Neural Processing Letters

, Volume 9, Issue 3, pp 293–300 | Cite as

Least Squares Support Vector Machine Classifiers

  • J.A.K. Suykens
  • J. Vandewalle


In this letter we discuss a least squares version for support vector machine (SVM) classifiers. Due to equality type constraints in the formulation, the solution follows from solving a set of linear equations, instead of quadratic programming for classical SVM's. The approach is illustrated on a two-spiral benchmark classification problem.

classification support vector machines linear least squares radial basis function kernel 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C.M. Bishop, Neural Networks for Pattern Recognition,Oxford University Press, 1995.Google Scholar
  2. 2.
    V. Cherkassky and F. Mulier, Learningfrom Data: Concepts, Theory and Methods, John Wiley and Sons, 1998.Google Scholar
  3. 3.
    R. Fletcher, Practical Methods of Optimization, John Wiley and Sons: Chichester and New York, 1987.Google Scholar
  4. 4.
    G.H. Golub and C.F. van Loan, MatrixComputations, Johns Hopkins University Press: Baltimore MD, 1989.Google Scholar
  5. 5.
    S. Haykin, Neural Networks: A Comprehensive Foundation, Macmillan College Publishing Company: Englewood Cliffs, 1994.Google Scholar
  6. 6.
    S. Ridella, S. Rovetta and R. Zunino, “Circular back propagation networks for classification, ” IEEE Transactions on Neural Networks, Vol. 8, No. 1, pp. 84–97, 1997.Google Scholar
  7. 7.
    C. Saunders, A. Gammerman and V. Vovk, “Ridge regression learning algorithm in dual variables, ” Proceedings of the 15th International Conference on Machine Learning ICML-98, Madison-Wisconsin, 1998.Google Scholar
  8. 8.
    B. Schölkopf, K.-K. Sung, C. Burges, F. Girosi, P. Niyogi, T. Poggio and V. Vapnik, “Comparing support vector machines with Gaussian kernels to radial basis function classifiers, ” IEEE Transactions on Signal Processing, Vol. 45, No. 11, pp. 2758–2765, 1997.Google Scholar
  9. 9.
    V. Vapnik, “The nature of statistical learning theory, ” Springer-Verlag: New York, 1995.Google Scholar
  10. 10.
    V. Vapnik, “Statistical learning theory, ” John Wiley: New York, 1998.Google Scholar
  11. 11.
    V. Vapnik, “The support vector method of function estimation, ” in J.A.K. Suykens and J. Vandewalle (Eds) Nonlinear Modeling: Advanced Black-Box Techniques, Kluwer Academic Publishers, Boston, pp. 55–85, 1998.Google Scholar
  12. 12.
    J.M. Zurada, Introduction to Artificial Neural Systems, West Publishing Company, 1992.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • J.A.K. Suykens
    • 1
  • J. Vandewalle
    • 1
  1. 1.Department of Electrical EngineeringKatholieke Universiteit LeuvenLeuven (Heverlee)Belgium, e-mail

Personalised recommendations