Title | ||
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Stability Analysis of the Modified Levenberg–Marquardt Algorithm for the Artificial Neural Network Training |
Abstract | ||
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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. |
Year | DOI | Venue |
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2021 | 10.1109/TNNLS.2020.3015200 | IEEE Transactions on Neural Networks and Learning Systems |
Keywords | DocType | Volume |
Error stability,Levenberg–Marquardt,Newton,weights boundedness | Journal | 32 |
Issue | ISSN | Citations |
8 | 2162-237X | 6 |
PageRank | References | Authors |
0.46 | 0 | 1 |
Name | Order | Citations | PageRank |
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José de Jesús Rubio | 1 | 55 | 4.09 |