Skip to main content
Log in

Clustering Rules: A Comparison of Partitioning and Hierarchical Clustering Algorithms

  • Published:
Journal of Mathematical Modelling and Algorithms

Abstract

Previous research has resulted in a number of different algorithms for rule discovery. Two approaches discussed here, the ‘all-rules’ algorithm and multi-objective metaheuristics, both result in the production of a large number of partial classification rules, or ‘nuggets’, for describing different subsets of the records in the class of interest. This paper describes the application of a number of different clustering algorithms to these rules, in order to identify similar rules and to better understand the data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bayardo, Jr., R. J. and Agrawal, R.: Mining the most interesting rules, in S. Chaudhuri and D. Madigan (eds.), Proceedings of the Fifth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Diego, California, United States, 1999, pp. 145–154.

  2. Bayardo, Jr., R. J., Agrawal, R. and Gunopulos, D.: Constraint-based rule mining in large, dense databases, in Proceedings of the 15th International Conference on Data Engineering, Sydney, Australia, 1999, pp. 188–197.

  3. Blake, C. and Merz, C.: ‘UCI Repository of machine learning databases,' (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html.

  4. Chu, S. C., Roddick, J. F. and Pan, J. S.: A comparative study and extensions to k-medoids algorithms, in Fifth International Conference on Optimization, Hong Kong, China, 2001, pp. 1708–1717.

  5. de la Iglesia, B., Philpott, M. S., Bagnall, A. J. and Rayward-Smith, V. J.: Data mining rules using multi-objective evolutionary algorithms, in R. Sarker, R. Reynolds, H. Abbass, K. C. Tan, B. McKay, D. Essam, and T. Gedeon (eds.), Proceedings of 2003 IEEE Congress on Evolutionary Computation, Canberra, Australia, 2003, pp. 1552–1559.

  6. de la Iglesia, B., Reynolds, A. and Rayward-Smith, V. J.: Developments on a Multi-Objective Metaheuristic (MOMH) algorithm for finding interesting sets of classification rules, in C. A. Coello Coello, A. H. Aguirre and E. Zitzler (eds.), Evolutionary Multi-Criterion Optimization: Third International Conference, EMO 2005, Guanajuato, Mexico, 2005, pp. 826–840.

  7. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms, Chichester, Wiley, England, 2001.

    MATH  Google Scholar 

  8. Deb, K., Agrawal, S., Pratab, A. and Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II,' in Marc Schoenauer and Kalyanmoy Deb, Günter Rudolph, Xin Yao, Evelyne Lutton, J. J. Merelo, Hans-Paul Schwefel (eds.), Proceedings of the Parallel Problem Solving from Nature VI Conference. Lecture Notes in Computer Science No. 1917, Paris, France, 2000, pp. 849–858.

  9. Gower, J. C. and Legendre, P.: Metric and Euclidean properties of dissimilarity coefficients, J. Classif. 3 (1986), 5–48.

    Article  MATH  MathSciNet  Google Scholar 

  10. Handl, J. and Knowles, J.: Evolutionary multiobjective clustering, in X. Yao, E. Burke, J. Lozano, J. Smith, J. Merelo-Guervs, J. Bullinaria, J. Rowe, P. Tino, A. Kabn, and H.-P. Schwefel (eds.), Proceedings of the Eighth International Conference on Parallel Problem Solving from Nature (PPSN VIII). Birmingham, UK, 2004, pp. 1081–1091.

  11. Handl, J. and Knowles, J.: Exploiting the trade-off – the benefits of multiple objectives in data clustering, in C. A. Coello Coello, A. H. Aguirre and E. Zitzler (eds.), Evolutionary Multi-Criterion Optimization: Third International Conference, EMO 2005, Guanajuato, Mexico, 2005, pp. 547–560.

  12. Jaccard, P.: Étude comparative de la distribution florale dans une portion des Alpes et des Jura, Bull. Soc. Vaud. Sci. Nat. 37 (1901), 547–579.

    Google Scholar 

  13. Kaufman, L. and Rousseeuw, P. J.: Finding Groups in Data: An Introduction to Cluster Analysis, Wiley series in probability and mathematical statistics, Wiley, 1990.

  14. MacQueen, J. B.: Some methods for classification and analysis of multivariate observations, in Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 1967, pp. 281–297.

  15. Ng, R. T. and Han, J.: CLARANS: a method for clustering objects for spatial data mining, IEEE Trans. Knowl. Data Eng. 14(5) (2002), 1003–1016.

    Article  Google Scholar 

  16. Reynolds, A. P., Richards, G. and Rayward-Smith, V. J.: The application of K-medoids and PAM to the clustering of rules, in Z. R. Yang, H. Yin, and R. Everson (eds.), in Proceedings of the Fifth International Conference on Intelligent Data Engineering and Automated Learning (IDEAL'04), 2004, pp. 173–178.

  17. Richards, G. and Rayward-Smith, V. J.: Discovery of association rules in tabular data, in N. Cercone, T. Y. Lin and X. Wu (eds.), in Proceedings of IEEE First International Conference on Data Mining, San Jose, California, USA, San Jose, California, 2001, pp. 465–473.

  18. Sokal, R. R. and Michener, C. D.: A statistical method for evaluating systematic relationships, Univ. Kans. Sci. Bull. 38 (1958), 1409–1438.

    Google Scholar 

  19. Sokal, R. R. and Sneath, P. H. A.: Principles of Numerical Taxonomy, Freeman, San Francisco, 1963.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. P. Reynolds.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reynolds, A.P., Richards, G., de la Iglesia, B. et al. Clustering Rules: A Comparison of Partitioning and Hierarchical Clustering Algorithms. J Math Model Algor 5, 475–504 (2006). https://doi.org/10.1007/s10852-005-9022-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10852-005-9022-1

Kew words

Mathematics Subject Classifications (2000)

Navigation