Online identification of nonlinear system in the Reproducing Kernel Hilbert Space using SVDKPCA method

This paper proposes a new method for online identification of a nonlinear system modelled on Reproducing Kernel Hilbert Space (RKHS). The proposed SVD-KPCA method uses the SVD technique to update the principal components. Then we use the Reduced Kernel Principal Component Analysis (RKPCA) to approach the principal components which represent the observations selected by the KPCA method.

[1]  S. V. N. Vishwanathan,et al.  Fast Iterative Kernel Principal Component Analysis , 2007, J. Mach. Learn. Res..

[2]  Vladimir Vovk,et al.  On-Line Regression Competitive with Reproducing Kernel Hilbert Spaces , 2005, TAMC.

[3]  Vladimir Vovk,et al.  Leading strategies in competitive on-line prediction , 2006, Theor. Comput. Sci..

[4]  Roman Rosipal,et al.  Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space , 2002, J. Mach. Learn. Res..

[5]  Wenjian Wang,et al.  Online prediction model based on support vector machine , 2008, Neurocomputing.

[6]  Vladimir Vovk.  Leading Strategies in Competitive On-Line Prediction , 2006, ALT.

[7]  Johan A. K. Suykens,et al.  Efficiently updating and tracking the dominant kernel principal components , 2007, Neural Networks.

[8]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[9]  Paul Honeine,et al.  Online Prediction of Time Series Data With Kernels , 2009, IEEE Transactions on Signal Processing.

[10]  Johan A. K. Suykens,et al.  Least Squares Support Vector Machines , 2002 .

[11]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[12]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[13]  H. Messaoud,et al.  Online prediction model based on Reduced Kernel Principal Component Analysis , 2009, 2009 3rd International Conference on Signals, Circuits and Systems (SCS).

[14]  Dustin Boswell,et al.  Introduction to Support Vector Machines , 2002 .

[15]  Alexander J. Smola,et al.  Learning with kernels , 1998 .