Knowledge and Information Systems

, Volume 16, Issue 2, pp 213–244 | Cite as

An information-theoretic approach to quantitative association rule mining

Regular Paper

Abstract

Quantitative association rule (QAR) mining has been recognized an influential research problem over the last decade due to the popularity of quantitative databases and the usefulness of association rules in real life. Unlike boolean association rules (BARs), which only consider boolean attributes, QARs consist of quantitative attributes which contain much richer information than the boolean attributes. However, the combination of these quantitative attributes and their value intervals always gives rise to the generation of an explosively large number of itemsets, thereby severely degrading the mining efficiency. In this paper, we propose an information-theoretic approach to avoid unrewarding combinations of both the attributes and their value intervals being generated in the mining process. We study the mutual information between the attributes in a quantitative database and devise a normalization on the mutual information to make it applicable in the context of QAR mining. To indicate the strong informative relationships among the attributes, we construct a mutual information graph (MI graph), whose edges are attribute pairs that have normalized mutual information no less than a predefined information threshold. We find that the cliques in the MI graph represent a majority of the frequent itemsets. We also show that frequent itemsets that do not form a clique in the MI graph are those whose attributes are not informatively correlated to each other. By utilizing the cliques in the MI graph, we devise an efficient algorithm that significantly reduces the number of value intervals of the attribute sets to be joined during the mining process. Extensive experiments show that our algorithm speeds up the mining process by up to two orders of magnitude. Most importantly, we are able to obtain most of the high-confidence QARs, whereas the QARs that are not returned by MIC are shown to be less interesting.

Keywords

Quantitative databases Association rules Information-theoretic approach Mutual information 

