A Spectral Clustering Algorithm Based on Hierarchical Method

  • Xiwei Chen
  • Li LiuEmail author
  • Dashi Luo
  • Guandong Xu
  • Yonggang Lu
  • Ming Liu
  • Rongmin Gao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8316)


Most of the clustering algorithms were designed to cluster the data in convex spherical sample space, but their ability was poor for clustering more complex structures. In the past few years, several spectral clustering algorithms were proposed to cluster arbitrarily shaped data in various real applications including image processing and web analysis. However, most of these algorithms were based on k-means, which is a randomized algorithm and makes the algorithm easy to fall into local optimal solutions. Hierarchical method could handle the local optimum well because it organizes data into different groups at different levels. In this paper, we propose a novel clustering algorithm called spectral clustering algorithm based on hierarchical clustering (SCHC), which combines the advantages of hierarchical clustering and spectral clustering algorithms to avoid the local optimum issues. The experiments on both synthetic data sets and real data sets show that SCHC outperforms other six popular clustering algorithms. The method is simple but is shown to be efficient in clustering both convex shaped data and arbitrarily shaped data.


Data mining Clustering Spectral clustering Hierarchical clustering 



This work was partially supported by the National Natural Science Foundation of China (grant no.61003240), the Scientific Research Foundation for the Returned Overseas Chinese Scholars(grant order no.44th), and the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (grant year 2012).


  1. 1.
    Qiu, H., Hancock, E.R.: Graph matching and clustering using spectral partitions. J. Pattern Recogn. Soc. 39(1), 22–24 (2006)CrossRefGoogle Scholar
  2. 2.
    Lloyd, P.S.: least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Bishop, C.M.: Pattern Recognition and Machine Learning, Ch. 9. Springer, New York (2006). ISBN 0-387-31073-8Google Scholar
  4. 4.
    Gao, Y., Gu, S., Tang, J.: Research on spectral clustering in machine learning. Comput. Sci. 34(2), 201–203 (2007)Google Scholar
  5. 5.
    Ng, A.Y., Jordan, M., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: Advances in Neural Information Processing Systems (NIPS) (2002)Google Scholar
  6. 6.
    Ding, S., Zhang, L., Zhang, Y.: Research on spectral clustering algorithms and prospects. In: The 2nd International Conference on Computer Engineering and Technology (ICCET), vol. 6, pp. 149–153, April 2010Google Scholar
  7. 7.
    Chen, W.Y., Song, Y., et al.: Parallel spectral clustering in distributed systems. IEEE Trans. Pattern Anal. Mach. Intell. 33(3), 568–586 (2011)CrossRefGoogle Scholar
  8. 8.
    Wang, C., Wang, J., Zhen, J.: Application of spectral clustering in image retrieval. Comput. Tech. Dev. 19(1), 207–210 (2009)MathSciNetGoogle Scholar
  9. 9.
    Ekin, A., Pankanti, S., Hampapur, A.: Initialization-independent spectral clustering with applications to automatic video analysis. In: IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 3, pp. 641–644, May 2004Google Scholar
  10. 10.
    Jiang, Y., Tang, C., et al.: CTSC: core-tag oriented spectral clustering algorithm on Web2.0 tags. In: The Sixth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 09), vol. 1, pp. 460–464, August 2009Google Scholar
  11. 11.
    Bach, F.R., Jordan, M.I.: Spectral clustering for speech separation. In: Automatic Speech and Speaker Recognition: Large Margin and Kernel, Methods, pp. 221–253, January 2009Google Scholar
  12. 12.
    Wang, H., Chen, J., Guo, K.: A genetic spectral clustering algorithm. J. Comput. Inf. Syst. 7(9), 3245–3252 (2011)Google Scholar
  13. 13.
    Qian, W., Zhou, A.: Analyzing popular clustering algorithms from different viewpoints. J. Softw. 13(8), 1382–1394 (2002)Google Scholar
  14. 14.
    Tian, Z., Li, X., Ju, Y.: The perturbation analysis of the spectral clustering. Chin. Sci. 37(4), 527–543 (2007)Google Scholar
  15. 15.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)CrossRefGoogle Scholar
  16. 16.
    Meila, M., Shi, J.: Learning segmentation with random walk. In: Advances in Neural Information Processing Systems (NIPS), pp. 470–477 (2001)Google Scholar
  17. 17.
    Yu, S., Shi, J.B.: Multiclass spectral clustering. In: Ninth IEEE International Conference on Computer Vision, vol. 1, pp. 313–319, October 2003Google Scholar
  18. 18.
    Gower, J.C., Ross, G.J.S.: Minimum spanning trees and single linkage cluster. J. Roy. Stat. Soc. Series C (Applied Statistics) 18(1), 54–64 (1969)MathSciNetGoogle Scholar
  19. 19.
    Bezdek, J.C., Ehrlich, R., Full, W.: FCM: the fuzzy c-means clustering algorithm. Comput. Geosci. 10(2–3), 191–203 (1984)CrossRefGoogle Scholar
  20. 20.
    Zhang, X., et al.: K-AP: generating specified K clusters by efficient affinity propagation. In: IEEE 10th International Conference on Data Mining (ICDM), pp. 1187–1192 (2010)Google Scholar
  21. 21.
    Hong, C., Yeung, D.Y.: Robust path-based spectral clustering. Pattern Recogn. 41(1), 191–203 (2008)CrossRefzbMATHGoogle Scholar
  22. 22.
    Gionis, A., Mannila, H., Tsaparas, P.: Clustering aggregation. In: 21st International Conference on Date of Conference, pp. 341–352, April 2005Google Scholar
  23. 23.
  24. 24.
    Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. 1, 224–227 (1979)CrossRefGoogle Scholar
  25. 25.
    Hubert, L.J., Arabie, P.: Comparing partitions. J. Classif. 2, 193–218 (1985)CrossRefGoogle Scholar
  26. 26.
  27. 27.
    Cao, L., Gorodetsky, V., Mitkas, P.: Agent mining: the synergy of agents and data mining. IEEE Intell. Syst. 24(3), 64–72 (2009)CrossRefGoogle Scholar
  28. 28.
    Lu, Y., Wan, Y.: Clustering by sorting potential values (CSPV): a novel potential-based clustering method. Pattern Recogn. 45(9), 3512–3522 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Xiwei Chen
    • 1
  • Li Liu
    • 1
    Email author
  • Dashi Luo
    • 1
  • Guandong Xu
    • 2
  • Yonggang Lu
    • 1
  • Ming Liu
    • 3
  • Rongmin Gao
    • 4
  1. 1.School of Information Science and EngineeringLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.Advanced Analytics InstituteUniversity of Technology SydneyUltimoAustralia
  3. 3.School of Electrical and Information EngineeringThe University of SydneySydneyAustralia
  4. 4.School of PharmacyLanzhou UniversityLanzhouPeople’s Republic of China

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