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On Some Clustering Algorithms Based on Tolerance

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Fuzzy Sets, Rough Sets, Multisets and Clustering

Part of the book series: Studies in Computational Intelligence ((SCI,volume 671))

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Abstract

A large number of clustering algorithms have been proposed to handle target data and deal with various real-world problems such as uncertain data mining, semi-supervised learning and so on. We focus above two topics and introduce two concepts to construct significant clustering algorithms. We propose tolerance and penalty-vector concepts for handling uncertain data. We also propose clusterwise tolerance concept for semi-supervised learning. These concepts are quite similar approach in the viewpoint of handling objects to be flexible to each clustering topics. We construct two clustering algorithms FCMT and FCMQ for handling uncertain data. We also construct two clustering algorithms FCMCT and SSFCMCT for semi-supervised learning. We consider that those concepts have a potential to resolve conventional and brand new clustering topics in various ways.

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References

  1. Aggarwal C. C., A survey of uncertain data algorithms and applications , IEEE Trans. on Knowledge and Data Engineering, Vol. 21, No. 5, pp. 609–623, 2008.

    Google Scholar 

  2. Bezdek J. C., ‘Pattern Recognition with Fuzzy Objective Function Algorithms’, Plenum Press, New York, 1981.

    Book  MATH  Google Scholar 

  3. Chapelle O., Schoölkopf B., and Zien A., eds., ‘Semi-Supervised Learning’, MIT Press, 2006.

    Google Scholar 

  4. Davidson I. and Ravi S.S., Agglomerative hierarchical clustering with constraints: theoretical and empirical results, Proc. of 9th European Conference on Principles and Practice of Knowledge Discovery in Databases (KDD 2005), pp. 59–70, 2005.

    Google Scholar 

  5. Endo Y., Murata R., Haruyama H., and Miyamoto S., Fuzzy \(c\)-means for data with tolerance’, Proc. of International Symposium on Nonlinear Theory and Its Applications (Nolta2005), pp. 345–348, 2005.

    Google Scholar 

  6. Endo Y., Hasegawa Y., Hamasuna Y., and Miyamoto S., Fuzzy \(c\)-means for data with rectangular maximum tolerance range, Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol. 12, No. 5, pp. 461–466, 2008.

    Article  Google Scholar 

  7. Endo Y., Kurihara K., Miyamoto S, and Hamasuna Y., Hard and fuzzy \(c\)-regression models for data with tolerance in independent and dependent variables, Proc. of The 2010 IEEE World Congress on Computational Intelligence (WCCI2010), pp. 1842–1849, 2010.

    Google Scholar 

  8. Endo Y., Hasegawa Y., Hamasuna Y., and Kanzawa Y., Fuzzy \(c\)-means clustering for uncertain data using quadratic regularization of penalty vectors, Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol. 15, No. 1, pp. 76–82, 2011.

    Article  Google Scholar 

  9. Hamasuna Y., Endo Y., Hasegawa Y., and Miyamoto S., Two clustering algorithms for data with tolerance based on hard \(c\)-means, 2007 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE2007), pp. 688–691 2007.

    Google Scholar 

  10. Hamasuna Y., Endo Y., and Miyamoto S., On tolerant fuzzy \(c\)-means clustering and tolerant possibilistic clustering, Soft Computing, Vol. 14, No. 5, pp. 487–494, 2010.

    Article  Google Scholar 

  11. Hamasuna Y. and Endo Y., On semi-supervised fuzzy \(c\)-means clustering for data with clusterwise tolerance by opposite criteria, Soft Computing, Vol. 17, No. 1, pp. 71–81, 2013.

    Article  Google Scholar 

  12. Hathaway R. J. and Bezdek J. C., Fuzzy \(c\)-means clustering of incomplete data, IEEE Trans. on Systems, Man, and Cybernetics Part B, Vol. 31, No. 5, pp. 735–744, 2001.

    Google Scholar 

  13. Jain A. K., Data clustering: 50 years beyond \(K\)-means, Pattern Recognition Letters, Vol. 31, No. 8, pp. 651–666, 2010.

    Article  Google Scholar 

  14. Klein D., Kamvar S., and Manning C., From instance-level constraints to space-level constraints: making the most of prior knowledge in data clustering, Proc. of the 19th International Conference on Machine Learning (ICML 2002), pp. 307–314, 2002.

    Google Scholar 

  15. Miyamoto S., Ichihashi H., and Honda K., ‘Algorithms for Fuzzy Clustering’, Springer, Heidelberg, 2008.

    MATH  Google Scholar 

  16. Miyamoto S., Yamazaki M., and Terami A., On semi-supervised clustering with pairwise constraints, Proc. of The 7th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2009), pp. 245–254, 2009 (CD-ROM).

    Google Scholar 

  17. Torra V., Endo Y., and Miyamoto S., Computationally Intensive Parameter Selection for Clustering Algorithms: The Case of Fuzzy \(c\)-Means with Tolerance, International Journal of Intelligent Systems, Vol. 26, No. 4, pp. 313–322, 2011.

    Article  Google Scholar 

  18. Wagstaff K., Cardie C., Rogers S., and Schroedl S., Constrained k-means clustering with background knowledge’, Proc. of the 18th International Conference on Machine Learning (ICML2001), pp. 577–584, 2001.

    Google Scholar 

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Correspondence to Yukihiro Hamasuna .

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Hamasuna, Y., Endo, Y. (2017). On Some Clustering Algorithms Based on Tolerance. In: Torra, V., Dahlbom, A., Narukawa, Y. (eds) Fuzzy Sets, Rough Sets, Multisets and Clustering. Studies in Computational Intelligence, vol 671. Springer, Cham. https://doi.org/10.1007/978-3-319-47557-8_6

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  • DOI: https://doi.org/10.1007/978-3-319-47557-8_6

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  • Publisher Name: Springer, Cham

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