Design of Echo State Network with Coordinate Descent Method and $$l_1$$ Regularization

The echo state networks (ESNs) have been applied in many applications. For an ESN, its training error and network size are closely related with output weight matrix. In this paper, the coordinate descent method based ESN (CD-ESN for short) is designed to deal with the relationship between training error and network size. In CD-ESN, the \({{l_1}}\) regularization is used to penalty the non-important values of output weight into 0. Moreover, the coordinate descent method is used to update the output weights of ESN. Experimental results imply that the proposed CD-ESN has better prediction accuracy and more sparse network topology than original ESN.