基于小世界无标度特征的回声状态小波网络

针对储备池的适应性问题,提出了一种复合回声状态网络模型(CESN).CESN依据增量生长准则构建小世界无标度进化状态储备池,解除了储备池谱半径的限制.同时,CESN将离散小波函数作为神经元的激活函数,用Symlets小波函数替代部分储备池神经元的S型函数,Symlets小波函数的伸缩和平移变换特征丰富了动态储备池的状态空间.将CESN应用于一些非线性时间序列逼近问题中,即NARMA系统、Henon映射和二氧化碳浓度预测.实验结果表明,在逼近高度复杂的非线性系统方面,CESN明显优于注入Symlets小波的经典回声状态网络(S-ESN)和具有高聚类系数的无标度回声状态网络(SHESN). 

Echo State Wavelet Network with Small-World Scale-Free Characteristics

For adaptability problems of the reservoir, a composite echo state network (CESN) model was proposed. The small-world scale-free evolving state reservoir was constructed based on the incremental growth rules to relax the restriction for the spectral radius of the state reservoir. Moreover, discrete wavelet function was used as the activation function of neurons in CESN. The Symlets wavelet function was substituted for the fractional S-function of reservoir neurons, its dilation and translation features contributed to expanding the state space of dynamic reservoir. CESN can be applied to solve some approximation problems of nonlinear time series, which are the NARMA system, Henon map and the CO₂ concentration prediction. The experiment results show that CESN is able to significantly outperform the ESN with injected Symlets wavelet (S-ESN) and scale-free highly clustered echo state network (SHESN) in approximating highly complex nonlinear dynamics.