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Topographical Estimation of Visual Population Receptive Fields by fMRI

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A variable projection approach for efficient estimation of RBF-ARX model.

Min Gan, Han-Xiong Li, Hui Peng

IEEE Transactions on Cybernetics

|July 3, 2014

Summary

This summary is machine-generated.

A new variable projection algorithm efficiently estimates Radial Basis Function network-based Autoregressive with Exogenous Inputs (RBF-ARX) model parameters. This method reduces computational load and improves conditioning for RBF-ARX models.

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Area of Science:

Computational Mathematics
System Identification
Machine Learning

Background:

Radial Basis Function network-based Autoregressive with Exogenous Inputs (RBF-ARX) models possess a structure with predominantly linear parameters.
Efficient parameter estimation is crucial for the practical application of complex nonlinear models.
Existing methods for RBF-ARX models can be computationally intensive and may face numerical challenges.

Purpose of the Study:

To develop a computationally efficient variable projection algorithm for RBF-ARX model parameter estimation.
To leverage the specific structure of RBF-ARX models by separating linear and nonlinear parameters.
To demonstrate the improved performance and applicability of the proposed algorithm on various nonlinear systems.

Main Methods:

A variable projection algorithm is proposed, utilizing orthogonal projection to eliminate linear parameters.
The algorithm's performance is evaluated using both the full Jacobian matrix (Golub and Pereyra) and a simplified version (Kaufman).
Numerical comparisons are conducted against established methods, including structured nonlinear parameter optimization and the Levenberg-Marquardt algorithm.

Main Results:

The proposed variable projection algorithm substantially reduces the parameter space dimension for RBF-ARX models.
The method results in a better-conditioned optimization problem compared to conventional approaches.
Demonstrated superior computational efficiency over existing methods in chaotic time series modeling and various nonlinear process applications.

Conclusions:

The variable projection algorithm offers a significant advancement in the efficient estimation of RBF-ARX model parameters.
The approach is robust and effective across simulated, time-varying, and real-world industrial nonlinear processes.
This method provides a valuable tool for system identification and control engineering applications involving nonlinear dynamics.