Gradient Based Methods: Functional vs Parametric Forms
| Authors: | Dodd Tony, The University of Sheffield, United Kingdom
Nair Sumitra, The University of Sheffield, United Kingdom
Harrison Robert F., The University of Sheffield, United Kingdom |
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| Topic: | 1.1 Modelling, Identification & Signal Processing |
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| Session: | Nonlinear System Identification - Kernel Methods |
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| Keywords: | reproducing kernel, Hilbert spaces, system identification, function approximation, Gaussian processes, iterative methods, least-squares approximation, regularisation |
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Abstract
Reproducing kernel Hilbert spaces (RKHS) provide a unified framework for the solution of a number of function approximation and signal estimation problems. A significant problem with RKHS methods for real applications is the poor scaling properties of the algorithms with the number of data. It is therefore often necessary to use iterative algorithms. Steepest descent and conjugate gradient solutions for approximation in RKHS are presented in this paper. Four different approaches are described and compared on a benchmark system identification problem.
