Recursive Variable Projection Algorithm for a Class of Separable Nonlinear Models.

In this article, we study the recursive algorithms for a class of separable nonlinear models (SNLMs) in which the parameters can be partitioned into a linear part and a nonlinear part. Such models are very common in machine learning, system identification, and signal processing. Utilizing the special structure of the SNLMs, we propose a recursive variable projection (RVP) algorithm, in which at each recursion, the linear parameters of the model are eliminated, and the nonlinear parameters are updated by the recursive Levenberg-Marquart algorithm. Then, based on the updated nonlinear parameters, the linear parameters are updated by the recursive least-squares algorithm. According to a convergence analysis of the RVP algorithm, the parameter estimation error is mean-square bounded. Numerical examples confirm the satisfactory performance of the proposed algorithm.

Citation

Min Gan, Yu Guan, Guang-Yong Chen, C L Philip Chen. Recursive Variable Projection Algorithm for a Class of Separable Nonlinear Models. IEEE transactions on neural networks and learning systems. 2021 Nov;32(11):4971-4982

PMID: 33017297

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