Adaptive echo state network with a recursive inverse-free weight update algorithm

Echo State Network (ESN) is widely applied in sequence prediction, physics, and economics. Moore-Penrose inversion is a typical solving process of ESN. However, in the era of big data, the traditional inversion is computationally costly and the data may be irreversible. To solve this problem, a recursive inverse-free algorithm ESN model, called RIFESN, is introduced in this article. The model also introduces an adaptive activation function based on the error between target value and predicted value, which greatly improves the nonlinear mapping capability of the network. Three simulation experiments are conducted on the Mackey-Glass-17 time series, sunspots series and daily exchange rate summary of eight countries from 1990 to 2016, respectively. The results of the three simulations show that RIFESN has better prediction accuracy and operational speed, which proves that it has a good application prospect.