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Journal of applied research and technology

versión On-line ISSN 2448-6736versión impresa ISSN 1665-6423

J. appl. res. technol vol.3 no.3 Ciudad de México dic. 2005

 

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 19th, 2003.
Accepted: September 30th, 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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