LAUSR

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.