Advertisement

Kernel k’-means Algorithm for Clustering Analysis

  • Yue Zhao
  • Shuyi Zhang
  • Jinwen Ma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7996)

Abstract

k’-means algorithm is a new improvement of k-means algorithm. It implements a rewarding and penalizing competitive learning mechanism into the k-means paradigm such that the number of clusters can be automatically determined for a given dataset. This paper further proposes the kernelized versions of k’-means algorithms with four different discrepancy metrics. It is demonstrated by the experiments on both synthetic and real-world datasets that these kernel k’-means algorithms can automatically detect the number of actual clusters in a dataset, with a classification accuracy rate being considerably better than those of the corresponding k’-means algorithms.

Keywords

Clustering analysis k-means algorithm Mercer kernels Kernel method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ma, J., Wang, T., Xu, L.: A Gradient BYY Harmony Learning Rule on Gaussian Mixture with Automated Model Selection. Neurocomputing 56, 481–487 (2004)CrossRefGoogle Scholar
  2. 2.
    MacQueen, J.: Some Methods for Classification and Analysis of Multivariate Observations. In: Proceedings of the fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297 (1967)Google Scholar
  3. 3.
    Kanungo, T., Mount, D., Netanyahu, N., et al.: An Efficient k-means Clustering Algorithm: Analysis and Implementation. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(7), 881–892 (2002)CrossRefGoogle Scholar
  4. 4.
    Ma, J., Wang, T.: A Cost-function Approach to Rival Penalized Competitive Learning (RPCL). IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 36(4), 722–737 (2006)CrossRefGoogle Scholar
  5. 5.
    Ma, J., He, X.: A Fast Fixed-point BYY Harmony Learning Algorithm on Gaussian Mixture with Automated Model Selection. Pattern Recognition Letters 29, 701–711 (2008)CrossRefGoogle Scholar
  6. 6.
    Ma, J., Liu, J., Ren, Z.: Parameter Estimation of Poisson Mixture with Automated Model Selection through BYY Harmony Learning. Pattern Recognition 42, 2659–2670 (2009)zbMATHCrossRefGoogle Scholar
  7. 7.
    Ma, J., Liu, J.: The BYY Annealing Learning Algorithm for Gaussian Mixture with Automated Model Selection. Pattern Recognition 40, 2029–2037 (2007)zbMATHCrossRefGoogle Scholar
  8. 8.
    Xu, L., Krzyzak, A., Oja, E.: Rival Penalized Competitive Learning for Clustering Analysis. RBF Net, and Curve Detection. IEEE Transactions on Neural Networks 4(4), 636–649 (1993)CrossRefGoogle Scholar
  9. 9.
    Ma, J., Cao, B.: The Mahalanobis Distance Based Rival Penalized Competitive Learning Algorithm. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 442–447. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Zalik, K.R.: An Efficient k’-means Clustering Algorithm. Pattern Recognition Letters 29, 1385–1391 (2008)CrossRefGoogle Scholar
  11. 11.
    Fang, C., Ma, J.: A Novel k’-means Algorithm for Clustering Analysis. In: Proceedings of the 2nd International Conference on Biomedical Engineering and Informatics (2009)Google Scholar
  12. 12.
    Fang, C., Jin, W., Ma, J.: k’-means Algorithms for Clustering Analysis with Frequency Sensitive Discrepancy Metrics. Pattern Recognition Letters 34, 580–586 (2013)CrossRefGoogle Scholar
  13. 13.
    Girolami, M.: Mercer Kernel-Based Clustering in Feature Space. IEEE Transactions on Neural Networks 13(3), 780–784 (2002)CrossRefGoogle Scholar
  14. 14.
    Taylor, J.S., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, London (2004)CrossRefGoogle Scholar
  15. 15.
    Filippone, M., Camastra, F., Masulli, F., Rovetta, S.: A Survey of Kernel and Spectral Methods for Clustering. Pattern Recognition 41(1), 176–190 (2008)zbMATHCrossRefGoogle Scholar
  16. 16.
    Muller, K., Mika, S., Ratsch, G., Tsuda, K., Scholkopf, B.: An Introduction to Kernel-Based Learning Algorithms. IEEE Transactions on Neural Networks 12(2), 181–201 (2001)CrossRefGoogle Scholar
  17. 17.
    Dhillon, I.S., Guan, Y., Kulis, B.: Kernel K-means, Spectral Clustering and Normalized Cuts. In: Proceedings of the tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 551–556 (2004)Google Scholar
  18. 18.
    Baudat, G., Anouar, F.: Generalized Discriminant Analysis Using a Kernel Approach. Neural Computation 12, 2385–2404 (2000)CrossRefGoogle Scholar
  19. 19.
    UCI Machine Learning Repository, http://mlearn.ics.uci.edu/databases
  20. 20.
    Shi, J., Malik, J.: Normalized Cuts and Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yue Zhao
    • 1
  • Shuyi Zhang
    • 1
  • Jinwen Ma
    • 1
  1. 1.Department of Information Science, School of Mathematical Sciences And LMAMPeking UniversityBeijingChina

Personalised recommendations