Details

Autor(en) / Beteiligte

• Rubio, Jose de Jesus

Titel

Stability Analysis of the Modified Levenberg-Marquardt Algorithm for the Artificial Neural Network Training

Ist Teil von

• IEEE transaction on neural networks and learning systems, 2021-08, Vol.32 (8), p.3510-3524

Ort / Verlag

Piscataway: IEEE

Erscheinungsjahr

2021

Quelle

IEEE Xplore

Beschreibungen/Notizen

• 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.