Research ArticleDimensionality reduction of RKHS model parameters

- This paper proposes a new method to reduce the parameter number of RKHS model.
- The proposed method entitled Reduced Kernel Partial Least Square (RKPLS).
- It consists on approximating the retained latent components by their closest observation vectors.
- The RKPLS method approaches each latent component {wj}j=1,...,P by a transformed input data Φ(xlatent(j))∈{Φ(x(i))}i=1,...,M so the value of its projection is the highest in the direction of wj.
- The proposed algorithm has been applied to identify a process Trainer PT326.

This paper proposes a new method to reduce the parameter number of models developed in the Reproducing Kernel Hilbert Space (RKHS). In fact, this number is equal to the number of observations used in the learning phase which is assumed to be high. The proposed method entitled Reduced Kernel Partial Least Square (RKPLS) consists on approximating the retained latent components determined using the Kernel Partial Least Square (KPLS) method by their closest observation vectors. The paper proposes the design and the comparative study of the proposed RKPLS method and the Support Vector Machines on Regression (SVR) technique. The proposed method is applied to identify a nonlinear Process Trainer PT326 which is a physical process available in our laboratory. Moreover as a thermal process with large time response may help record easily effective observations which contribute to model identification. Compared to the SVR technique, the results from the proposed RKPLS method are satisfactory.