Abstract
In this chapter a novel modular product unit neural network architecture is presented to model singly constrained spatial interaction flows. The efficacy of the model approach is demonstrated for the origin-constrained case of spatial interaction using Austrian interregional telecommunication traffic data. The model requires a global search procedure for parameter estimation, such as the Alopex procedure. A benchmark comparison against the standard origin-constrained gravity model and the two-stage neural network approach, suggested by Openshaw (1998), illustrates the superiority of the proposed model in terms of the generalisation performance measured by ARV and SRMSE.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alonso W. (1978): A theory of movement. In: Hansen N.M. (ed.) Human Settlement Systems, Ballinger, Cambridge [MA], pp. 197–212
Aufhauser E. and Fischer M.M. (1985): Log-linear modelling and spatial analysis, Environment and Planning A 17(7), 931–951
Bergkvist E. (2000): Forecasting interregional freight flows by gravity models, Jahrbuch für Regionalwissenschaft 20, 133–148
Bia A. (2000): A study of possible improvements to the Alopex training algorithm. In: Proceedings of the VIth Brazilian Symposium on Neural Networks, IEEE Computer Society Press, pp. 125–130
Bishop C.M. (1995): Neural Networks for Pattern Recognition, Oxford, Clarendon Press
Black W.R. (1995): Spatial interaction modelling using artificial neural networks, Journal of Transport Geography 3(3), 159–166
Cover T.M. (1965): Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition, IEEE Transactions on Electronic Computers 14(3), 326–334
Durbin R. and Rumelhart D.E. (1989): Product units: A computationally powerful and biologically plausible extension to backpropagation, Neural Computation 1, 133–142
Fischer M.M. (2002): Learning in neural spatial interaction models: A statistical perspective, Journal of Geographical Systems 4(3), 287–299
Fischer M.M. (2000): Methodological challenges in neural spatial interaction modelling: The issue of model selection. In: Reggiani A. (ed.) Spatial Economic Science: New Frontiers in Theory and Methodology, Springer, Berlin, Heidelberg, New York, pp. 89–101
Fischer M.M. and Getis A. (1999): Introduction. New advances in spatial interaction theory, Papers in Regional Science 78(2), 117–118
Fischer M.M. and Gopal S. (1994): Artificial neural networks: A new approach to modelling interregional telecommunication flows, Journal of Regional Science 34(4), 503–527
Fischer M.M. and Reismann M. (2002a): Evaluating neural spatial interaction modelling by bootstrapping, Paper presented at the 6th World Congress of the Regional Science Association International, Lugano, Switzerland, May 16–20, 2000 [accepted for publication in Networks and Spatial Economics].
Fischer M.M. and Reismann M. (2002b): A methodology for neural spatial interaction modelling, Geographical Analysis 34, 207–228
Fischer M.M., Hlavácková-Schindler K. and Reismann M. (1999): A global search procedure for parameter estimation in neural spatial interaction modelling, Papers in Regional Science 78(2), 119–134
Fotheringham A.S. and O’Kelly M.E. (1989): Spatial Interaction Models: Formulations and Applications, Kluwer Academic Publishers, Dordrecht, Boston, London
Giles C. and Maxwell T. (1987): Learning, invariance, and generalization in high-order neural networks, Applied Optics 26(23), 4972–4978
Gopal S. and Fischer M.M. (1993): Neural network based interregional telephone traffic models. In: Proceedings of the International Joint Conference on Neural Networks IJCNN 93 Nagoya, Japan, October 25–29, pp. 2041–2044
Harth E. and Pandya A.S. (1988): Dynamics of ALOPEX process: Application to optimization problems. In: Ricciardi L.M. (ed.) Biomathematics and Related Computational Problems. Kluwer Academic Publishers, Dordrecht, Boston, London, pp. 459–471
Hassoun M.H. (1995): Fundamentals of Neural Networks, MIT Press, Cambridge [MA] and London [England]
Hecht-Nielsen R. (1990): Neurocomputing, Addison-Wesley, Reading [MA]
Hornik K., Stinchcombe M. and White H. (1989): Multi-layer feedforward networks are universal approximators, Neural Networks 2(5), 359–366
Mozolin M., Thill J.-C. and Usery E.L. (2000): Trip distribution forecasting with multilayer perceptron neural networks: A critical evaluation, Transportation Research B 34(1), 53–73
Openshaw S. (1998): Neural network, genetic, and fuzzy logic models of spatial interaction, Environment and Planning A 30(11), 1857–1872
Openshaw S. (1993): Modelling spatial interaction using a neural net. In: Fischer M.M. and Nijkamp P. (eds.) Geographic Information Systems, Spatial Modelling, and Policy Evaluation, Springer, Berlin, Heidelberg, New York, pp. 147–164
Press W.H., Teukolsky S.A., Vetterling W.T. and Flannery B.P. (1992): Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, Cambridge [MA]
Reggiani A. and Tritapepe T. (2000): Neural networks and logit models applied to commuters’ mobility in the metropolitan area of milan. In: Himanen V., Nijkamp P. and Reggiani A. (eds.) Neural Networks in Transport Applications, Ashgate, Aldershot, pp. 111–129
Rumelhart D.E., Hinton G.E. and Williams R.J. (1986): Learning internal representations by error propagation. In: Rumelhart D.E., McClelland J.L. and the PDP Research Group (eds.) Parallel Distributed Processing: Explorations in the Microstructures of Cognition, MIT Press, Cambridge [MA], pp. 318–362
Sen A. and Smith T.E. (1995): Gravity Models of Spatial Interaction Behavior, Springer Berlin, Heidelberg, New York
Senior M.L. (1979): From gravity modelling to entropy maximizing: A pedagogic guide, Progress in Human Geography 3(2), 175–210
Tobler W. (1983): An alternative formulation for spatial interaction modelling, Environment and Planning A 15(5), 693–703
Turton I., Openshaw S. and Diplock G.J. (1997): A genetic programming approach to building new spatial models relevant to GIS. In: Kemp Z. (ed.) Innovations in GIS 4, Taylor & Francis, London, pp. 89–104
Unnikrishnan K.P. and Venugopal K.P. (1994): Alopex: A correlation-based learning algorithm for feedforward and recurrent neural networks, Neural Computation 6(3), 469–490
Weigend A.S., David E.R. and Huberman B.A. (1991): Back-propagation, weight-elimination and time series prediction. In: Touretzky D.S., Elman J.L., Sejnowski T.J. and Hinton G.E. (eds.) Connectionist Models: Proceedings of the 1990 Summer School, Morgan Kaufmann Publishers, San Mateo [CA], pp. 105–116
White H. (1980): Using least squares to approximate unknown regression functions, International Economic Review 21(1), 149–170
Wilson A.G. (1967): A statistical theory of spatial distribution models, Transportation Research 1, 253–269
Rights and permissions
Copyright information
© 2006 Springer Berlin · Heidelberg
About this chapter
Cite this chapter
Reismann, M., Hlavácková-Schindler, K. (2006). Neural Network Modelling of Constrained Spatial Interaction Flows. In: Spatial Analysis and GeoComputation. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-35730-0_12
Download citation
DOI: https://doi.org/10.1007/3-540-35730-0_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35729-2
Online ISBN: 978-3-540-35730-8
eBook Packages: Business and EconomicsEconomics and Finance (R0)