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Remotely Sensed Data Clustering Using K-Harmonic Means Algorithm and Cluster Validity Index

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Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT,volume 456)


In this paper, we propose a new clustering method based on the combination of K-harmonic means (KHM) clustering algorithm and cluster validity index for remotely sensed data clustering. The KHM is essentially insensitive to the initialization of the centers. In addition, cluster validity index is introduced to determine the optimal number of clusters in the data studied. Four cluster validity indices were compared in this work namely, DB index, XB index, PBMF index, WB-index and a new index has been deduced namely, WXI. The Experimental results and comparison with both K-means (KM) and fuzzy C-means (FCM) algorithms confirm the effectiveness of the proposed methodology.


  • Clustering
  • KHM
  • Cluster validity indices
  • Remotely sensed data
  • K-means
  • FCM


  1. Gan, G., Ma, C., Wu, J.: Data Clustering: Theory, Algorithms, and Applications. ASA-SIAM Serieson Statistics and Applied Probability. SIAM, Philadelphia (2007)

    CrossRef  Google Scholar 

  2. Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice-Hall, Englewood (1988)

    MATH  Google Scholar 

  3. Pakhira, M.K., Bandyopadhyay, S., Maulik, U.: A Study of Some Fuzzy Cluster Validity Indices, Genetic Clustering and Application to Pixel Classification. Fuzzy Sets and Systems 155, 191–214 (2005)

    CrossRef  MathSciNet  Google Scholar 

  4. Bezdeck, J.C.: FCM: Fuzzy C-Means algorithm. Computers and Geoscience 10, 191–203 (1984)

    CrossRef  Google Scholar 

  5. Gong, X.-J., Ci, L.-L., Yao, K.-Z.: A FCM algorithm for remote-sensing image classification considering spatial relationship and its parallel implementation. In: International Conference on Wavelet Analysis and Pattern Recognition, ICWAPR 2007, November 2-4, vol. 3, pp. 994–998 (2007)

    Google Scholar 

  6. Gao, Y., Wang, S., Liu, S.: Automatic Clustering Based on GA-FCM for Pattern Recognition. In: Second International Symposium on Computational Intelligence and Design, ISCID 2009, December 12-14, vol. 2, pp. 146–149 (2009)

    Google Scholar 

  7. McQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proc. 5th Berkeley Symp. Mathematics, Statistics and Probability, pp. 281–296 (1967)

    Google Scholar 

  8. Ball, G., Hall, D.: ISODATA: A novel method of data analysis and pattern classification. In Technical report, Stanford Research Institute, Menlo Park, CA, USA (1965)

    Google Scholar 

  9. Huang, K.: A Synergistic Automatic Clustering Technique (Syneract) for Multispectral Image Analysis. Photogrammetric Engineering and Remote Sensing 1(1), 33–40 (2002)

    Google Scholar 

  10. Zhao, Q.: Cluster validity in clustering methods. Ph.D. dissertation. University of Eastern Finland (2012)

    Google Scholar 

  11. Korgaonkar, G.S., Sedamkar, R.R., KiranBhandari.: Hyperspectral Image Classification on Decision level fusion. In: IJCA Proceedings on International Conference and Workshop on Emerging Trends in Technology, vol. 7, pp. 1–9 (2012)

    Google Scholar 

  12. Xie, X.L., Beni, A.: Validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 3, 841–846 (1991)

    CrossRef  Google Scholar 

  13. Bezdek, J.C.: Cluster validity with fuzzy sets. J. Cybernet. 3, 58–73 (1974)

    CrossRef  MathSciNet  Google Scholar 

  14. Bezdek, J.C.: Mathematical models for systematics and taxonomy. In: Eighth International Conference on Numerical Taxonomy, San Francisco, CA, pp. 143–165 (1975)

    Google Scholar 

  15. Davies, D., Bouldin, D.: A cluster separation measure. IEEE PAMI 1(2), 224–227 (1979)

    CrossRef  Google Scholar 

  16. Dunn, J.C.: A fuzzy relative of the isodata process and its use in detecting compact well separated clusters. J. Cybernet. 3, 32–57 (1973)

    CrossRef  MATH  MathSciNet  Google Scholar 

  17. Calinski, R.B., Harabasz, J.: Adendrite method for cluster analysis. Commun. Statist. 1–27 (1974)

    Google Scholar 

  18. Arbelaitz, O., Gurrutxaga, I., Muguerza, J., Prez, J.M., Perona, I.: An extensive comparative study of cluster validity indices. Pattern Recognition 46(1), 243–256 (2013)

    CrossRef  Google Scholar 

  19. Halkidi, M., Batistakis, Y., Vazirgiannis, M.: Clustering validity checking methods: Part II. SIGMOD Record 31(3), 19–27 (2002)

    CrossRef  Google Scholar 

  20. Zhang, B.: Generalized K-Harmonic Means Boosting in Unsupervised Learning. Technical Reports, Hewllet Laborotories, HPL-2000-137 (2000)

    Google Scholar 

  21. Zhang, L., Mao, L., Gong, H., Yang, H.: A K-harmonic Means Clustering Algorithm Based on Enhanced Differential Evolution. In: 2013 Fifth International Conference on Measuring Technology and Mechatronics Automation, 2014 Sixth International Conference on Measuring Technology and Mechatronics Automation, pp. 13–16 (2013)

    Google Scholar 

  22. Thangavel, K., Karthikeyani Visalakshi, K.: Ensemble based Distributed K- Harmonic Means Clustering. International Journal of Recent Trends in Engineering 2(1), 125–129 (2009)

    Google Scholar 

  23. Zhao, Q., Fränti, P.: WB-index: a sum-of-squares based index for cluster validity. Knowledge and Data Engineering 92, 77–89 (2014)

    CrossRef  Google Scholar 

  24. Malinen, M.I., Mariescu-Istodor, R., Fränti K-means*, P.: Clustering by gradual data transformation. Pattern Recognition 47(10), 3376–3386 (2014)

    Google Scholar 

  25. Thomas, J.C.R.: New Version of Davies-Bouldin Index for Clustering Validation Based on Cylindrical Distance. In: V Chilean Workshop on Pattern Recognition, November 11-15 (2013)

    Google Scholar 

  26. Zhang, L., Mao, L., Gong, H., Yang, H.: A K-harmonic Means Clustering Algorithm Based on Enhanced Differential Evolution. In: 2013 Fifth International Conference on Measuring Technology and Mechatronics Automation (ICMTMA), January 16-17, pp. 13–16 (2013), doi:10.1109/ICMTMA.2013.1

    Google Scholar 

  27. Emre, C.M., Kingravi, H.A., Vela, P.A.: A comparative study of efficient initialization methods for the k-means clustering algorithm. Expert Systems with Applications (2013)

    Google Scholar 

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Correspondence to Habib Mahi .

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Mahi, H., Farhi, N., Labed, K. (2015). Remotely Sensed Data Clustering Using K-Harmonic Means Algorithm and Cluster Validity Index. In: Amine, A., Bellatreche, L., Elberrichi, Z., Neuhold, E., Wrembel, R. (eds) Computer Science and Its Applications. CIIA 2015. IFIP Advances in Information and Communication Technology, vol 456. Springer, Cham.

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