Advertisement

Slice_OP: Selecting Initial Cluster Centers Using Observation Points

  • Md Abdul MasudEmail author
  • Joshua Zhexue Huang
  • Ming Zhong
  • Xianghua Fu
  • Mohammad Sultan Mahmud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11323)

Abstract

This paper proposes a new algorithm, Slice_OP, which selects the initial cluster centers on high-dimensional data. A set of observation points is allocated to transform the high-dimensional data into one-dimensional distance data. Multiple Gamma models are built on distance data, which are fitted with the expectation-maximization algorithm. The best-fitted model is selected with the second-order Akaike information criterion. We estimate the candidate initial centers from the objects in each component of the best-fitted model. A cluster tree is built based on the distance matrix of candidate initial centers and the cluster tree is divided into K branches. Objects in each branch are analyzed with k-nearest neighbor algorithm to select initial cluster centers. The experimental results show that the Slice_OP algorithm outperformed the state-of-the-art Kmeans++ algorithm and random center initialization in the k-means algorithm on synthetic and real-world datasets.

Keywords

Initial cluster center Clustering algorithm Center initialization Observation point 

Notes

Acknowledgment

This paper was supported by National Natural Science Foundations of China (under Grant No. 61473194 and 61472258) and Shenzhen-Hong Kong Technology Cooperation Foundation (under Grant No. SGLH20161209101100926).

References

  1. 1.
    Alcalafdez, J., Fernandez, A., Luengo, J., Derrac, J., Garcia, S.: KEEL data-mining software tool: data set repository, integration of algorithms and experimental analysis framework. Soft Comput. 17, 255–287 (2011)Google Scholar
  2. 2.
    Arthur, D., Vassilvitskii, S.: k-means++: the advantages of careful seeding. In: Symposium on Discrete Algorithms (SODA), pp. 1027–1035. Society for Industrial and Applied Mathematics (2007)Google Scholar
  3. 3.
    Banfield, J.D., Raftery, A.E.: Model-based Gaussian and non-Gaussian clustering. Biometrics 49(3), 803–821 (1993)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bradley, P.S., Fayyad, U.M.: Refining initial points for k-means clustering. In: Proceedings of 15th International Conference on Machine Learning, pp. 91–99. Morgan Kaufmann, San Francisco (1998)Google Scholar
  5. 5.
    Deelers, S., Auwatanamongkol, S.: Enhancing k-means algorithm with initial cluster centers derived from data partitioning along the data axis with the highest variance. Int. J. Phys. Math. Sci. 1(11), 518–523 (2007)Google Scholar
  6. 6.
    Dennis, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs (1983)zbMATHGoogle Scholar
  7. 7.
    Dheeru, D., Karra Taniskidou, E.: UCI machine learning repository (2017). http://archive.ics.uci.edu/ml
  8. 8.
    Erisoglu, M., Calis, N., Sakallioglu, S.: A new algorithm for initial cluster centers in k-means algorithm. Pattern Recogn. Lett. 32, 1701–1705 (2011)CrossRefGoogle Scholar
  9. 9.
    Figueiredo, M.A.T., Jain, A.K.: Unsupervised learning of finite mixture models. IEEE Trans. Pattern Anal. Mach. Intell. 24(3), 381–396 (2002)CrossRefGoogle Scholar
  10. 10.
    Fraley, C., Raftery, A.E.: Model-based clustering, discriminant analysis, and density estimation. J. Am. Stat. Assoc. 97(458), 611–631 (2002)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fraley, C., Raftery, A.E.: Bayesian regularization for normal mixture estimation and model-based clustering. J. Classif. 24(2), 155–181 (2007)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs (1998)zbMATHGoogle Scholar
  13. 13.
    Khan, S.S., Ahmad, A.: Cluster center initialization algorithm for k-means clustering. Pattern Recogn. Lett. 25(11), 1293–1302 (2004)CrossRefGoogle Scholar
  14. 14.
    Kuncheva, L.I., Hadjitodorov, S.: Using diversity in cluster ensembles. In: International Conference on System, Man and Cybernetics, vol. 2, pp. 1214–1219 (2004)Google Scholar
  15. 15.
    Lloyd, S.P.: Least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Manning, C.D., Raghavan, P., Schutze, H.: Introduction to Information Retrieval. Cambridge University Press, Cambridge, New York (2008). http://opac.inria.fr/record=b1127339CrossRefGoogle Scholar
  17. 17.
    Masud, M.A., Huang, J.Z., Wei, C., Wang, J., Khan, I., Zhong, M.: I-nice: a new approach for identifying the number of clusters and initial cluster centres. Inf. Sci. 466, 129–151 (2018)CrossRefGoogle Scholar
  18. 18.
    Sbhatia, M.P., Khurana, D.: Analysis of initial centers for k-means clustering algorithm. Int. J. Comput. Appl. 71(5), 9–12 (2013)Google Scholar
  19. 19.
    Sugiura, N.: Further analysis of the data by Akaike’ s information criterion and the finite corrections. Commun. Stat.-Theory Methods 7(1), 13–26 (1978)CrossRefGoogle Scholar
  20. 20.
    Tzortzis, G., Likas, A.: The minmax k-means clustering algorithm. Pattern Recogn. 47(7), 2505–2516 (2014)CrossRefGoogle Scholar
  21. 21.
    Vegas-Sáchez-Ferrero, G., et al.: Gamma mixture classifier for plaque detection in intravascular ultrasonic images. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 61(1), 44–61 (2014)CrossRefGoogle Scholar
  22. 22.
    Ye, Y., Huang, J.Z., Chen, X., Zhou, S., Williams, G., Xu, X.: Neighborhood density method for selecting initial cluster centers in k-means clustering. In: Ng, W.-K., Kitsuregawa, M., Li, J., Chang, K. (eds.) PAKDD 2006. LNCS (LNAI), vol. 3918, pp. 189–198. Springer, Heidelberg (2006).  https://doi.org/10.1007/11731139_23CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Md Abdul Masud
    • 1
    Email author
  • Joshua Zhexue Huang
    • 1
  • Ming Zhong
    • 1
  • Xianghua Fu
    • 1
  • Mohammad Sultan Mahmud
    • 1
  1. 1.Big Data Institute, College of Computer Science and Software EngineeringShenzhen UniversityShenzhenChina

Personalised recommendations