An echo state network based on Levenberg-Marquardt algorithm

An abnormal solution might occur during the learning process of echo state network if the least singular value of reservoir state matrix is very close zero. To solve this problem, an echo state network based on Levenberg-Marquardt (LM-ESN) algorithm replacing linear regression for output weights is proposed and a new damping term is given. In the proposed method, it is demonstrated that the output weights sequence has quadratical convergence if the norm of error vector provides a local error bound. Simulations show that the new method could deal with abnormal solution problems effectively, also it has better performance and robustness for time series prediction than some existing methods.