Abstract
The general goal of data mining is to extract interesting correlated information from large collection of data. A key computationally-intensive subproblem of data mining involves finding frequent sets in order to help mine association rules for market basket analysis. Given a bag of sets and a probability, the frequent set problem is to determine which subsets occur in the bag with some minimum probability. This paper provides a convincing application of program calculation in the derivation of a completely new and fast algorithm for this practical problem. Beginning with a simple but inefficient specifocation expressed in a functional language, the new algorithm is calculated in a systematic manner from the specification by applying a sequence of known calculation techniques.
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
R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large databases. In 1993 International Conference on Management of Data (SIGMOD’93), pages 207–216, May 1993.
R.S. Bird and O. de Moor. Algebras of Programming. Prentice Hall, 1996.
R. Bird. Tabulation techniques for recursive programs. ACM Computing Surveys, 12(4):403–417, 1980.
R. Bird. The promotion and accumulation strategies in transformational programming. ACM Transactions on Programming Languages and Systems, 6(4):487–504, 1984.
R. Bird. Constructive functional programming. In STOP Summer School on Constructive Algorithmics, Abeland, 9 1989.
C.L. Blake and C.J. Merz. UCI repository of machine learning databases, 1998. http://www.ics.uci.edu/~mlearn/MLRepository.html.
S. Brin, R. Motwani, J. Ullman, and S. Tsur. Dynamic itemset counting and implication rules for market basket data. In 1997 International Conference on Management of Data (SIGMOD’97), pages 255–264, AZ, USA, 1997. ACM Press.
W. Chin and M. Hagiya. A transformation method for dynamic-sized tabulation. Acta Informatica, 32:93–115, 1995.
W.N. Chin. Automatic Methods for Program Transformation. Phd thesis, Department of Computing, Imperial College of Science, Technology and Medicone, University of London, May 1990.
W. Chin. Safe fusion of functional expressions. In Proc. Conference on Lisp and Functional Programming, pages 11–20, San Francisco, California, June 1992.
A. Gill, J. Launchbury, and S. Peyton Jones. A short cut to deforestation. In Proc. Conference on Functional Programming Languages and Computer Architecture, pages 223–232, Copenhagen, June 1993.
Z. Hu, H. Iwasaki, and M. Takeichi. Caculating accumulations. New Generation Computing, 17(2):153–73, 1999.
C. Herrmann, C. Lengauer, R. Gunz, J. Laitenberger, and C. Schaller. A compiler for HDC. Technical Report MIP-9907, Fakultat fur Mathematik und Informatik, Universitat Passau, May 1999.
Z. Hu, M. Takeichi, and W.N. Chin. Parallelization in calculational forms. In 25th ACM Symposium on Principles of Programming Languages, pages 316–328, San Diego, California, USA, January 1998.
J. Jeuring. Theories for Algorithm Calculation. Ph.D thesis, Faculty of Science, Utrecht University, 1993.
D. Knuth. The Art of Computer Programming: Volume 3 / Sorting and Searching. Addison-Wesley, Longman, 1997. Second Edition.
D. Lin and Z. Kedem. Princer Search: A new algorithm for discovering the maximum frequent set. In VI Intl. Conference on Extending Database Technology, Valencia, Spain, March 1998.
H. Mannila and H. Toivonen. Multiple uses of frequent sets and condensed representations. In 2nd International Conference on Knowledge Discovery and Data Mining (KDD’96), pages 189–194, Portland, Oregon, August 1996. AAAI Press.
A. Takano and E. Meijer. Shortcut deforestation in calculational form. In Proc. Conference on Functional Programming Languages and Computer Architecture, pages 306–313, La Jolla, California, June 1995.
H. Toivonen. Discovery of Frequent Patterns in Large Data Collections. Ph.D thesis, Department of Computer Science, University of Helsinki, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Basket Analysis, M., Hu, Z., Chin, WN., Takeichi, M. (1999). Calculating a New Data Mining Algorithm for. In: Pontelli, E., Santos Costa, V. (eds) Practical Aspects of Declarative Languages. PADL 2000. Lecture Notes in Computer Science, vol 1753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46584-7_12
Download citation
DOI: https://doi.org/10.1007/3-540-46584-7_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66992-0
Online ISBN: 978-3-540-46584-3
eBook Packages: Springer Book Archive