Training Echo State Networks with Regularization through Dimensionality Reduction
This is an incremental improvement for researchers in time-series analysis and reservoir computing, focusing on better generalization in chaotic systems.
The paper tackles the problem of improving Echo State Networks for real-valued time-series prediction by introducing a framework that projects internal layer outputs to a lower-dimensional space with regularization, achieving superior predictive performance on benchmark tests.
In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before training the output layer to learn the target task. Notably, we enforce a regularization constraint that leads to better generalization capabilities. We evaluate the performances of our approach on several benchmark tests, using different techniques to train the readout of the network, achieving superior predictive performance when using the proposed framework. Finally, we provide an insight on the effectiveness of the implemented mechanics through a visualization of the trajectory in the phase space and relying on the methodologies of nonlinear time-series analysis. By applying our method on well known chaotic systems, we provide evidence that the lower dimensional embedding retains the dynamical properties of the underlying system better than the full-dimensional internal states of the network.