Skip to main content

Part of the book series: Computer Science Workbench ((WORKBENCH))

Abstract

Clustering, also referred to as cluster analysis, is a class of unsupervised classification methods for data analysis. There have been numerous studies of clustering, which are both theoretical and applicational. Applications to scientific classifications, engineering problems, behavioral sciences. etc., have been investigated and usefulness of this technique has been appreciated.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.R. Anderberg, Cluster Analysis for Applications, Academic Press, New York, 1973.

    MATH  Google Scholar 

  2. E. Backer, Cluster Analysis by Optimal Decomposition of Induced Fuzzy Sets, Delft Univ. Press, Delft, The Netherlands, 1978.

    Google Scholar 

  3. J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum, New York, 1981.

    MATH  Google Scholar 

  4. L. Bobrowski, J.C. Bezdek, “c-means clustering with the ℓ1 and ℓ norms,” IEEE 7rans. on Syst., Man, and Cybern., Vol. 21, No.3, pp.545–554, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Chardrand, L. Lesniak, Graphs and Digraphs, 2nd ed., Wadsworth, Monterey, C alifornia, 1986.

    Google Scholar 

  6. A.P. Dempster, N.M. Laird, D.B. Rubin, “MAXIMUM likelihood from incomplete data via the EM algorithm,” J. of the Royal Statistical Society, B., Vol.39, pp.1–38, 1977.

    MathSciNet  MATH  Google Scholar 

  7. R.O. Duda, P.E. Hart, Pattern Classification and Scene Analysis, Wiley, New York, 1973.

    MATH  Google Scholar 

  8. J.C. Dunn, “A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters,” J. of Cybernetics, Vol.3, pp.32–57, 1974.

    Article  MathSciNet  Google Scholar 

  9. J.C. Dunn, “Well-separated clusters and optimal fuzzy partitions,” J. of Cybernetics, Vol.4, pp.95–104, 1974.

    Article  MathSciNet  Google Scholar 

  10. J.C. Dunn, “A graph theoretic analysis of pattern classification via Tamura’s fuzzy relation,” IEEE Trans., Syst., Man, and Cybern., Vol.4, pp.310–313, 1974.

    MATH  Google Scholar 

  11. B.S. Everitt, Cluster Analysis, 3rd ed., Arnold, London, 1993.

    Google Scholar 

  12. R.J. Hathaway and J.C. Bezdek, “Switching regression models and fuzzy clustering,” IEEE Trans. on Fuzzy Syst., Vol.1, pp.195–204, 1993.

    Article  Google Scholar 

  13. F. Hüppner, F. Klawonn, R Kruse, and T. Runkler, Fuzzy Cluster Analysis, Wiley, Chichester, 1999.

    Google Scholar 

  14. A.K. Jain and R.C. Dubes, Algorithms for Clustering Data, Prentice Hall, Englewood Cliffs, NJ, 1988.

    MATH  Google Scholar 

  15. K. Jajuga, “L1-norm based fuzzy clustering,” Fuzzy Sets and Systems, Vol. 39, pp.43–50, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  16. J.M. Keller, M.R. Gray, and J.A. Givens, Jr., “A fuzzy k-nearest neighbor algorithm,” IEEE Tmns., on Syst., Man, and Cybern., Vol.5, pp.580–585, 1985.

    Google Scholar 

  17. T. Kohonen, Self-Organizing Maps, 2nd Ed., Springer, Berlin, 1997.

    MATH  Google Scholar 

  18. R Krishnapuram and J.M. Keller, “A possibilistic approach to clustering,” IEEE Trans. on Fuzzy Syst., Vol.1, No.2, pp.98–110, 1993.

    Article  Google Scholar 

  19. J.B. Kruskal, Jr., “On the shortest spanning subtree of a graph and the traveling salesman problem,” Proc. Amer. Math. Soc., Vol.7, No.1, pp.48–50, 1956.

    Article  MathSciNet  MATH  Google Scholar 

  20. R.-P. Li and M. Mukaidono, “A maximum entropy approach to fuzzy clustering,” Proc. of the 4th IEEE Intern. Conf. on Fuzzy Systems (FUZZ-IEEE/IFES’95), Yokohama, Japan, March 20-24, 1995, pp.2227–2232, 1995.

    Google Scholar 

  21. J.B. MacQueen, “Some methods of classification and analysis of multivariate observations,” Proc. of 5th Berkeley Symposium on Math. Stat. and Prob., pp.281–297, 1967.

    Google Scholar 

  22. F. Masulli, M. Artuso, P. Bogus, and A. Schenone, “Fuzzy clustering methods for the segmentation of multivariate medical images,” Proc. of the 7th International Fuzzy Systems Association World Congress (IFSA’ 97), June 25-30, 1997, Prague,Chech, pp.123–128, 1997.

    Google Scholar 

  23. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, Berlin, 1992.

    MATH  Google Scholar 

  24. S. Miyamoto, Fuzzy Sets in Information Retrieval and Cluster Analysis, Kluwer Academic Publishers, Dordrecht, 1990.

    MATH  Google Scholar 

  25. S. Miyamoto, “Fuzzy graphs as a basic tool for agglomerative clustering and information retrieval,” In: O. Opitz, et. al., (Eds.), Information and Classification: Concepts, Methods, and Applications, Springer-Verlag, Berlin, pp.268–281, 1993.

