Abstract
This paper proposes the design and a comparative study of two proposed online kernel methods identification in the reproducing kernel Hilbert space and other two kernel method existing in the literature. The two proposed methods, titled SVD-KPCA, online RKPCA. The two other techniques named Sliding Window Kernel Recursive Least Square and the Kernel Recursive Least Square. The considered performances are the Normalized Means Square Error, the consumed time and the numerical complexity. All methods are evaluated by handling a chemical process known as the Continuous Stirred Tank Reactor and Wiener-Hammerstein benchmark.
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References
Chin T.-J., Schindler K, Suter D (2006) Incremental kernel SVD for face recognition with image sets. In: Proceedings of the 7th international conference on automatic face and gesture recognition FGR.
Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines. Cambridge University Press, Cambridge
Demuth H, Beale M, Hagan M, (2007) Neural network toolbox 5, User’s Guide, The Math Works
Elaissi I, Taouali O, Messaoud H (2010) Dimensionality reduction for supervised learning with reproducing kernel hilbert space. Int Rev Autom Control (I.RE.A.CO.) 3(2) Mars
Engel Y, Mannor S, Meir R (2003) The kernel recursive least squares algorithm. Rapport technique
Ghate VN, Dudul SV (2009) Fast induction machine fault detection using support vector machine based classifier. WSEAS Trans Syst 8: 591–603
Gunter S, Schraudolph NN, Vishwanathan SVN (2007) Fast Iterative kernel principal component analysis. J Mach Learn Res 8: 1893–1918
Hoegaerts L, Lathauwer L, De Goethals I, Suykens J, Vendewalle J, De Moor B (2007) Efficiently updating and tracking the dominant kernel principal components. Neural Netw 20: 220–229
Kuzmin D, Warmuth MK (2007) Online kernel PCA with entropic matrix updates. In: Proceedings of the 24 the international conference on machine learning, Corvallis, OR
Richard C Sr., Bermudez JCM, Honeine P (2009) Online prediction of time series data with kernels. IEEE Trans Signal Process 57: 1058–1067
Rosipal R, Trecho LJ (2001) Partial Least Squares in Reproducing Kernel Hilbert Spaces. J Mach Learn Res 2: 97–123
Scholkopf B, Smola A, Muller KR (1998) Nonlinear component analysis as kernel eigenvalue problem. Neural Comput 10: 1299–1319
Scholkopf B, Smola A (2002) Learning with kernels. The MIT press, Cambridge
Taouali O, Aissi I, Villa N, Messaoud H (2009)Identification of nonlinear multivariable processes modelled on reproducing kernel hilbert space: application to tennessee process. In: Proceedings of 2nd IFAC international conference on intelligent control systems and signal processing, ICONS, Istanbul, pp 1–6
Taouali O, Elaissi I, Messaoud H (2010) Online prediction model based on reduced kernel principal component analysis. Neural Comput Appl J 19
Vandersteen G (1997) Identification of linear and nonlinear systems in an errors-in-variables least squares and total least squares framework. Phd thesis, Vrije Universiteit Brussel
Van Vaerenbergh S, Vıa J, Santamarıa I (2007) Nonlinear system identification using a new sliding-window kernel RLS algorithm. J Commun 2(3)
Vapnik VN (1995) The nature of statistical learning theory. Springer, New York
Vapnik VN (1998) Statistical learning theory. Wiley, New York
Veropoulos K, Cristianini N, Campbell C (1999) The application of support vector machines to medical decision support: a case study, ACAI conference
Vovk V (2008) Leading trategies in competitive on-line prediction. Theor Comput Sci 405: 285–296
Vovk V (2006) On-line regression competitive with reproducing kernel hilbert spaces, Technical Report arXiv:cs.LG/0511058(version 2), arXiv.org e-Print archive, January, 2006
Wahba G (2000) An introduction to model building with reproducing kernel hilbert spaces, Technical report No 1020. Department of Statistics, University of Wisconsin-Madison, Madison
Wanga W, Mena C, Lub W (2008) Online prediction model based on support vector machine. Neurocomputing 71: 550–558
Yang MH, (2002) Kernel eigenfaces vs kernel first faces : face recognition using kernel method. In: IEEE FGR, pp 215-220
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Taouali, O., Elaissi, E. & Messaoud, H. Design and comparative study of online kernel methods identification of nonlinear system in RKHS space. Artif Intell Rev 37, 289–300 (2012). https://doi.org/10.1007/s10462-011-9231-0
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DOI: https://doi.org/10.1007/s10462-011-9231-0