Title: Meteorological time series forecasting with pruned multi-layer perceptron and two-stage Levenberg-Marquardt method

Authors: Cyril Voyant; Wani Tamas; Marie-Laure Nivet; Gilles Notton; Christophe Paoli; Aurélia Balu; Marc Muselli

Addresses: University of Corsica, UMR CNRS 6134 SPE, Campus Grimaldi, BP 52, 20250 Corte, France ' University of Corsica, UMR CNRS 6134 SPE, Campus Grimaldi, BP 52, 20250 Corte, France ' University of Corsica, UMR CNRS 6134 SPE, Campus Grimaldi, BP 52, 20250 Corte, France ' University of Corsica, UMR CNRS 6134 SPE, Campus Grimaldi, BP 52, 20250 Corte, France ' Departement de Genie Informatique, Universite Galatasaray, No. 36 34357 Ortakoy, Istanbul, Turkey ' University of Corsica, UMR CNRS 6134 SPE, Campus Grimaldi, BP 52, 20250 Corte, France ' University of Corsica, UMR CNRS 6134 SPE, Campus Grimaldi, BP 52, 20250 Corte, France

Abstract: A multi-layer perceptron (MLP) defines a family of artificial neural networks often used in TS modelling and forecasting. Because of its 'black box' aspect, many researchers refuse to use it. Moreover, the optimisation (often based on the exhaustive approach where 'all' configurations are tested) and learning phases of this artificial intelligence tool (often based on the Levenberg-Marquardt algorithm - LMA) are weaknesses of this approach (exhaustively and local minima). These two tasks must be repeated depending on the knowledge of each new problem studied, making the process, long, laborious and not systematically robust. In this paper, a pruning process is proposed. This method allows, during the training phase, to carry out an inputs selecting method activating (or not) inter-nodes connections in order to verify if forecasting is improved. We propose to use iteratively the popular damped least-squares method to activate inputs and neurons. A first pass is applied to 10% of the learning sample to determine weights significantly different from 0 and delete other. Then, a classical batch process based on LMA is used with the new MLP. The validation is done using 25 measured meteorological TS and cross-comparing the prediction results of the classical LMA and the two-stage LMA.

Keywords: pruning; regularisation; multi-layer perceptron; MLP; optimisation; meteorological time series; time series forecasting; two-stage LMA; Levenberg-Marquardt algorithm; artificial neural networks; ANNs; damped least squares.

DOI: 10.1504/IJMIC.2015.069952

International Journal of Modelling, Identification and Control, 2015 Vol.23 No.3, pp.287 - 294

Received: 06 Feb 2014
Accepted: 08 Jul 2014
Published online: 16 Jun 2015 *

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