Abstract
In this paper we introduce new algebraic forms, SOP + and DSOP + , to represent functions f:{0,1}n →ℕ, based on arithmetic sums of products. These expressions are a direct generalization of the classical SOP and DSOP forms. We propose optimal and heuristic algorithms for minimal SOP + and DSOP + synthesis. We then show how the DSOP + form can be exploited for Data Mining applications. In particular we propose a new compact representation for the database of transactions to be used by the LCM algorithms for mining frequent closed itemsets.
This is a preview of subscription content, log in via an institution to check access.
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, A., Mannila, H., Srikant, S., Toivonen, H., Verkamo, A.I.: Fast Discovery of Association Rules. In: Advances in Knowledge Discovery and Data Mining, pp. 307–328. MIT Press, Cambridge (1998)
Bernasconi, A., Ciriani, V., Luccio, F., Pagli, L.: A New Heuristic for DSOP Minimization. In: Proc. 8th International Workshop on Boolean Problems (2008)
Han, J., Kamber, M.: Data Mining: Concept and Techniques, 2nd edn. Bibliographic Notes for Chapter 5. Morgan Kauffman Publ., San Francisco (2006)
Han, J., Pei, J., Yin, Y.: Mining Frequent Patterns without Candidate Generation. In: SIGMOD 2000, pp. 1–12 (2000)
Kirsch, A., Mitzenmacher, M., Pucci, G., Pietracaprina, A., Upfal, E., Vandin, F.: An Efficient Rigorous Approach for Identifying Statistically Significant Frequent Itemsets. In: Proc. 27th ACM Symposium on Principles of Database Systems (PODS), pp. 117–126 (2009)
Minato, S., Arimura, H.: Frequent Closed Item Set Mining Based on Zero-suppressed BDDs. Information and Media Technologies 2(1), 309–316 (2007)
Pietracaprina, A., Vandin, F.: Efficient Incremental Mining of Top-K Frequent Closed Itemsets. In: Corruble, V., Takeda, M., Suzuki, E. (eds.) DS 2007. LNCS (LNAI), vol. 4755, pp. 275–280. Springer, Heidelberg (2007)
Silverstein, C., Brin, S., Motwani, R.: Beyond Market Baskets: Generalizing Association Rules to Dependence Rules. J. Data Mining and Knowledge Discovery 2(1), 36–68 (1998)
Uno, T., Asai, T., Uchida, Y., Arimura, H.: LCM: An Efficient Algorithm for Enumerating Frequent Closed Item Sets. In: Proc. IEEE ICDM 2003 Workshop FIMI 2003 (2003)
Uno, T., Asai, T., Uchida, Y., Arimura, H.: An Efficient Algorithm for Enumerating Closed Patterns in Transaction Databases. In: Suzuki, E., Arikawa, S. (eds.) DS 2004. LNCS (LNAI), vol. 3245, pp. 16–31. Springer, Heidelberg (2004)
Uno, T., Kiyomi, M., Arimura, H.: LCM ver. 2: Efficient Mining Algorithms for Frequent/Closed/Maximal Itemsets. In: Proc. IEEE ICDM 2004 Workshop FIMI 2004 (2004)
Uno, T., Kiyomi, M., Arimura, H.: LCM ver.3: Collaboration of Array, Bitmap and Prefix Tree for Frequent Itemset Mining. In: Proc. of the 1st International Workshop on Open Source Data Mining, OSDM 2005, pp. 77–86 (2005)
Wang, J., Han, J., Lu, Y., Tzvetkov, P.: TFP: An Efficient Algorithm for Mining Top-K Frequent Closed Itemsets. IEEE Transactions on Knowledge and Data Engineering 17, 652–664 (2005)
Yang, G.: The Complexity of Mining Maximal Frequent Itemsets and Maximal Frequent Patterns. In: Proc. of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 344–353 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bernasconi, A., Ciriani, V., Luccio, F., Pagli, L. (2010). Fun at a Department Store: Data Mining Meets Switching Theory. In: Boldi, P., Gargano, L. (eds) Fun with Algorithms. FUN 2010. Lecture Notes in Computer Science, vol 6099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13122-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-13122-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13121-9
Online ISBN: 978-3-642-13122-6
eBook Packages: Computer ScienceComputer Science (R0)