Fuzzy Multi-Sphere Support Vector Data Description

  • Trung Le
  • Dat Tran
  • Wanli Ma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7819)


Current well-known data description methods such as Support Vector Data Description and Small Sphere Large Margin are conducted with assumption that data samples of a class in feature space are drawn from a single distribution. Based on this assumption, a single hypersphere is constructed to provide a good data description for the data. However, real-world data samples may be drawn from some distinctive distributions and hence it does not guarantee that a single hypersphere can offer the best data description. In this paper, we introduce a Fuzzy Multi-sphere Support Vector Data Description approach to address this issue. We propose to use a set of hyperspheres to provide a better data description for a given data set. Calculations for determining optimal hyperspheres and experimental results for applying this proposed approach to classification problems are presented.


Kernel Methods Fuzzy Interference Support Vector Data Description Multi-Sphere Support Vector Data Description 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ben-Hur, A., Horn, D., Siegelmann, H.T., Vapnik, V.: Support vector clustering. Journal of Machine Learning Research 2, 125–137 (2001)Google Scholar
  2. 2.
    Boser, B.E., Guyon, I.M., Vapnik, V.: A training algorithm for optimal margin classifiers. In: Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory, pp. 144–152. ACM Press (1992)Google Scholar
  3. 3.
    Boyd, S., Vandenberghe, L.: Convex Optimisation. Cambridge University Press (2004)Google Scholar
  4. 4.
    Burges, C.J.C.: A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery 2, 121–167 (1998)CrossRefGoogle Scholar
  5. 5.
    Chen, Y., Zhou, X., Huang, T.S.: One-class svm for learning in image retrieval. In: ICIP (2001)Google Scholar
  6. 6.
    Chiang, J.-H., Hao, P.-Y.: A new kernel-based fuzzy clustering approach:support vector clustering with cell growing. IEEE Transactions on Fuzzy Systems 11(4), 518–527 (2003)CrossRefGoogle Scholar
  7. 7.
    Le, T., Tran, D., Ma, W., Sharma, D.: An optimal sphere and two large margins approach for novelty detection. In: The 2010 International Joint Conference on Neural Networks (IJCNN), pp. 1–6 (2010)Google Scholar
  8. 8.
    Le, T., Tran, D., Ma, W., Sharma, D.: A theoretical framework for multi-sphere support vector data description. In: Wong, K.W., Mendis, B.S.U., Bouzerdoum, A. (eds.) ICONIP 2010, Part II. LNCS, vol. 6444, pp. 132–142. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Lee, K., Kim, W., Lee, K.H., Lee, D.: Density-induced support vector data description. IEEE Transactions on Neural Networks 18(1), 284–289 (2007)CrossRefGoogle Scholar
  10. 10.
    GhasemiGol, M., Monsefi, R., Yazdi, H.S.: Ellipse support vector data description. In: Palmer-Brown, D., Draganova, C., Pimenidis, E., Mouratidis, H. (eds.) EANN 2009. CCIS, vol. 43, pp. 257–268. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Moya, M.M., Koch, M.W., Hostetler, L.D.: One-class classifier networks for target recognition applications, pp. 797–801 (1991)Google Scholar
  12. 12.
    Scott, C.D., Nowak, R.D.: Learning minimum volume sets. Journal of Machine Learning Research 7, 665–704 (2006)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Tax, D.M.J., Duin, R.P.W.: Support vector data description. Journal of Machine Learning Research 54(1), 45–66 (2004)zbMATHCrossRefGoogle Scholar
  14. 14.
    Tax, D.M.J., Duin, R.P.W.: Support vector domain description. Pattern Recognition Letters 20, 1191–1199 (1999)CrossRefGoogle Scholar
  15. 15.
    Wu, M., Ye, J.: A small sphere and large margin approach for novelty detection using training data with outliers. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(11), 2088–2092 (2009)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Xiao, Y., Liu, B., Cao, L., Wu, X., Zhang, C., Hao, Z., Yang, F., Cao, J.: Multi-sphere support vector data description for outliers detection on multi-distribution data. In: ICDM Workshops, pp. 82–87 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Trung Le
    • 1
  • Dat Tran
    • 2
  • Wanli Ma
    • 2
  1. 1.HCM City University of EducationVietnam
  2. 2.University of CanberraAustralia

Personalised recommendations