To Boost Graph Clustering Based on Power Iteration by Removing Outliers

  • Amin AzmoodehEmail author
  • Sattar Hashemi
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 285)


Power Iteration Clustering (PIC) is an applicable and scalable graph clustering algorithm using Power Iteration (PI) for embedding the graph into the low-dimensional eigenspace what makes graph clustering tractable. This paper investigates the negative impacts of outliers on power iteration clustering and based on this understanding we present a novel approach to remove outlier nodes in a given graph what in turn brings significant benefits to graph clustering paradigms. In the original PIC algorithm, outliers have a high potential to be mis-clustered, and hence, they impress the output of PI embedding. As a result, the embedded space offered by PIC couldn’t be deemed as a reasonable illustration of the graph in question. The statistical outlier detection method applied in this paper detects and removes outlier nodes in an iterative manner to enhance the embedded space for clustering. Experiments on several datasets across different domain show the advantages of the proposed method compared to the rival approaches.


Clustering Graph clustering Outlier detection Spectral clustering Power iteration method Eigenspace Spectrum 


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  1. 1.
    Frank Lin,William.W.Cohen : “Power Iteration Clustering”,International Conference on Machine Learning.pp.655-662,2010Google Scholar
  2. 2.
    Satu Elisa Schaeffer : “Graph clustering, survey “,Computer Science Review,2007, pp. 27-64Google Scholar
  3. 3.
    Benjamin Auffarth, “Spectral Graph Clustering “, Tech.Rep. Polytechnic University of Catalunya.2007Google Scholar
  4. 4.
    Ulrike von Luxburg. “A tutorial on spectral clustering”. Max Planck Institute for Biological Cybernetics.Tech.Rep.2007Google Scholar
  5. 5.
    D. Verma, M. Meila, “A comparison of spectral clustering algorithms”, Tech.Rep, Department of CSE University of Washington Seattle, WA, 98195–2350, 2005Google Scholar
  6. 6.
    Chung, F. R. K. “Spectral graph theory”. American Mathematical Society.1996Google Scholar
  7. 7.
    Shi, J. and Malik, J. “Normalized cuts and image segmentation”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 888 – 905.Google Scholar
  8. 8.
    Ng, A., Jordan, M., and Weiss.Y. “On spectral clustering: analysis and an algorithm”. Advances in Neural Information Processing Systems 2002, pp. 849 - 856Google Scholar
  9. 9.
    V. Chandola, A. Banerjee, and V. Kumar. “Anomaly Detection: A Survey”. ACM Computing Surveys, Volume 41 Issue 3, July 2009Google Scholar
  10. 10.
    Suzuki, E.; Watanabe, T.; Yokoi, H.; Takabayashi, K., “Detecting interesting exceptions from medical test data with visual summarization”. IEEE International Conference on Data Mining, Nov 2003, pp.315-322Google Scholar
  11. 11.
    Richard J. Bolton and David J. Hand. “Unsupervised profiling methods for fraud detection “. In Proceedings of the Conference on Credit Scoring and Credit Control VII, Edinburgh, UK,2001Google Scholar
  12. 12.
    Sun, P. and Chawla, S. “On local spatial outliers “. In Proceedings of 4th IEEE International Conference on Data Mining. 2004, pp.209-216.Google Scholar
  13. 13.
    Vinueza, A. and Grudic, G. “Unsupervised outlier detection and semi-supervised learning “.Tech. Rep. Univ. of Colorado at Boulder. May 2004Google Scholar
  14. 14.
    Anscombe, F. J. and Guttman, I. “Rejection of outliers”. Technimetrics. Vol. 2, No. 2.pp. 123-147. May 1960Google Scholar
  15. 15.
    Manning, Christopher D., Raghavan, Prabhakar, and Schtze, Hinrich. “Introduction to Information Retrieval “. Cambridge University Press, 2008.Google Scholar
  16. 16.
    Mariá C.V. Nascimento and André C.P.L.F. de Carvalho. “Spectral methods for graph clustering – A survey”. European Journal of Operational Research,Vol.211.No.2,pp. 221–231,June 2011Google Scholar
  17. 17.
    Anh Pham et al. “Deflation based power iteration clustering “. Applied Intelligence.February 2013 [Online].Available : [Accessed Aug. 11, 2013]
  18. 18.
    Zhenguo Li; Jianzhuang Liu; Shifeng Chen; Xiaoou Tang, “Noise Robust Spectral Clustering,” Computer Vision, 2007. ICCV 2007. IEEE 11th International Conference on, vol., no., pp.1,8, 14-21 Oct. 2007Google Scholar
  19. 19.
    Sivaraman Balakrishnan, Min Xu, Akshay Krishnamurthy, Aarti Singh, “Noise thresholds for spectral clustering,” Advances in Neural Information Processing Systems 2011, pp. 954 - 962Google Scholar

Copyright information

© Springer Science+Business Media Singapore 2014

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringShiraz UniversityShirazIslamic Republic of Iran

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