期刊
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
卷 32, 期 8, 页码 3510-3524出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2020.3015200
关键词
Biological neural networks; Cost function; Prediction algorithms; Stability analysis; Training; Testing; Error stability; Levenberg-Marquardt; Newton; weights boundedness
The article introduces a modified Levenberg-Marquardt algorithm based on Levenberg-Marquardt and Newton algorithms, ensuring error stability and weights boundedness through Lyapunov technique. Comparative studies were conducted with other algorithms for learning electric and brain signal datasets.
The Levenberg-Marquardt and Newton are two algorithms that use the Hessian for the artificial neural network learning. In this article, we propose a modified Levenberg-Marquardt algorithm for the artificial neural network learning containing the training and testing stages. The modified Levenberg-Marquardt algorithm is based on the Levenberg-Marquardt and Newton algorithms but with the following two differences to assure the error stability and weights boundedness: 1) there is a singularity point in the learning rates of the Levenberg-Marquardt and Newton algorithms, while there is not a singularity point in the learning rate of the modified Levenberg-Marquardt algorithm and 2) the Levenberg-Marquardt and Newton algorithms have three different learning rates, while the modified Levenberg-Marquardt algorithm only has one learning rate. The error stability and weights boundedness of the modified Levenberg-Marquardt algorithm are assured based on the Lyapunov technique. We compare the artificial neural network learning with the modified Levenberg-Marquardt, Levenberg-Marquardt, Newton, and stable gradient algorithms for the learning of the electric and brain signals data set.
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