Performance evaluation of new echo state networks based on complex network

Recently, echo state networks (ESN) have aroused a lot of interest in their nonlinear dynamic system modeling capabilities. In a classical ESN, its dynamic reservoir (DR) has a sparse and random topology, but the performance of ESN with its DR taking another kind of topology is still unknown. So based on complex network theory, three new ESNs are proposed and investigated in this paper. The small-world topology, scale-free topology and the mixed topology of small-world effect and scale-free feature are considered in these new ESNs. We studied the relationship between DR architecture and prediction capability. In our simulation experiments, we used two widely used time series to test the prediction performance among the new ESNs and classical ESN, and used the independent identically distributed (i.i.d) time series to analyze the short-term memory (STM) capability. We answer the following questions: What are the differences of these ESNs in the prediction performance? Can the spectral radius of the internal weights matrix be wider? What is the short-term memory capability? The experimental results show that the proposed new ESNs have better prediction performance, wider spectral radius and almost the same STM capacity as classical ESN's.