1. Echo State Wavelet-sigmoid Networks and Their Application to Nonlinear System Identification.
- Author
-
Xiaochuan Sun, Yingqi Li, Jiayu Liu, and Minghui Zhang
- Subjects
- *
NONLINEAR systems , *SYSTEM identification , *IMPULSE response , *WAVELET transforms , *APPROXIMATION theory - Abstract
Wavelet theory has become popular in modeling echo state network. One of the most promising directions is usage of the wavelets as membership activation functions of its reservoir. However, only Symlets wavelet seems to be suitable for hybrid wavelet-sigmoid activation functions. To enhance a systematic study of the field, we concentrate on developing more wavelets towards the typical ESN representation, and ask: What are the more outstanding wavelets of reservoir structure for obtaining competitive models and what is the memory capacity of such reservoirs for obtaining competitive models? In the paper, three echo state wavelet-sigmoid networks (ESWNs) are proposed, considering Shannon wavelet, frequency B-spline wavelet and impulse response wavelet, respectively. The corresponding wavelet functions are instead of sigmoid one in part to construct wavelet-sigmoid reservoirs. On three widely used system nonlinear approximation tasks of different origin and characteristics, as well as by conducting a theoretical analysis we show that the proposed ESWNs are superior to the popular echo state network with build-in Symlets wavelet. [ABSTRACT FROM AUTHOR]
- Published
- 2017