Polynomial harmonic GMDH learning networks for time series modeling

Authors:
Nikolay Y. Nikolaev;Hitoshi Iba
Affiliations:
Department of Computing, Goldsmiths College, University of London, New Cross, London SE14 6NW, UK;Department of Information and Communication Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Venue:
Neural Networks
Year:
2003

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Abstract

This paper presents a constructive approach to neural network modeling of polynomial harmonic functions. This is an approach to growing higher-order networks like these build by the multilayer GMDH algorithm using activation polynomials. Two contributions for enhancement of the neural network learning are offered: (1) extending the expressive power of the network representation with another compositional scheme for combining polynomial terms and harmonics obtained analytically from the data; (2) space improving the higher-order network performance with a backpropagation algorithm for further gradient descent learning of the weights, initialized by least squares fitting during the growing phase. Empirical results show that the polynomial harmonic version phGMDH outperforms the GMDH, a Neurofuzzy GMDH and traditional MLP neural networks on time series modeling tasks. Applying next backpropagation training helps to achieve superior polynomial network performances.