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Projected Gustafson Kessel Clustering

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Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5908))

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Abstract

Fuzzy techniques have been used for handling vague boundaries of arbitrarily oriented cluster structures. However, traditional clustering algorithms tend to break down in high dimensional spaces due to inherent sparsity of data. In order to model the uncertainties of high dimensional data, we propose modification of objective functions of Gustafson Kessel algorithm for subspace clustering, through automatic selection of weight vectors and present the results of applying the proposed approach to UCI data sets.

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References

  1. Wiswedel, B., Berthold, M.R.: Fuzzy clustering in parallel universies. NAFIPS, 567–572 (2005)

    Google Scholar 

  2. Babuka, R., van der Veen, P.J.: Kaymak, Improved covariance estimation for Gustafson-Kessel clustering. In: FUZZ-IEEE 2002, vol. 2, pp. 1081–1085 (2002)

    Google Scholar 

  3. Aggarwal, C., Wolf, J., Yu, P., Procopiuc, C., Park, J.: Fast algorithms for projected clustering. ACM SIGMOD, 61–72 (1999)

    Google Scholar 

  4. Gustafson, D.E., Kessel, W.: Fuzzy clustering with a Fuzzy Covariance Matrix. In: Proc. IEEE-CDC, vol. 2, pp. 761–766 (1979)

    Google Scholar 

  5. Achtert, E., Böhm, C., David, J., Kröger, P., Zimek, A.: Robust Clustering in Arbitrarily Oriented Subspaces. SDM, 763–774 (2008)

    Google Scholar 

  6. Ruspini, E.H.: A New Approach to Clustering Information and Control, pp. 22–32 (1969)

    Google Scholar 

  7. Hoppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis: Methods for Classification, Data Analysis, and Image Recognition. John Wiley & Sons, Chichester

    Google Scholar 

  8. Gan, G., Wu, J., Yang, Z.: PARTCAT: A Subspace Clustering Algorithm for High Dimensional Categorical Data. IJCNN, 4406–4412 (2006)

    Google Scholar 

  9. Nagesh, H., Goil, S., Choudhary, A.: MAFIA: Efficient and Scalable Subspace Clustering for Very Large Data Sets, Technical Report, Northwestern Univ. (1999)

    Google Scholar 

  10. Assent, I., Krieger, R., Müller, E., Seidl, T.: DUSC: Dimensionality Unbiased Subspace Clustering. In: ICDM 2007 (2007)

    Google Scholar 

  11. Assent, I., Krieger, R., Müller, E., Seidl, T.: EDSC: efficient density-based subspace clustering. In: Proceeding of the 17th ACM conference on Information and knowledge management (2008)

    Google Scholar 

  12. Abonyi, J.: Balazas Feil, Cluster Analysis for Data Mining and System Identification, Birkhauser

    Google Scholar 

  13. Bezdek, J.C.: Pattern recognition with Fuzzy Objective Function Algorithm. Plenum Press, New York (1981)

    Google Scholar 

  14. Dunn, J.: A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters. J. Cybernetics 3, 32–57 (1974)

    Article  MathSciNet  Google Scholar 

  15. Beyer, K., Goldstein, J., Ramakrishnan, R., Shaft, U.: When is ”nearest neighbor” meaningful? In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 217–235. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  16. Kelling, K., Peter, H., Kröger, P.: A Generic Framework for Efficient Subspace Clustering of High-Dimensional Data. In: ICDM, pp. 205–257 (2005)

    Google Scholar 

  17. Kailing, K., Kriegel, H.-P., Kroger, P.: Density-Connected Subspace Clustering for High Dimensional Data, pp. 246–257. SIAM, Philadelphia (2004)

    Google Scholar 

  18. Sequeira, K., Zaki, M.: SCHISM: A new approach for interesting subspace mining. In: Proc. IEEE ICDM, Hong Kong (2004)

    Google Scholar 

  19. Agrawal, R., Gehrke, J., Gunopolos, D., Raghavan, P.: Automatic Subspace Clustering of High Dimensional Data for Data Mining Applications. In: ACM SIGMOD (1998)

    Google Scholar 

  20. Xie, X.L., Beni, G.: A validity measure for fuzzy clustering. Pattern Analysis and Machine Intelligence 13, 841–847 (1991)

    Article  Google Scholar 

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© 2009 Springer-Verlag Berlin Heidelberg

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Kumar, N., Puri, C. (2009). Projected Gustafson Kessel Clustering. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2009. Lecture Notes in Computer Science(), vol 5908. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10646-0_52

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  • DOI: https://doi.org/10.1007/978-3-642-10646-0_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10645-3

  • Online ISBN: 978-3-642-10646-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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