Skip to main content

A modified mountain clustering algorithm

Abstract

In this paper, we modify the mountain method and then create a modified mountain clustering algorithm. The proposed algorithm can automatically estimate the parameters in the modified mountain function in accordance with the structure of the data set based on the correlation self-comparison method. This algorithm can also estimate the number of clusters based on the proposed validity index. As a clustering tool to a grouped data set, the modified mountain algorithm becomes a new unsupervised approximate clustering method. Some examples are presented to demonstrate this algorithm’s simplicity and effectiveness and the computational complexity is also analyzed.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

References

  1. Duda RO, Hart PE (1973) Pattern classification and scene analysis. Wiley, New York

    Google Scholar 

  2. Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York

    Google Scholar 

  3. Yang MS (1993) A survey of fuzzy clustering. Math Comput Modelling 18:1–16

    Article  Google Scholar 

  4. Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353

    Article  Google Scholar 

  5. Höppner F, Klawonn F, Kruse R, Runkler T (1999) Fuzzy cluster analysis. Wiley, New York

    Google Scholar 

  6. Wu KL, Yang MS (2002) Alternative c-means clustering algorithm. Pattern Recognit 35:2267–2278

    Article  Google Scholar 

  7. Yang MS, Hu YJ, Lin KCR, Lin CCL (2002) Segmentation techniques for tissue differentiation in MRI of ophthalmology using fuzzy clustering algorithms. Magn Reson Imaging 20:173–179

    Article  PubMed  Google Scholar 

  8. Bezdek JC (1974) Cluster validity with fuzzy sets. J Cybernetics 3:58–73

    Google Scholar 

  9. Gath I, Geva AB (1989) Unsupervised optimal fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 11:773–781

    Article  Google Scholar 

  10. Windham MP (1982) Cluster validity for the fuzzy c-means clustering algorithm. IEEE Trans Pattern Anal Mach Intell 11:357–363

    Google Scholar 

  11. Xie XL, Beni G (1991) A validity measure for fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 13:841–847

    Article  Google Scholar 

  12. Yager RR, Filev DP (1994) Approximate clustering via the mountain method. IEEE Trans Syst Man Cybern 24:1279–1284

    Article  Google Scholar 

  13. Chiu SL (1994) Fuzzy model identification based on cluster estimation. J Intel Fuzzy Syst 2:267–278

    Article  Google Scholar 

  14. Pal NR, Chakraborty D (2000) Mountain and subtractive clustering method: improvements and generalizations. Int J Intell Syst 15:329–341

    Article  Google Scholar 

  15. Yager RR, Filev DP (1994) Generation of fuzzy rules by mountain clustering. J Intell Fuzzy Syst 2:209–219

    Google Scholar 

  16. Velthuizen BP, Hall LO, Clarke LP, Silbiger ML (1997) An investigation of mountain method clustering for large data sets. Pattern Recognit 30:1121–1135

    Article  Google Scholar 

  17. Beni G, Liu X (1994) A least biased fuzzy clustering method. IEEE Trans Pattern Anal Mach Intell 16:954–960

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments and suggestions to improve the presentation of the paper This work was supported in part by the National Science Council of Taiwan, under Grant NSC-89-2213-E-033-057

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Miin-Shen Yang.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Yang, MS., Wu, KL. A modified mountain clustering algorithm. Pattern Anal Applic 8, 125–138 (2005). https://doi.org/10.1007/s10044-005-0250-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10044-005-0250-9

Keywords

  • Mountain method
  • Modified mountain algorithm
  • Parameter estimation
  • Validity index
  • Unsupervised clustering