Wavelet-network based on L₁-norm minimisation for learning chaotic time series

 

V. Alarcon-Aquino¹, E. S. Garcia-Treviño¹, R. Rosas-Romero¹, J. F. Ramirez-Cruz², L. G. Guerrero-Ojeda¹, & J. Rodriguez-Asomoza¹

 

¹ Department of Electrical and Electronic Engineering Communications and Signal Processing Group, CENTIA Universidad de las Americas, Puebla 72820 Cholula, Puebla Mexico.

² Department of Computer Science Instituto Tecnológico de Apizaco Tlaxcala Mexico.

 

Received: April 19^th, 2003.
Accepted: September 30^th, 2005.

 

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 well-known 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.

Keywords: Wavelet-networks, Wavelets, Multi-resolution Analysis, Learning Chaotic Time Series.

 

Resumen

En este artículo se presenta una red neuronal-wavelet basada en la minimización de la norma L₁ para aprendizaje de series de tiempo caóticas. El método propuesto, el cuál se basa en un análisis multi-resolución, utiliza wavelets como funciones de activación en la capa oculta de la red neuronal-wavelet. Se propone utilizar la norma L₁, en lugar de la tradicional norma L₂, debido a que la norma L₁ es superior a la norma L₂ cuando la señal tiene distribuciones sesgadas o de colas pesadas. Se presenta una comparación del método propuesto con esquemas reportados previamente utilizando series de tiempo caóticas conocidas. Los resultados de simulación revelan que la red neuronal-wavelet basada en la norma L₁ tiene una mejor eficiencia que la red neuronal con propagación hacia atrás y la red neuronal-wavelet basada en la tradicional norma L₂ cuando se aplica a datos sintéticos.

 

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