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Neural Network Modelling of Constrained Spatial Interaction Flows

Design, Estimation and Performance Issues

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Book cover Spatial Analysis and GeoComputation

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.

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References

  • Alonso W. (1978): A theory of movement. In: Hansen N.M. (ed.) Human Settlement Systems, Ballinger, Cambridge [MA], pp. 197–212

    Google Scholar 

  • Aufhauser E. and Fischer M.M. (1985): Log-linear modelling and spatial analysis, Environment and Planning A 17(7), 931–951

    Article  Google Scholar 

  • Bergkvist E. (2000): Forecasting interregional freight flows by gravity models, Jahrbuch für Regionalwissenschaft 20, 133–148

    Google Scholar 

  • 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

    Google Scholar 

  • Bishop C.M. (1995): Neural Networks for Pattern Recognition, Oxford, Clarendon Press

    MATH  Google Scholar 

  • Black W.R. (1995): Spatial interaction modelling using artificial neural networks, Journal of Transport Geography 3(3), 159–166

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Durbin R. and Rumelhart D.E. (1989): Product units: A computationally powerful and biologically plausible extension to backpropagation, Neural Computation 1, 133–142

    Article  Google Scholar 

  • Fischer M.M. (2002): Learning in neural spatial interaction models: A statistical perspective, Journal of Geographical Systems 4(3), 287–299

    Article  ADS  Google Scholar 

  • 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

    Google Scholar 

  • Fischer M.M. and Getis A. (1999): Introduction. New advances in spatial interaction theory, Papers in Regional Science 78(2), 117–118

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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].

    Google Scholar 

  • Fischer M.M. and Reismann M. (2002b): A methodology for neural spatial interaction modelling, Geographical Analysis 34, 207–228

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Fotheringham A.S. and O’Kelly M.E. (1989): Spatial Interaction Models: Formulations and Applications, Kluwer Academic Publishers, Dordrecht, Boston, London

    Google Scholar 

  • Giles C. and Maxwell T. (1987): Learning, invariance, and generalization in high-order neural networks, Applied Optics 26(23), 4972–4978

    Article  ADS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Hassoun M.H. (1995): Fundamentals of Neural Networks, MIT Press, Cambridge [MA] and London [England]

    Google Scholar 

  • Hecht-Nielsen R. (1990): Neurocomputing, Addison-Wesley, Reading [MA]

    Google Scholar 

  • Hornik K., Stinchcombe M. and White H. (1989): Multi-layer feedforward networks are universal approximators, Neural Networks 2(5), 359–366

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Openshaw S. (1998): Neural network, genetic, and fuzzy logic models of spatial interaction, Environment and Planning A 30(11), 1857–1872

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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]

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Sen A. and Smith T.E. (1995): Gravity Models of Spatial Interaction Behavior, Springer Berlin, Heidelberg, New York

    Google Scholar 

  • Senior M.L. (1979): From gravity modelling to entropy maximizing: A pedagogic guide, Progress in Human Geography 3(2), 175–210

    Google Scholar 

  • Tobler W. (1983): An alternative formulation for spatial interaction modelling, Environment and Planning A 15(5), 693–703

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • White H. (1980): Using least squares to approximate unknown regression functions, International Economic Review 21(1), 149–170

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Wilson A.G. (1967): A statistical theory of spatial distribution models, Transportation Research 1, 253–269

    Article  CAS  ADS  Google Scholar 

Download references

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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

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