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Evolutionary Rough K-Means Clustering

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Rough Sets and Knowledge Technology (RSKT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5589))

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Abstract

Rough K-means algorithm and its extensions have been useful in situations where clusters do not necessarily have crisp boundaries. Experimentation with the rough K-means algorithm has shown that it provides a reasonable set of lower and upper bounds for a given dataset. Evaluation of clustering obtained from rough K-means using various cluster validity measures has also been promising. However, rough K-means algorithm has not been explicitly shown to provide optimal rough clustering. This paper proposes an evolutionary rough K-means algorithm that minimizes a rough within-group-error. The proposal is different from previous Genetic Algorithms (GAs) based rough clustering, as it combines the efficiency of rough K-means algorithm with the optimization ability of GAs. The evolutionary rough K-means algorithm provides flexibility in terms of the optimization criterion. It can be used for optimizing rough clusters based on different criteria.

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References

  1. Buckles, B.P., Petry, F.E.: Genetic Algorithms. IEEE Computer Press, Los Alamitos (1994)

    MATH  Google Scholar 

  2. Hartigan, J.A., Wong, M.A.: Algorithm AS136: A K-Means Clustering Algorithm. Applied Statistics 28, 100–108 (1979)

    Article  MATH  Google Scholar 

  3. Hirano, S., Tsumoto, S.: Rough Clustering and Its Application to Medicine. Journal of Information Science 124, 125–137 (2000)

    Article  Google Scholar 

  4. Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  5. Lingras, P.: Unsupervised Rough Set Classification using GAs. Journal Of Intelligent Information Systems 16(3), 215–228 (2001)

    Article  MATH  Google Scholar 

  6. Lingras, P., Chen, M., Miao, D.: Rough multi-category decision theoretic framework. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS, vol. 5009, pp. 676–683. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Lingras, P., Chen, M., Miao, D.: Rough Cluster Quality Index Based on Decision Theory. Submitted to IEEE Transactions on Knowledge and Data Enginering (2008)

    Google Scholar 

  8. Lingras, P., West, C.: Interval Set Clustering of Web Users with Rough K-means. Journal of Intelligent Information Systems 23(1), 5–16 (2004)

    Article  MATH  Google Scholar 

  9. Lingras, P., Hogo, M., Snorek, M.: Interval Set Clustering of Web Users using Modified Kohonen Self-Organizing Maps based on the Properties of Rough Sets. Web Intelligence and Agent Systems: An International Journal 2(3) (2004)

    Google Scholar 

  10. MacQueen, J.: Some Methods for Classification and Analysis of Multivariate Observations. In: Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297 (1967)

    Google Scholar 

  11. Mitra, S., Bank, H., Pedrycz, W.: Rough-Fuzzy Collaborative Clustering. IEEE Trans. on Systems, Man and Cybernetics 36(4), 795–805 (2006)

    Article  Google Scholar 

  12. Nguyen, H.S.: Rough Document Clustering and the Internet. Handbook on Granular Computing (2007)

    Google Scholar 

  13. Pawlak, Z.: Rough Sets. International Journal of Information and Computer Sciences 11(145-172) (1982)

    Google Scholar 

  14. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1992)

    MATH  Google Scholar 

  15. Peters, G.: Some Refinements of Rough k-Means. Pattern Recognition 39(8), 1481–1491 (2006)

    Article  MATH  Google Scholar 

  16. Peters, J.F., Skowron, A., Suraj, Z., Rzasa, W., Borkowski, M.: Clustering: A rough set approach to constructing information granules. In: Soft Computing and Distributed Processing. Proceedings of 6th International Conference, SCDP 2002, pp. 57–61 (2002)

    Google Scholar 

  17. Polkowski, L., Skowron, A.: Rough Mereology: A New Paradigm for Approximate Reasoning. International Journal of Approximate Reasoning 15(4), 333–365 (1996)

    Article  MATH  Google Scholar 

  18. Sharma, S.C., Werner, A.: Improved method of grouping provincewide permanent traffic counters. Transportation Research Record 815, 13–18 (1981)

    Google Scholar 

  19. Skowron, A., Stepaniuk, J.: Information granules in distributed environment. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 357–365. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  20. Voges, K.E., Pope, N.K.L.l., Brown, M.R.: Cluster Analysis of Marketing Data: A Comparison of K-Means, Rough Set, and Rough Genetic Approaches. In: Abbas, H.A., Sarker, R.A., Newton, C.S. (eds.) Heuristics and Optimization for Knowledge Discovery, pp. 208–216. Idea Group Publishing (2002)

    Google Scholar 

  21. Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Information Sciences 109, 21–47 (1998)

    Article  MATH  Google Scholar 

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Lingras, P. (2009). Evolutionary Rough K-Means Clustering. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds) Rough Sets and Knowledge Technology. RSKT 2009. Lecture Notes in Computer Science(), vol 5589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02962-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-02962-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02961-5

  • Online ISBN: 978-3-642-02962-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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