    Google Scholar 

  26. S. Miyamoto and Y. Agusta, “An efficient algorithm for ℓ1 fuzzy c-means and its termination,” Control and Cybernetics Vol. 24, No.4, pp.421–436, 1995.

    MATH  Google Scholar 

  27. S. Miyamoto and S. Katoh, “Metaheuristic methods for optimal clustering,” Computing Science and Statistics, Vol.29, No.2, pp.439–443, 1997.

    Google Scholar 

  28. S. Miyamoto and M. Mukaidono, “Fuzzy c-means as a regularization and maximum entropy approach,” Proc. of the 7th International Fuzzy Systems Association World Congress (IFSA’ 97), June 25-30, 1997, Prague, Chech, Vol.II, pp.86–92, 1997.

    Google Scholar 

  29. S. Miyamoto and Y. Agusta, “Algorithms for L1 and Lp fuzzy c-means and their convergence,” in: C. Hayashi, et. al., (Eds.), Data Science, Classification, and Related Methods, Springer-Verlag, Tokyo, pp.295–302, 1997.

    Google Scholar 

  30. S. Miyamoto and S. Katoh, “Crisp and fuzzy methods of optimal clustering on networks of objects,” Proc. of KES’98, April 21-23, 1998, Adelaide, Australia, pp.177–182, 1998.

    Google Scholar 

  31. S. Miyamoto and K. Umayahara, “Fuzzy clustering by quadratic regularization,” Proc. of FUZZ-IEEE’98, May 4-9, 1998, Anchorage, Alaska, pp.1394–1399, 1998.

    Google Scholar 

  32. S. Miyamoto and K. Umayahara, “Two methods of fuzzy c-means and classification functions,” Proceedings of the 6th Conference of the International Federation of Classification Societies (IFCS-98), Rome, 21-24, July, 1998, pp.105–110, 1998.

    Google Scholar 

  33. Y. Nakamori, M. Ryoke, and K. Umayahara, “Multivariate analysis for fuzzy modeling,” Proc. of the 7th International Fuzzy Systems Association World Congress (IFSA’ 97), June 25-30, 1997, Prague, Chech, Vol.II, pp.93–98, 1997.

    Google Scholar 

  34. N.K. Pal, J.C. Bezdek, and E.C.-K. Tsao, “Generalized clustering networks and Kohonen’s self-organizing scheme,” IEEE Trans. on Neural Networks, Vol.4, No.4, pp.549–557, 1993.

    Article  Google Scholar 

  35. F.P. Preparata and M.L. Shamos, Computational Geometry: An Introduction, Springer, New York, 1985.

    Google Scholar 

  36. V.V. Raghavan and K. Birchard, “A clustering strategy based on a formalism of the reproductive processes in natural systems,” Proceedings of the Second International Conference on Information Retrieval, pp.10–22, 1979.

    Google Scholar 

  37. R.A. Redner and H.F. Walker, “Mixture densities, maximum likelihood and the EM algorithm,” SIAM Review, Vol.26, No.2, pp.195–239, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  38. K. Rose, E. Gurewitz, and G. Fox, “A deterministic annealing approach to clustering,” Pattern Recognition Letters, Vol.11, pp.589–594, 1990.

    Article  MATH  Google Scholar 

  39. E.H. Ruspini, “A new approach to clustering,” Information and Control, Vol. 15, pp.22–32, 1969.

    Article  MATH  Google Scholar 

  40. M. Sato and Y. Sato, “On a general fuzzy additive clustering model,” Intern. J. of Intelligent Automation and Soft Computing, Vol.1, No.4, pp.439–448, 1995.

    Google Scholar 

  41. R.N. Shepard and P. Arabie, “Additive clustering: representation of similarities as combinations of discrete overlapping properties,” Psychological Review, Vol.86, No.2, pp.87–123, 1979.

    Article  Google Scholar 

  42. S. Tamura, S. Higuchi, and K. Tanaka, “Pattern classifications based on fuzzy relations,” IEEE Trans. on Syst., Man, and Cybern., Vol.1, No.1, pp.61–66, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  43. A.N. Tihonov, “Solutions of incorrectly formulated problems and the regularization method,” Dokl. Akad. Nauk. SSSR, Vol.151, pp.1035–1038, 1963.

    MathSciNet  Google Scholar 

  44. A.N. Tihonov and V.Y. Arsenin, Solutions of Ill-Posed Problems, Wiley, New York, 1977.

    Google Scholar 

  45. K. Umayahara and Y. Nakamori, “N-dimensional views in fuzzy data analysis,” Proc. of 1997 IEEE Intern. Conf. on Intelligent Processing Systems, Oct.28-31, Beijing, China, pp.54–57, 1997.

    Google Scholar 

  46. N. Wu, The Maximum Entropy Method, Springer, Berlin, 1997.

    Book  MATH  Google Scholar 

  47. L.A. Zadeh, “Fuzzy sets,” Information and Control, Vol.8, pp.338–353, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  48. L.A. Zadeh, “Similarity relations and fuzzy orderings,” Information Sciences, Vol.3, pp.177–200, 1971.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Tokyo

About this chapter

Cite this chapter

Miyamoto, S., Umayahara, K. (2000). Methods in Hard and Fuzzy Clustering. In: Liu, ZQ., Miyamoto, S. (eds) Soft Computing and Human-Centered Machines. Computer Science Workbench. Springer, Tokyo. https://doi.org/10.1007/978-4-431-67907-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-67907-3_5

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-70279-5

  • Online ISBN: 978-4-431-67907-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics