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Pattern Analysis and Applications

, Volume 20, Issue 2, pp 495–506 | Cite as

Spectral clustering based on similarity and dissimilarity criterion

  • Bangjun WangEmail author
  • Li Zhang
  • Caili Wu
  • Fan-zhang Li
  • Zhao Zhang
Theoretical Advances

Abstract

The clustering assumption is to maximize the within-cluster similarity and simultaneously to minimize the between-cluster similarity for a given unlabeled dataset. This paper deals with a new spectral clustering algorithm based on a similarity and dissimilarity criterion by incorporating a dissimilarity criterion into the normalized cut criterion. The within-cluster similarity and the between-cluster dissimilarity can be enhanced to result in good clustering performance. Experimental results on toy and real-world datasets show that the new spectral clustering algorithm has a promising performance.

Keywords

Spectral clustering Normalized cut Similarity criterion Dissimilarity criterion 

References

  1. 1.
    Barreto A, Araujo AA, Kremer S (2003) A taxonomy for spatiotemporal connectionist networks revisited: the unsupervised case. Neural Comput 15:1255–1320CrossRefzbMATHGoogle Scholar
  2. 2.
    Bezdek JC, Pal RN (1998) Some new indexes of cluster validity. IEEE Trans Pattern Recognit Mach Intell 28(3):301–315Google Scholar
  3. 3.
    Chen W, Feng G (2012) Spectral clustering: a semisupervised approach. Neurocomputing 77(1):229–242CrossRefGoogle Scholar
  4. 4.
    Chen WY, Song Y, Bai H, Lin C-J, Chang E (2011) Parallel spectral clustering in distributed systems. IEEE Trans Pattern Recognit Mach Intell 33(3):568–586CrossRefGoogle Scholar
  5. 5.
    Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Recognit Mach Intell 1(4):224–227CrossRefGoogle Scholar
  6. 6.
    Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MathSciNetzbMATHGoogle Scholar
  7. 7.
    CHQ Ding, X He, H Zha, M Gu, HD Simon (2001) A min-max cut algorithm for graph partitioning and data clustering. In: Proceedings of the first IEEE International Conference on Data Mining (ICDM), Washington. DC, USA, pp 107–114Google Scholar
  8. 8.
    Duda R, Hart P, Stork D (2000) Pattern classification. Wiley-Interscience, LondonzbMATHGoogle Scholar
  9. 9.
    Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc 32:675–701CrossRefzbMATHGoogle Scholar
  10. 10.
    Graham DB, Allinson NM (1998) Characterizing virtual Eigensignatures for general purpose face recognition. Face Recognit: From Theory Appl, NATO ASI Ser F, Comput Syst Sci 163:446–456CrossRefGoogle Scholar
  11. 11.
    Hagen L, Kahng AB (1992) New spectral methods for ratio cut partitioning and clustering. IEEE Trans Comput Aided Des Integr Circuits Syst 11(9):1074–1085CrossRefGoogle Scholar
  12. 12.
    Lago-Fernández LF, Corbacho F (2010) Normality-based validation for crisp clustering. Pattern Recogn 43(3):782–795CrossRefzbMATHGoogle Scholar
  13. 13.
    Z Lu, M Carreira-Perpinan (2008) Constrained spectral clustering through affinity propagation. In: Proceedings of CVPR, Anchorage, Alaska, USA, pp 1–8Google Scholar
  14. 14.
    Lu H, Fu Z, Shu X (2014) Non-negative and sparse spectral clustering. Pattern Recogn 47(1):418–426CrossRefzbMATHGoogle Scholar
  15. 15.
    Luxburg U (2007) A tutorial on spectral clustering. Statistics and computing 17(4):395–416MathSciNetCrossRefGoogle Scholar
  16. 16.
    Rousseeuw PJ (1987) Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math 20:53–65CrossRefzbMATHGoogle Scholar
  17. 17.
    Serkar S, Soundararajan P (2000) Supervised learning of large perceptual organization: graph spectral partitioning and learning automata. IEEE Trans Pattern Anal Mach Intell 22(5):504–525CrossRefGoogle Scholar
  18. 18.
    Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905CrossRefGoogle Scholar
  19. 19.
    Wacquet G, Caillault EP, Hamad D, H´ebert P-A (2013) Constrained spectral embedding for k-way data clustering. Pattern Recogn Lett 34(9):1009–1017CrossRefGoogle Scholar
  20. 20.
    X Wang, I Davidson (2010) Flexible constrained spectral clustering. In: The 16th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Washington DC, USA, pp 563–572Google Scholar
  21. 21.
    Wang S, Siskind J (2003) Image segmentation with ratio cut. IEEE Trans Pattern Anal Mach Intell 25(6):675–690CrossRefGoogle Scholar
  22. 22.
    Wu Z, Leahy R (1993) An optimal graph theoretic approach to data clustering: theory and its application to image segmentation. IEEE Trans Pattern Anal Mach Intell 15(11):1101–1113CrossRefGoogle Scholar
  23. 23.
    AY Ng, MI Jordan (2002) On spectral clustering: analysis and an algorithm. In: Advances in neural information processing systems. Vancouver, British Columbia, Canada, pp 849–856Google Scholar
  24. 24.
    L Zelnik-Manor, P Perona (2004) Self-tuning spectral clustering. In: Saul LK, Weiss Y, Bottou L (eds) The 18th annual conference on neural information processing systems, Vancouver, British Columbia, Canada, pp 1601–1608Google Scholar
  25. 25.
    HS Zou, WD Zhou, L Zhang, CL Wu, RC Liu, LC Jiao (2009) A new constrained spectral clustering for sar image segmentation. In: Proceedings 2009 2nd Asian-Pacific Conference on Synthetic Aperture Radar, Xian, China, pp 680–683Google Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Bangjun Wang
    • 1
    • 2
    Email author
  • Li Zhang
    • 2
  • Caili Wu
    • 2
  • Fan-zhang Li
    • 2
  • Zhao Zhang
    • 2
  1. 1.Beijing Jiaotong UniversityBeijingChina
  2. 2.Soochow UniversitySuzhouChina

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