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

Abstract

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.