Effects of connectivity structure of complex echo state network on its prediction performance for nonlinear time series

Reservoir computing methods have become popular; however, the nature of the dynamical reservoir (DR) is not thoroughly understood yet. We propose complex echo state network (CESN), the construction process of its DR is determined by five growth factors. The relationships between CESN connectivity structure and its performance are investigated when predicting nonlinear time series. We also introduce a quantifiable characteristic for the connectivity structure-the connectivity index, and a tool to measure the richness of reservoir states-the omega-complexity index. It is demonstrated from the experimental results that connectivity structure of the reservoirs has significant effect on theirs prediction performance, the omega-complexity index can be used as a performance predictor, and particular configuration of the growth factors and corresponding connectivity index can yield optimal performance. (C) 2010 Elsevier B.V. All rights reserved.