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References

  1. 1.
    Agrawal R, Imielinski T and Swami A (1993). Database mining: a performance perspective. IEEE Trans Knowl Data Eng 5(6): 914–925 CrossRefGoogle Scholar
  2. 2.
    Agrawal R, Imielinski T, Swami A (1993) Mining association rules between sets of items in large databases. In: Buneman P, Jajodia S (eds) Proceedings of the ACM SIGMOD international conference on management of data, Washington DC, May 1993, pp 207–216Google Scholar
  3. 3.
    Agrawal R, Srikant R (1994) Fast algorithms for mining association rules in large databases. In: Bocca J, Jarke M, Zaniolo C (eds) Proceedings of 20th international conference on very large data bases, Santiago de Chile, Chile, September 1994, pp 487–499Google Scholar
  4. 4.
    Asuncion A, Newman DJ (2007) UCI machine learning repository [http://www.ics.uci.edu/~mlearn/MLRepository.html]. Irvine, CA: University of California, Department of Information and Computer ScienceGoogle Scholar
  5. 5.
    Aumann Y and Lindell Y (2003). A statistical theory for quantitative association rules. J Intell Inf Syst 20(3): 255–283 CrossRefGoogle Scholar
  6. 6.
    Brin S, Motwani R, Silverstein C (1997) Beyond market baskets: generalizing association rules to correlations. In: Peckham J (eds) Proceedings of the ACM SIGMOD international conference on management of data, Arizona, May 1997, pp 265–276Google Scholar
  7. 7.
    Brin S, Rastogi R and Shim K (2003). Mining optimized gain rules for numeric attributes. IEEE Trans Knowl Data Eng 15(2): 324–338 CrossRefGoogle Scholar
  8. 8.
    Chen ZY, Liu GH (2005) Quantitative association rules mining methods with privacy-preserving. In: Proceedings of the Sixth International Conference on Parallel and Distributed Computing Applications and Technologies, Dalian, China, December 2005, pp 910–912Google Scholar
  9. 9.
    Cormen TH, Leiserson CE, Rivest RL and Stein C (2001). Introduction to algorithms, 2nd edn. MIT Press, Cambridge MATHGoogle Scholar
  10. 10.
    Cover TM and Thomas JA (1991). Elements of information theory. Wiley, New York MATHGoogle Scholar
  11. 11.
    Fukuda T, Morimoto Y, Morishita S and Tokuyama T (2001). Data mining with optimized two-dimensional association rules. ACM Trans Database Syst 26(2): 179–213 MATHCrossRefGoogle Scholar
  12. 12.
    Furnkranz J (1999). Separate-and-conquer rule learning. Artif Intell Rev 13(1): 3–54 CrossRefGoogle Scholar
  13. 13.
    Holt JD and Chung SM (2001). Multipass algorithms for mining association rules in text databases. Knowl Inf Syst 3(2): 168–183 MATHCrossRefGoogle Scholar
  14. 14.
    IBM (1993) Quest synthetic data generation code for classification. http://www.almaden.ibm.com/software/projects/iis/hdb/Projects/data_mining/mining.shtmlGoogle Scholar
  15. 15.
    Jing W, Huang L, Luo Y, Xu W, Yao Y (2006) An algorithm for privacy-preserving quantitative association rules mining. In: Proceedings of the 2nd IEEE International Symposium on Dependable, Autonomic and Secure Computing, Indianapolis, Indiana, USA, September 2006, pp 315–324Google Scholar
  16. 16.
    Kaya M, Alhajj R (2005) Novel approach to optimize quantitative association rules by employing multi-objective genetic algorithm. In: Ali M, Esposito F (eds) Proceedings of the 18th international conference on innovations in applied artificial intelligence, Bari, Italy, June 2005, pp 560–562Google Scholar
  17. 17.
    Ke Y, Cheng J, Ng W (2006) MIC framework: an information-theoretic approach to quantitative association rule mining. In: Liu L, Reuter A, Whang KY, Zhang J (eds) Proceedings of the 22nd International Conference on Data Engineering, Atlanta, GA, USA, April 2006, p 112Google Scholar
  18. 18.
    Ke Y, Cheng J, Ng W (2006) Mining quantitative correlated patterns using an information-theoretic approach. In: Eliassi-Rad T, Ungar LH, Craven M, Gunopulos D (eds) Proceedings of the 12th ACM SIGKDD international conference on knowledge discovery and data mining, Philadelphia, PA, USA, August 2006, pp 227–236Google Scholar
  19. 19.
    Mata J, Alvarez JL, Riquelme JC (2002) Discovering numeric association rules via evolutionary algorithm. In: Cheng MS, Yu PS, Liu B (eds) Proceedings of the sixth Pacific–Asia Conference on Advances in Knowledge Discovery and Data Mining, Taipei, Taiwan, May 2002, pp 40–51Google Scholar
  20. 20.
    Mata J, Alvarez JL, Riquelme JC (2002) An evolutionary algorithm to discover numeric association rules. In: Proceedings of the ACM SAC symposium on applied computing, Madrid, Spain, March 2002, pp 590–594Google Scholar
  21. 21.
    Miller RJ, Yang Y (1997) Association rules over interval data. In: Peckham J (eds) Proceedings of the ACM SIGMOD international conference on management of data, Tucson, Arizona, USA, May 1997, pp 452–461Google Scholar
  22. 22.
    Ordonez C, Ezquerra N and Santana CA (2006). Constraining and summarizing association rules in medical data. Knowl Inf Syst 9(3): 1–2 CrossRefGoogle Scholar
  23. 23.
    Piatetsky-Shapiro G (1991) Discovery, analysis, and presentation of strong rules. In: Piatetsky-Shapiro G, Frawley WJ (eds) Knowledge Discovery in Databases, pp 229–248Google Scholar
  24. 24.
    Rastogi R and Shim K (2002). Mining optimized association rules with categorical and numeric attributes. IEEE Trans Knowl Data Eng 14(1): 29–50 CrossRefGoogle Scholar
  25. 25.
    Rückert U, Richter L, Kramer S (2004) Quantitative association rules based on half-spaces: an optimization approach. In: Proceedings of the 4th IEEE international conference on data mining, Brighton, UK, November 2004, pp 507–510Google Scholar
  26. 26.
    Salleb-Aouissi A, Vrain C, Nortet C (2007) Quantminer: a genetic algorithm for mining quantitative association rules. In: Veloso MM (eds) Proceedings of the 20th international joint conference on artificial intelligence, Hyderabad, India, January 2007, pp 1035–1040Google Scholar
  27. 27.
    Shannon C (1948) A mathematical theory of communication, i and ii. Bell Syst Tech J 27:379–423, 623–656, July, OctoberGoogle Scholar
  28. 28.
    Srikant R, Agrawal R (1996) Mining quantitative association rules in large relational tables. In: Jagadish HV, Mumick IS (eds) Proceedings of the ACM SIGMOD international conference on management of data, Montreal, Quebec, Canada, June 1996, pp 1–12Google Scholar
  29. 29.
    Strehl A (2002) Relationship-based clustering and cluster ensembles for high-dimensional data mining. PhD thesis, The University of Texas, AustinGoogle Scholar
  30. 30.
    Studholme C, Hawkes DJ and Hill DLG (1999). An overlap invariant entropy measure of 3d medical image alignment. Pattern Recognit 32(1): 71–86 CrossRefGoogle Scholar
  31. 31.
    Thabtah FA, Cowling P and Peng Y (2006). Multiple labels associative classification. Knowl Inf Syst 9(1): 109–129 CrossRefGoogle Scholar
  32. 32.
    Wang K, Tay SHW, Liu B (1998) Interestingness-based interval merger for numeric association rules. In: Agrawal R, Stolorz PE, Piatetsky-Shapiro G (eds) Proceedings of the 4th ACM SIGKDD international conference on knowledge discovery and data mining, New York City, New York, USA, August 1998, pp 121–128Google Scholar
  33. 33.
    Webb GI (2001) Discovering associations with numeric variables. In: Proceedings of the seventh ACM SIGKDD international conference on knowledge discovery and data mining, San Francisco, CA, USA, August 2001, pp 383–388Google Scholar
  34. 34.
    Zaki MJ, Gouda K (2003) Fast vertical mining using diffsets. In: Getoor L, Senator TE, Domingos P, Faloutsos C (eds) Proceedings of the Ninth ACM SIGKDD International Conference on knowledge discovery and data mining, Washington, DC, USA, August 2003, pp 326–335Google Scholar
  35. 35.
    Zhang H, Padmanabhan B, Tuzhilin A (2004) On the discovery of significant statistical quantitative rules. In: Kim W, Kohavi R, Gehrke J, DuMouchel W (eds) Proceedings of the Tenth ACM SIGKDD international conference on knowledge discovery and data mining, Seattle, Washington, USA, August 2004, pp 374–383Google Scholar
  36. 36.
    Zhang Z, Lu Y, Zhang B (1997) An effective partitioning-combining algorithm for discovering quantitative association rules. In: Proceedings of the first Pacific–Asia conference on knowledge discovery and data mining, Singapore, April 1997, pp 241–251Google Scholar

Copyright information

© Springer-Verlag London Limited 2007

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringThe Hong Kong University of Science and TechnologyKowloonHong Kong

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