New Criterion for Choosing the Number of Parameters in a RKHS Model

Nadia Souilem; Ilyes Elaissi; Okba Taouali; Hassani Messaoud

doi:10.15866/ireaco.v7i6.2931

New Criterion for Choosing the Number of Parameters in a RKHS Model

Nadia Souilem^(1*), Ilyes Elaissi⁽²⁾, Okba Taouali⁽³⁾, Hassani Messaoud⁽⁴⁾

^(*) Corresponding author

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DOI: https://doi.org/10.15866/ireaco.v7i6.2931

Abstract

This paper proposes a new algorithm to estimate the required number of parameters in the models developed in Reproducing Kernel Hilbert Space (RKHS). The proposed method considers models with growing complexities and calculates for each a given matrix, such that these matrices tend to singularity. The required number of parameters is given by verifying a criterion on the determinants of these matrices.
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Keywords

Determinant Ratio; RKHS; RKPCA

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References

I. Aissi, Modélisation, Identification et Commande Prédictive des systèmes non linéaires par utilisations des espaces RKHS,(thèse de doctorat 2009, ENIT Tunisie).

Elaissi Ilyes, Taouali Okba, Messaoud Hassani, Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Space, (2010) International Review of Automatic Control (IREACO), 3. (2), pp. 152-160.

Elaissi, I., Taouali, O., Messaoud, H., Online prediction model based on new kernel method, (2014) International Review of Automatic Control (IREACO), 7 (1), pp. 107-113.

I. Aisii and M. Hassani, “Complexity Reduction of RKHS models,” IMACS Conference Paris-France, 11-15 july, 2005, P4-R-00-03-66.

A. Banerjee and Y. Arkun. Control configuration design applied to the Tennessee Eastman plant-wide control problem. Computers Chemical Engineering, 19, pp. 453-480, 1995.
http://dx.doi.org/10.1016/0098-1354(94)00058-v

N. Cristianini and J. Shawe-Taylor, An Introduction to Support Vector Machines, Cambridge University. (Press, Cambridge, UK, 2000).
http://dx.doi.org/10.1017/cbo9780511801389

Downs, J.J and Vogel, E. (1993). A plant-wide industrial process control problem. Computers and Chemical Engineering, 17, 245–255.
http://dx.doi.org/10.1016/0098-1354(93)80018-i

Jihane Ben Slimane Dhifallah, Kaouther Laabidi, Moufida Ksouri Lahmari, Support Vector Machines for Failures Diagnosis, (2009) International Review of Automatic Control (IREACO), 2. (5), pp. 505-511.

Mauricio Sales Cruz, A. (2004). Tennessee Eastman Plant –wide Industrial Process. Technical report, CAPEC, Technical University of Denmark, disponible à http://www.capec.kt.dtu.dk/documents/softhttp://www.capec.kt.dtu.dk/documents/software/tutorials/TE_Complete.pdfware/tutorials/TE_Complete.pdf

J. F Paiement, “ Généralisation d’algorithmes de réduction de dimension, ” Mémoire de Mastère présenté à la faculté des études supérieures, University de Montréal-Canada, November, 2003.

B. Philippe, M. Ledoux, Probabilité, 1 février 2007.

R. Rosipal, and L. J. Trejo, “ Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space,” 2, 97-123. Journal of Machine Learning Research,2001.

R. Sriniwas and Y. Arkun. Control of the Tennessee Eastman process using input–output models. Journal of Process Control, 7, pp. 387-400, 1997.
http://dx.doi.org/10.1016/s0959-1524(97)00015-2

B. Scholkopf, A. Smola et K-R Muller, Nonlinear component analysis as Kernel eigenvalue problem, Neural computation. 10, (1998), 1299-1319.
http://dx.doi.org/10.1162/089976698300017467

B. Scholkopf and A. Smola, Learning with kernels. (The MIT press, 2002).
http://dx.doi.org/10.1145/1027914.1027921

J. Suykens, A. K., Van Gestel, T., De Brabanter, J., De Moor, B. et Vandewalle,J, Least squares support vector machines, (Singapore: WorldScientific, 2002).
http://dx.doi.org/10.1142/9789812776655

Tat-Jun Chin, Konrad Schindler, David Suter, Incremental Kernel SVD for Face Recognition with Image Sets, Proceedings of the 7th International Conference on Automatic Face and Gesture Recognition FGR (2006).
http://dx.doi.org/10.1109/fgr.2006.67

Fabien Lauer, Machines à Vecteurs de Support et Identification de Systèmes Hybrides, thèse de doctorat de l’Université Henri Poincaré – Nancy 1, octobre 2008, Nancy, France.

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