A methodology for neural spatial interaction modelling
This paper presents a methodology for neural spatial interaction modelling. Particular emphasis is laid on design, estimation and performance issues in both cases, unconstrained and singly constrained spatial interaction. Families of classical neural network models, but also less classical ones such as product unit neural network models are considered. Some novel classes of product unit and summation unit models are presented for the case of origin or destination constrained spatial interaction flows. The models are based on a modular connectionist architecture that may be viewed as a linked collection of functionally independent neural modules with identical feedforward topologies, operating under supervised learning algorithms. Parameter estimation is viewed as Maximum Likelihood (ML) learning. The nonconvex nature of the loss function makes the Alopex procedure, a global search procedure, an attractive and appropriate optimising scheme for ML learning. A benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained, neural network model versions in terms of generalization performance measured by Kullback and Leibler`s information criterion. Hereby, the authors make use of the bootstrapping pairs approach to overcome the largely neglected problem of sensitivity to the specific splitting of the data into training, internal validation and testing data sets, and to get a better statistical picture of prediction variability of the models. Keywords: Neural spatial interaction models, origin constrained or destination constrained spatial interaction, product unit network, Alopex procedure, boostrapping, benchmark performance tests.
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- Fischer, M.M. & Nijkamp, P., 1992.
"Geographic information systems and spatial analysis,"
Serie Research Memoranda
0054, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
- Fischer, Manfred M & Nijkamp, Peter, 1992. "Geographic Information Systems and Spatial Analysis," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 26(1), pages 3-17, April.
- Manfred M. Fischer & Martin Reismann, 2001. "Neural Network Modelling of Constrained Spatial Interaction Flows," ERSA conference papers ersa01p165, European Regional Science Association.
- Fischer, Manfred M. & Reismann, Martin & Hlavackova-Schindler, Katerina, 2000. "Evaluating Neural Spatial Interaction. Modelling By Bootstrapping," ERSA conference papers ersa00p370, European Regional Science Association.
- Manfred M. Fischer & Yee Leung, 1998. "A genetic-algorithms based evolutionary computational neural network for modelling spatial interaction data," ERSA conference papers ersa98p478, European Regional Science Association.
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