • 1
  • Riadh Ben Messaoud
    • 2
  • Sadok Ben Yahia
    • 1
  1. 1.Faculty of Sciences of TunisTunisTunisia
  2. 2.Faculty of Economic and Management Sciences of NabeulNabeulTunisia

Personalised recommendations