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Nonlinear identification using orthogonal forward regression with nested optimal regularization
An efficient data based-modeling algorithm for
nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization
parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization
parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification
examples are included to demonstrate the effectiveness of
this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm
A multiple beta wavelet-based locally regularized ultraorthogonal forward regression algorithm for time-varying system identification with applications to EEG
Time-varying (TV) nonlinear systems widely exist in various fields of engineering and science. Effective identification and modeling of TV systems is a challenging problem due to the nonstationarity and nonlinearity of the associated processes. In this paper, a novel parametric modeling algorithm is proposed to deal with this problem based on a TV nonlinear autoregressive with exogenous input (TV-NARX) model. A new class of multiple beta wavelet (MBW) basis functions is introduced to represent the TV coefficients of the TV-NARX model to enable the tracking of both smooth trends and sharp changes of the system behavior. To produce a parsimonious model structure, a locally regularized ultraorthogonal forward regression (LRUOFR) algorithm aided by the adjustable prediction error sum of squares (APRESS) criterion is investigated for sparse model term selection and parameter estimation. Simulation studies and a real application to EEG data show that the proposed MBW-LRUOFR algorithm can effectively capture the global and local features of nonstationary systems and obtain an optimal model, even for signals contaminated with severe colored noise