Xia Yili, Jelfs Beth, Van Hulle Marc M, Principe José C, Mandic Danilo P
Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, U.K. yili.xia06
IEEE Trans Neural Netw. 2011 Jan;22(1):74-83. doi: 10.1109/TNN.2010.2085444. Epub 2010 Nov 11.
A novel complex echo state network (ESN), utilizing full second-order statistical information in the complex domain, is introduced. This is achieved through the use of the so-called augmented complex statistics, thus making complex ESNs suitable for processing the generality of complex-valued signals, both second-order circular (proper) and noncircular (improper). Next, in order to deal with nonstationary processes with large nonlinear dynamics, a nonlinear readout layer is introduced and is further equipped with an adaptive amplitude of the nonlinearity. This combination of augmented complex statistics and enhanced adaptivity within ESNs also facilitates the processing of bivariate signals with strong component correlations. Simulations in the prediction setting on both circular and noncircular synthetic benchmark processes and real-world noncircular and nonstationary wind signals support the analysis.
介绍了一种新颖的复数回声状态网络（ESN），它在复数域中利用完整的二阶统计信息。这是通过使用所谓的增强复数统计来实现的，从而使复数ESN适用于处理复数信号的一般性，包括二阶循环（恰当）和非循环（非恰当）信号。接下来，为了处理具有大非线性动力学的非平稳过程，引入了一个非线性读出层，并进一步配备了非线性的自适应幅度。ESN中增强复数统计和增强适应性的这种结合也有助于处理具有强分量相关性的双变量信号。在循环和非循环合成基准过程以及实际非循环和非平稳风信号的预测设置中的仿真支持了该分析。
