Abstract.
In this paper, we consider an instance of the constraint pattern problem: the frequent multidimensional patterns. We propose the first concise representation of frequent multidimensional patterns which on one hand is not based on the powerset lattice framework and on the other hand differs from the representations by closed patterns and non derivable patterns. From such a representation, we show that any frequent multidimensional pattern along with its conjunction, disjunction and negation frequencies can be obtained using inclusion-exclusion identities.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Inkeri Verkamo, A.: Fast Discovery of Association Rules. In: Advances in Knowledge Discovery and Data Mining, pp. 307–328 (1996)
Bayardo Jr., R.J.: Efficiently Mining Long Patterns from Databases. In: Proceedings of the International Conference on Management of Data, SIGMOD, pp. 85–93 (1998)
Beyer, K., Ramakrishnan, R.: Bottom-Up Computation of Sparse and Iceberg CUBEs. In: Proceedings of the International Conference on Management of Data, SIGMOD, pp. 359–370 (1999)
Bastide, Y., Taouil, R., Pasquier, N., Stumme, G., Lakhal, L.: Mining Frequent Patterns with Counting Inference. SIGKDD Explorations 2(2), 66–75 (2000)
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, SDM (2003)
Calders, T., Goethals, B.: Mining all non-derivable frequent itemsets. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) PKDD 2002. LNCS (LNAI), vol. 2431, pp. 74–85. Springer, Heidelberg (2002)
Gray, J., Chaudhuri, S., Bosworth, A., Layman, A., Reichart, D., Venkatrao, M., Pellow, F., Pirahesh, H.: Data cube: A relational aggregation operator generalizing group-by, cross-tab, and sub-totals. Data Mining and Knowledge Discovery 1(1), 29–53 (1997)
Ganter, B., Wille, R.: Fomal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
Han, J.: Data mining, data warehousing, and knowledge discovery in databases, http://db.cs.sfu.ca/sections/publication/kdd/kdd.html
Mitchell, T.M.: Machine learning. MacGraw-Hill Series in Computer Science (1997)
Mannila, H., Toivonen, H.: Levelwise Search and Borders of Theories in Knowledge Discovery. Data Mining and Knowledge Discovery 1(3), 241–258 (1997)
Narushima, H.: Principle of Inclusion-Exclusion on Partially Oder Sets. Discrete Math. 42, 243–250 (1982)
Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Discovering frequent closed itemsets for association rules. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 398–416. Springer, Heidelberg (1998)
Pei, J., Han, J., Mao, R.: CLOSET: An Efficient Algorithm for Mining Frequent Closed Itemsets. In: Workshop on Research Issues in Data Mining and Knowledge Discovery, DMKD, pp. 21–30 (2000)
Srikant, R., Agrawal, R.: Mining quantitative association rules in large relational tables. In: Proceedings of the International Conference on Management of Data, SIGMOD, pp. 1–12 (1996)
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)
Valtchev, P., Missaoui, R., Godin, R., Meridji, M.: Generating Frequent Itemsets Incrementally: Two Novel Approaches based on Galois Lattice Theory. Experimental and Theoretical Artificial Intelligence (JETAI): Special Issue on Concept Lattice-based theory, methods and tools for Knowledge Discovery in Databases 14(2/3), 115–142 (2002)
Zaki, M.J., Hsio, C.-J.: CHARM: An Efficient Algorithm for Closed Itemset Mining. In: Proceedings of the 2nd SIAM International Conference on Data mining (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Casali, A., Cicchetti, R., Lakhal, L. (2003). Mining Concise Representations of Frequent Multidimensional Patterns. In: Ganter, B., de Moor, A., Lex, W. (eds) Conceptual Structures for Knowledge Creation and Communication. ICCS 2003. Lecture Notes in Computer Science(), vol 2746. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45091-7_25
Download citation
DOI: https://doi.org/10.1007/978-3-540-45091-7_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40576-4
Online ISBN: 978-3-540-45091-7
eBook Packages: Springer Book Archive