A New Algorithm for Computing the Minimal Enclosing Sphere in Feature Space

  • Conference paper
Fuzzy Systems and Knowledge Discovery (FSKD 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3614))

Included in the following conference series:

  • 1347 Accesses

Abstract

The problem of computing the minimal enclosing sphere (MES) of a set of points in the high dimensional kernel-induced feature space is considered. In this paper we develop an entropy-based algorithm that is suitable for any Mercer kernel map**. The proposed algorithm is based on maximum entropy principle and it is very simple to implement. The convergence of the novel algorithm is analyzed and the validity of this algorithm is confirmed by preliminary numerical results.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Berg, M.: Computational geometry: algorithms and application. Springer, New york (1997)

    Google Scholar 

  2. Elzinga, D.J., Hearn, D.W.: The minimum covering sphere problem. Management Science 19, 96–104 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  3. Schölkopf, B., Burges, C., Vapnik, V.: Extracting support data for a given task. In: Fayyad, U.M., Uthurusamy, R. (eds.) Proceedings First International Conference on Knowledge Discovery & Data Mining, pp. 252–257. AAAI Press, Menlo Park (1995)

    Google Scholar 

  4. Megiddo, N.: Linear-time algorithms for linear programming in R 3 and related problems. SIAM J. Comput. 12, 759–776 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  5. Welzl, E.: Smallest enclosing disks (balls and ellipses). In: Maurer, H. (ed.) New Results and New Trends in Computer Science. LNCS, vol. 555, pp. 359–370. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  6. Gärtner, B.: Fast and robust smallest enclosing balls. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 325–338. Springer, Heidelberg (1999)

    Google Scholar 

  7. Vapnik, V.: Statistical learning theory. John wiley & Sons, New York (1998)

    MATH  Google Scholar 

  8. Ben-Hur, A., Horn, D., Siegelmann, H.T., Vapnik, V.: Support vector clustering. Journal of Machine Learning Research 2, 125–137 (2001)

    Article  Google Scholar 

  9. Horn, D.: Clustering via Hibert space. Physica A 302, 70–79 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Platt, J.: Fast training of support vector machines using sequential minimal optimization. In: Scholkopf, B., Burges, C.J.C., Smola, A.J. (eds.) Advances in Kernel Methods — Support Vector Learning, pp. 185–208. MIT Press, Cambridge (1999)

    Google Scholar 

  11. Li, X.S.: An information entropy for optimization problems. Chinese Journal of Operations Research 8(1), 759–776 (1989)

    Google Scholar 

  12. Templeman, A.B., Li, X.S.: An maximum entropy approach to constrained non-linear programming. Engineering Optimization 12, 191–205 (1987)

    Article  Google Scholar 

  13. Kress, R.: Numerical analysis. Springer, New York (1998)

    MATH  Google Scholar 

  14. Blake, C.L., Merz, C.J.: UCI repository of machine learning databases, available at (1998), at http://www.ics.uci.edu/~mlearn/MLRepository.html

  15. Polak, E., Royset, J.O., Womersley, R.S.: Algorithms for adaptive smoothing for finite minimax problem. Journal of Optimization Theory and Applications 119(3), 459–484 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Guo, C., Lu, M., Sun, J., Lu, Y. (2005). A New Algorithm for Computing the Minimal Enclosing Sphere in Feature Space. In: Wang, L., **, Y. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2005. Lecture Notes in Computer Science(), vol 3614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11540007_24

Download citation

  • DOI: https://doi.org/10.1007/11540007_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28331-7

  • Online ISBN: 978-3-540-31828-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Navigation