Abstract
It is well recognized that data cubes often produce huge outputs. Several efforts were devoted to this problem through closed cubes, where cells preserving aggregation semantics are losslessly reduced to one cell. In this paper, we introduce the concept of closed non derivable data cube, denoted \(\mathcal{CND}\) - \(\mathcal{C}\)ube, which generalizes the notion of bi-dimensional frequent closed non derivable patterns to the multidimensional context. We propose a novel algorithm to mine \(\mathcal{CND}\) - \(\mathcal{C}\)ube from multidimensional databases considering three anti-monotone constraints, namely “to be frequent”, “to be non derivable” and “to be minimal generator”. Experiments show that our proposal provides the smallest representation of a data cube and thus is the most efficient for saving storage space.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chaudhuri, S., Dayal, U.: An overview of data warehousing and OLAP technology. SIGMOD Record 26(1), 65–74 (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)
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)
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)
Han, J., Pei, J., Dong, G., Wang, K.: Efficient computation of iceberg cubes with complex measures. In: Proceedings of the International Conference on Management of Data (SIGMOD 2001), Santa Barbara, California, USA, pp. 441–448 (2001)
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)
Lakshmanan, L., Pei, J., Han, J.: Quotient cube: How to summarize the semantics of a data cube. In: Proceedings of the 28th International Conference on Very Large Databases (VLDB 2002), Hong Kong, China, pp. 778–789 (2002)
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)
Casali, A., Cicchetti, R., Lakhal, L.: Closed cubes lattices. Annals of Information Systems 3, 145–165 (2009); Special Issue on New Trends in Data Warehousing and Data Analysis
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)
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)
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)
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)
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 (2009)
Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Heidelberg (1999)
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, vol. 1861, pp. 972–986. Springer, Heidelberg (2000)
Calders, T., Goethals, B.: Non-derivable itemset mining. Data Mining and Knowledge Discovery 14(1), 171–206 (2007)
Gunopulos, D., Khardon, R., Mannila, H., Toivonen, H.: Data mining, hypergraph transversals, and machine learning. In: Proc. of the 16th ACM Symp. on Principles of Database Systems (PODS), Tuscon (1997)
Muhonen, J., Toivonen, H.: Closed non-derivable itemsets. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) PKDD 2006. LNCS, vol. 4213, pp. 601–608. Springer, Heidelberg (2006)
Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L.: Computing Iceberg concept lattices with Titanic. Data and Knowledge Engineering 42(2), 189–222 (2002)
Messaoud, R.B., 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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brahmi, H., Hamrouni, T., Ben Messaoud, R., Ben Yahia, S. (2009). 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) Advanced Data Mining and Applications. ADMA 2009. Lecture Notes in Computer Science(), vol 5678. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03348-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-03348-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03347-6
Online ISBN: 978-3-642-03348-3
eBook Packages: Computer ScienceComputer Science (R0)