Wavelet-Network based on L1-Norm minimisation for learning chaotic time series

V. Alarcon-Aquino, E. S. Garcia-Treviño, R. Rosas-Romero, J. F. Ramirez-Cruz, L. G. Guerrero-Ojeda, J. Rodriguez- Asomoza


This paper presents a wavelet-neural network based on the L1-norm minimisation for learning chaotic time series. The proposed approach, which is based on multi-resolution analysis, uses wavelets as activation functions in the hidden layer of the wavelet-network. We propose using the L1-norm, as opposed to the L2-norm, due to the wellknown fact that the L1-norm is superior to the L2-norm criterion when the signal has heavy tailed distributions or outliers. A comparison of the proposed approach with previous reported schemes using a time series benchmark is presented. Simulation results show that the proposed wavelet network based on the L1-norm performs better than the standard back-propagation network and the wavelet-network based on the traditional L2-norm when applied to synthetic data.


Wavelet-networks; Wavelets; Multi-resolution Analysis; Learning Chaotic Time Series

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