Skip to main content
Springer Nature Link
Log in

Graph Based Kernel k-Means Using Representative Data Points as Initial Centers

  • Conference paper
  • First Online:
Intelligent Computing Theories and Methodologies (ICIC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9225))

Included in the following conference series:

  • 1794 Accesses

Abstract

The k-means algorithm is undoubtedly the most widely used data clustering algorithm due to its relative simplicity. It can only handle data that are linearly separable. A generalization of k-means is kernel k-means, which can handle data that are not linearly separable. Standard k-means and kernel k-means have the same disadvantage of being sensitive to the initial placement of the cluster centers. A novel kernel k-means algorithm is proposed in the paper. The proposed algorithm uses a graph based kernel matrix and finds k data points as initial centers for kernel k-means. Since finding the optimal data points as initial centers is an NP-hard problem, this problem is relaxed to obtain k representative data points as initial centers. Matching pursuit algorithm for multiple vectors is used to greedily find k representative data points. The proposed algorithm is tested on synthetic and real-world datasets and compared with kernel k-means algorithms using other initialization techniques. Our empirical study shows encouraging results of the proposed algorithm.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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 EPUB and 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

Similar content being viewed by others

References

  1. Jain, A.K.: Data clustering, 50 years beyond K-means. Pattern Recogn. Lett. 31, 651–666 (2010)

    Article  Google Scholar 

  2. Macqueen, J.: Some methods for classification and analysis of multivariate observations. In: Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–296 (1967)

    Google Scholar 

  3. Celebi, E.E., Kingravi, H.A., Vela, P.A.: A comparative study of efficient initialization methods for the K-means clustering algorithm. Expert Syst. Appl. 40, 200–210 (2013)

    Article  Google Scholar 

  4. Dhillon, I.S., Guan, Y., Kulis, B.: Weighted graph cuts without eigenvectors: a multilevel approach. IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 1944–1957 (2007)

    Article  Google Scholar 

  5. Schölkopf, B., Smola, A., Müller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10, 1299–1319 (1998)

    Article  Google Scholar 

  6. Hochbaum, D., Shmoys, D.: A best possible heuristic for the K-center problem. Math. Oper. Res. 10(2), 180–184 (1985)

    Article  MathSciNet  Google Scholar 

  7. Ball, G.H., Hall, D.J.: A clustering technique for summarizing multivariate data. Behav. Sci. 12(2), 153–155 (1967)

    Article  Google Scholar 

  8. Arthur, D., Vassilvitskii, S.: K-means++: the advantages of careful seeding. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1027–1035 (2007)

    Google Scholar 

  9. Hasan, M.A., Chaoji, V., Salem, S., Zaki, M.: Robust partitional clustering by outlier and density insensitive seeding. Pattern Recogn. 30(11), 994–1002 (2009)

    Article  Google Scholar 

  10. Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances In Neural Information Processing Systems, pp. 585–591 (2001)

    Google Scholar 

  11. Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)

    Article  Google Scholar 

  12. Smola, A.J., Kondor, R.: Kernels and regularization on graphs. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT/Kernel 2003. LNCS (LNAI), vol. 2777, pp. 144–158. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Velmurugan, T., Santhanam, T.: A survey of partition based clustering algorithms in data mining: an experimental approach. Inf. Technol. J. 10(3), 478–484 (2011)

    Article  Google Scholar 

  14. Yu, K., Bi, J., Tresp, V.: Active learning via transductive experimental design. In: International Conference on Machine Learning (2006)

    Google Scholar 

  15. Mallat, S.G., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Sig. Process. 41(12), 3397–3415 (1993)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (11374245).

Author information

Authors and Affiliations

  1. Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Minister of Education, Xiamen University, Xiamen, China

    Wuyi Yang & Liguo Tang

Authors
  1. Wuyi Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liguo Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wuyi Yang .

Editor information

Editors and Affiliations

  1. Tongji University, Shanghai, China

    De-Shuang Huang

  2. Polytecnic of Bari, Bari, Italy

    Vitoantonio Bevilacqua

  3. University of Wollongong, North Wollongong, New South Wales, Australia

    Prashan Premaratne

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Yang, W., Tang, L. (2015). Graph Based Kernel k-Means Using Representative Data Points as Initial Centers. In: Huang, DS., Bevilacqua, V., Premaratne, P. (eds) Intelligent Computing Theories and Methodologies. ICIC 2015. Lecture Notes in Computer Science(), vol 9225. Springer, Cham. https://doi.org/10.1007/978-3-319-22180-9_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22180-9_29

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22179-3

  • Online ISBN: 978-3-319-22180-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics