A comparative study of LS-SVM's applied to the Silver Box identification problem

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 37, Issue 13, 2004, Pages 369-374

  Espinoza, Marcelo ^a   Pelckmans, Kristiaan ^a   Hoegaerts, Luc ^a   Suykens, Johan A K ^a   De Moor, Bart ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Identification; Nonlinear models

Indexed keywords

IDENTIFICATION (CONTROL SYSTEMS); LEAST SQUARES APPROXIMATIONS; MEAN SQUARE ERROR; NONLINEAR SYSTEMS; REGRESSION ANALYSIS; SILVER;

COMPARATIVE STUDIES; DUAL REPRESENTATION; IDENTIFICATION PROBLEM; NON-LINEAR MODEL; NONLINEAR MAPPINGS; ORDINARY LEAST SQUARES; PARTIAL LEAST SQUARE (PLS); ROOT MEAN SQUARED ERRORS;

ITERATIVE METHODS;

EID: 78650848517     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1016/S1474-6670(17)31251-X     Document Type: Conference Paper

References (17)

1. Cristianini, N., and Shawe-Taylor, J., An introduction to Support Vector Machines, Cambridge University Press, 2000.
2. Espinoza, M., Suykens, J. A. K. and De Moor B. L. R. "Least Squares Support Vector Machines and Primal Space Estimation", In Proc. of the 42nd IEEE Conference on Decision and Control, Maui, USA, pp. 3451-3456, 2003.
3. Giruiami, M. "Orthogonal Series Density Estimation and the Kernel Eigenvalue Problem", Neural Computation 14(3), 669-688, 2003.
4. Girosi, F. "An Equivalence Between Sparse Approximation and Support Vector Machines", Neural Computation, 10(6), 1455-1480, 1998
5. Hoerl, A. E. and Kennard, R. W. "Ridge Regression: Biased Estimation for Non Orthogonal Problems", Technometrics 8, 27-51, 1970.
6. Ljung, L. System Identification: Theory for the User. 2nd Edition, Prentice Hall, New Jersey, 1999.
7. MacKay, D. J. C. "Probable Networks and Plausible Predictions - A Review of Practical Bayesian Methods for Supervised Neural Networks", Networks: Computations in Neural Systems, 6, 469-505, 1995.
8. Poggio, T. and Girosi, F. "Networks for Approximation and Learning", Proceedings of the IEEE, 78(9), 1481-1497, 1990.
9. Rosipal R. and Trejo, J. "Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space", Journal of Machine Learning Research, 2, 97-123, 2001.
10. Shawe-Taylor, J. and Williams, C. K. I. "The Stability of Kernel Principal Components Analysis and its Relation to the Process Eigenspectrum", in Advances in Neural Information Processing Systems 15, MIT Press, 2003.
11. Schoukons J., Nemeth G., Crania P., Rolain V., Pintelon R. "Fast Approximate Identification of Nonlinear Systems", Automatica 39(7), 2003.
12. Sjoberg, J., Zhang, Q., Ljung, L., Benveniste, A., Delyon, B., Glorennec, P.-Y., Hjahnarsson H., Juditsky, A., "Nonlinear Black-Box Modelling in Systems Identification: A Unified Overview", Automatica 31(12), 1691-1724, 1995.
13. Suykens, J. A. K., Vandewalle, J. "Least Squares Support Vector Machines Classifiers", Neural Processing Letters 9, 293-300, (1999).
14. Suykens J. A. K., De Brabanter J., Lukas, L. Vandewalle J., "Weighted Least Squares Support Vector Machines: Robustness and Sparse Approximation", Neurocomputing, vol. 48, no. 1-4, pp. 85-105, 2002.
15. Suykens J. A. K., Van Gestel T., De Brabanter J., De Moor B., Vandewalle J., Least Squares Support Vector Machines. World Scientific, 2002, Singapore.
16. Vapnik, V. Statistical Learning Theory, John Wiley & Sons, New York, 1998.
17. Williams, C. K. I and Seeger, M. "Using the Nyström Method to Speed Up Kernel Machines", in T. Leen, T. Dietterieh, V. Tresp (Eds.), Proc. NIPS-2000, vol 13., MIT press.